INTERNATIONAL DOCTORAL
SCHOOL OF THE USC
Alexand e
B ea Rod íguez
PhD Thesis
Sea ch o iola ion o lep onic
uni e sali y in semilep onic
decays o s ange pa icles in
LHCb
San iago de Compos ela, 2023
Doc o al P og amme in Nuclea and Pa icles Physics
DOCTORAL THESIS
SEARCH FOR VIOLATION OF
LEPTONIC UNIVERSALITY IN
SEMILEPTONIC DECAYS OF STRANGE
PARTICLES IN LHCb
Au ho
Alexand e B ea Rod íguez
Supe iso /s: Diego Ma ínez San os
Xabie Cid Vidal
Tu o : Xabie Cid Vidal
PHD PROGRAMME IN NUCLEAR AND PARTICLE PHYSICS
SANTIAGO DE COMPOSTELA
To Rocío
ABSTRACT
Theo e ical s udies ha e demons a ed ha Semilep onic Hype on Decays (SHD)
can be sensi i e o Beyond he S anda d Model (BSM) dynamics ha b eak lep onic
la ou uni e sali y (LFU). The LFU es obse able de ined as he a io be ween
muon and elec on modes
𝑅𝜇𝑒 =
Γ(𝐵1→𝐵2𝜇−¯
𝜈𝜇)
Γ(𝐵1→𝐵2𝑒−¯
𝜈𝑒)
is sensi i e o non s anda d scala and enso con ibu ions. Mo eo e , in he
S anda d Model, he dependency on he o m ac o s is an icipa ed o simpli y when
conside ing he a io, leading o a p ecise heo e ical p edic ion.
Λ→𝑝𝜇−¯
𝜈𝜇
was p oposed as one o he mos p omising SHD o be s udied
a LHCb, due o i s high accep ance e iciency and abundance in LHCb e en s. In
addi ion, he elec on mode has al eady been measu ed p ecisely and an imp o emen
in he measu emen o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
di ec ly ansla es in o igh e bounds in
LFU in 𝑠→𝑢qua k ansi ions.
In his hesis is p esen ed he blinded measu emen o he b anching ac ion
B(Λ→𝑝𝜇−¯
𝜈𝜇)=(3.485 ±0.059 (𝑠𝑡𝑎𝑡) ±0.23 (𝑠𝑦𝑠𝑡)) ×10−4
and he consequences o he p ecision achie ed is discussed. I should be no ed
ha his alue is mul iplied by a blinding cons an and ha he calcula ion o he
sys ema ic unce ain y is no comple ely inalized, so he inal esul o his unce ain y
may a y sligh ly. The measu emen is pe o med using Run 2 LHCb da a, p oduced
colliding p o ons a 13 TeV o ene gy in he cen e o mass du ing he yea s 2016-2018,
eaching an in eg a ed luminosi y o 5.4 𝑓 𝑏−1.
In addi ion some p ospec s o e u u e SHD measu emen s a e included.
iii
con en s
A.8.4 Lppi S ipping Fil e ed 2018 . . . . . . . . . . . . . . . . . . . 121
A.8.5 Lppi S ipping Fil e ed 2017 . . . . . . . . . . . . . . . . . . . 122
A.8.6 Lppi S ipping Fil e ed 2016 . . . . . . . . . . . . . . . . . . . 122
A.8.7 Lpmunu S ipping Fil e ed 2018 . . . . . . . . . . . . . . . . . 122
A.8.8 Lpmunu S ipping Fil e ed 2017 . . . . . . . . . . . . . . . . . 123
A.8.9 Lpmunu S ipping Fil e ed 2016 . . . . . . . . . . . . . . . . . 123
A.8.10 MinBiasMC2018.........................123
A.8.11 Signal P i a e P oduc ion o co ec S ipping e : . . . . . . . 124
A.9 DecFiles ..................................128
A.9.1 Lppi: Tigh Cu (33102103) . . . . . . . . . . . . . . . . . . . . 128
A.9.2 Lpmunu: Tigh Cu SHD (33512008) . . . . . . . . . . . . . . . 129
A.10PIDCalib2 .................................131
A.10.1 SignalLine ............................131
A.10.2 No mLine.............................132
A.11PIDCalib2Schemes ............................134
A.11.1 Signal S ipping Line . . . . . . . . . . . . . . . . . . . . . . . 134
A.11.2 No m S ipping Line . . . . . . . . . . . . . . . . . . . . . . . 139
Bibliog aphy 145
Glossa y 151
x
FOREWORD
One o he undamen al
ques ions ha has consis en ly in igued us h ough-
ou ime is: ’Wha exac ly is ou wo ld made o ?’. Despi e emaining qui e un-
ce ain abou o he undamen al ques ions, we ha e made signi ican p og ess
in add essing his one.
Nowadays, we know ha all he ma e a ound us is composed o a oms, wi h
p o ons and neu ons in hei nucleus, and elec ons in quan um o bi als a ound hem.
Fo he i s ime, we gained a sys ema ic unde s anding o he cons i uen s o ou
wo ld.
Ye , ou jou ney did no culmina e he e; i ex ended deepe in o he suba omic
ealm, e ealing ha p o ons and neu ons, once hough o be elemen a y pa icles,
a e hemsel es in ica e s uc u es composed o pa icles known as qua ks. In ou
cu en pa adigm, elec ons and qua ks se e as he undamen al building blocks o
ma e , o ming he e y essence o he wo ld a ound us.
In ou ques o del e deepe in o ou unde s anding o pa icles, nume ous expe -
imen s ha e been conduc ed, esul ing in he disco e y o a as a ay o pa icles
ha ini ially le us e en mo e pe plexed han be o e. Fu he mo e, hese pa icles
exhibi ed sensi i i y o new undamen al in e ac ions, he s ong and weak nuclea
in e ac ions, no ypically encoun e ed in ou daily expe iences.
Howe e , ollowing signi ican collec i e heo e ical e o s in he 20 h cen u y, a
model desc ibing all he known pa icles and hei in e ac ions, excluding g a i y, was
cons uc ed. I is called S anda d Model (SM), and i achie ed imp essi e p edic i e
powe and esis ed all o ou a emp s o unco e phenomena beyond i .
In he SM, ma e is composed o pa icles wi h hal -odd-in ege quan um spin
numbe s, known as e mions, while in e ac ions a e media ed by pa icles wi h
in ege spin quan um numbe s, e e ed o as bosons. I desc ibes h ee undamen al
in e ac ions: elec omagne ism, he s ong in e ac ion, and he weak in e ac ion.
G a i y is he only in e ac ion ha alls ou side o he model.
The e a e wo ypes o e mions: lep ons and qua ks, and we obse e a simila
pa e n in bo h ca ego ies, wi h wo ypes o pa icles (up and down qua ks, and
elec on and elec on neu ino lep ons), as well as wo addi ional, hea ie -gene a ion
coun e pa s, known as he second and hi d gene a ions.
Only qua ks a e a ec ed by he s ong in e ac ion, which is media ed by gluons
and con ines hem wi hin mesons ( ypically pai s o qua ks) o ba yons ( ypically
consis ing o 3 qua ks). In con as , lep ons do no in e ac wi h he s ong in e ac ion
and can exis independen ly.
xi
con en s
The pho on, he pa icle associa ed wi h ligh , se es as he media o o he elec-
omagne ic in e ac ion, and only cha ged pa icles can in e ac wi h i . Addi ionally,
all e mions can in e ac wi h he
𝑊±
and
𝑍0
bosons, which ac as media o s o he
weak in e ac ion. The elec omagne ic and weak in e ac ions a e, in ac , wo dis inc
mani es a ions o a singula uni ied in e ac ion known as he elec oweak in e ac ion.
The coupling o he gauge bosons o lep ons wi hin he elec oweak in e ac ion is
in a ian wi h espec o he la o o he lep on, a phenomenon e e ed o as lep on
la o uni e sali y.
In he SM, pa icles a e ini ially massless and acqui e mass h ough in e ac ions
wi h he Higgs ield. This mechanism was p oposed in 1964, and wi h he disco e y o
he Higgs boson in 2012 by he ATLAS and CMS collabo a ions in he La ge Had on
Collide (LHC), he S anda d Model was comple ed.
Despi e he g ea success o he S anda d Model, se e al well-known issues emain
unexplained. O dina y ma e can only accoun o app oxima ely 5 % o he obse ed
ene gy in he uni e se, wi h a ound 25 % a ibu ed o da k ma e and app oxima ely
70 % o da k ene gy. The na u e o bo h ene gy sou ces is comple ely unknown as
o now. Mo eo e , he obse a ion o neu ino oscilla ions implies ha hey ha e
mass, bu i is no ye es ablished how hey acqui e i . In addi ion, he obse ed
ma e -an ima e imbalance in he uni e se canno be explained wi h he known
sou ces o CP iola ion and we don’ know how o i g a i y in he model.
Figu e 1: App oxima e con ibu ion om o dina y ma e , da k ma e and da k ene gy o
he obse ed ene gy in he uni e se.
This is he con ex in which his hesis is amed. Semilep onic Hype on Decays
we e p oposed o es lep on la o uni e sali y, one o he main ea u es o he
SM. The
Λ
(uds) pa icle is he ligh es hype on and he b anching a io o he
Λ→𝑝𝜇−¯
𝜈𝜇
decay is sensi i e o BSM physics since he a io be ween he elec onic
and muonic b anching ac ions is p ecisely p edic ed by he SM, and he elec onic
mode b anching a io is accu a ely measu ed. Addi ionally, i can also con ibu e o
xii
con en s
es ing he uni a i y o he CKM ma ix, which will be explained in de ail in he main
ex .
The LHC is cu en ly ou mos powe ul ool o es ing he S anda d Model in
o de o iden i y any de ia ions om i s p edic ions ha can gi e us a hin o wha is
going . An ex ensi e campaign o di ec and indi ec sea ches o physics Beyond
he S anda d Model (BSM) is being conduc ed in he ou majo expe imen s a he
LHC: A To oidaL Apa a uS (ATLAS), Compac Muon Solenoid (CMS), La ge Had on
Collide beau y (LHCb), and A La ge Ion Collide Expe imen (ALICE).
Among he expe imen s a he LHC, LHCb is he only one capable o a emp ing
o imp o e he cu en measu emen s o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
, and ha i is p ecisely
he main goal o his hesis. The measu emen is done using pp collision da a collec ed
by he LHCb expe imen a a cen e-o -mass ene gy o 13 TeV in he pe iod 2016-2018,
co esponding o an in eg a ed luminosi y o 5.4 b−1.
xiii
chap e 1
INTRODUCTION
The
S anda d Model (SM) is he heo e ical amewo k ha desc ibes he known
undamen al pa icles and hei in e ac ions h ough h ee o he ou unda-
men al in e ac ions: elec omagne ic, weak and s ong in e ac ions.
In he SM, ma e is composed o pa icles wi h hal -odd-in ege quan um spin
numbe s, known as e mions, while in e ac ions a e media ed by pa icles wi h
in ege spin quan um numbe s, e e ed o as bosons. I desc ibes h ee undamen al
in e ac ions: elec omagne ism, he s ong in e ac ions, and he weak in e ac ions.
G a i y is he only o ce ha alls ou side o he model. A schema ic summa y o he
SM pa icles can be ound in Figu e 1.1.
The e a e wo ypes o e mions: lep ons and qua ks, and we obse e a simila
pa e n in bo h ca ego ies, wi h wo ypes o pa icles (up and down qua ks, and
elec on and elec on neu ino lep ons), as well as wo addi ional, hea ie -gene a ion
coun e pa s, known as he second and hi d gene a ions.
F om a ma hema ical poin o iew, he elec oweak gauge symme y
𝑆𝑈 (2)𝑊×
𝑈(1)𝑌
is chi al and, as a consequence, qua ks a e o ganized in h ee le -handed
double s
𝑄𝑖
𝐿
wi h i=1,2,3, whe e
𝑄1
𝐿
=
𝑢𝐿
𝑑𝐿
,
𝑄2
𝐿
=
𝑐𝐿
𝑠𝐿
,
𝑄3
𝐿
=
𝑡𝐿
𝑏𝐿
wi h he co esponden s
igh -handed qua k single s 𝑢𝑅,𝑑𝑅,𝑐𝑅,𝑠𝑅,𝑡𝑅and 𝑏𝑅.
Some hing simila happens wi h he lep ons, being o ganized in h ee le -handed
double s
𝐿𝑖
𝐿
wi h i=1,2,3, whe e
𝐿1
𝐿
=
𝜈𝑒𝐿
𝑒𝐿
,
𝐿2
𝐿
=
𝜈𝜇𝐿
𝜇𝐿
,
𝐿3
𝐿
=
𝜈𝜏𝐿
𝜏𝐿
wi h he igh -handed
lep on single s
𝑒𝑅
,
𝜇𝑅
,
𝜏𝑅
. No ice ha , om ou cu en unde s anding, he e a e no
igh -handed neu inos.
Only qua ks a e a ec ed by he s ong in e ac ion, which is media ed by gluons
and con ines hem wi hin mesons ( ypically pai s o qua ks) o ba yons ( ypically
consis ing o 3 qua ks). In con as , lep ons do no in e ac wi h gluons and can exis
decon ined.
The pho on, he pa icle associa ed wi h ligh , se es as he media o o he
1
chap e 1. in oduc ion
elec omagne ic o ce, and only cha ged pa icles can in e ac wi h i . Addi ionally,
all e mions can in e ac wi h he
𝑊±
and
𝑍0
bosons, which ac as media o s o he
weak in e ac ion.
In he SM, pa icles a e ini ially massless and acqui e mass h ough in e ac ions
wi h he Higgs ield. This mechanism was p oposed in 1964, and wi h he disco e y o
he Higgs boson in 2012 by he ATLAS and CMS collabo a ions in he La ge Had on
Collide (LHC), he S anda d Model was comple ed.
μ−
e−
τ−
νe
νμ
ντ
u
d
c
s
b
Lep ons
Qua ks
2
3
1
2
2
3
1
2
2
3
1
2
−1
3
1
2
−1
3
1
2
−1
3
1
2
cha ge
spin
1
2
1
2
1
2
1
2
1
2
1
2
−1
−1
−1
0
0
0
I
II
III
Fe mions :3 Gene a ions
Bosons :Fo ce ca ie s
g
0
1
Z0
0
1
W±
±1
1
H
0
0
Higgs
Gauge Bosons
S ong
Weak
up
down
s ange
bo om
cha m
op
elec on
muon
au
(elec on)
neu ino
(muon)
neu ino
( au)
neu ino
γ
0
1
EM
Elec o
Magne ic
Fe mions
pho on
gluon
Scala
Boson
Figu e 1.1: S anda d Model pa icles and in e ac ions. In he SM, e e y pa icle has a
co esponding an ipa icle. Howe e , he e a e speci ic ins ances whe e a pa icle is i s
own an ipa icle, such as he 𝛾, 𝑍0and Higgs bosons.
Despi e he g ea success o he S anda d Model, se e al well-known issues emain
unexplained. O dina y ma e can only accoun o app oxima ely 5 % o he obse ed
ene gy in he uni e se, wi h a ound 25 % a ibu ed o da k ma e and app oxima ely
70 % o da k ene gy. The na u e o bo h ene gy sou ces is comple ely unknown as
o now. Mo eo e , he obse a ion o neu ino oscilla ions implies ha hey ha e
mass, bu i is no ye es ablished how hey acqui e i . In addi ion, he obse ed
ma e -an ima e imbalance in he uni e se canno be explained wi h he known
sou ces o CP iola ion and we do no know how o i g a i y in he model.
2
1.1. an almos symme ic wo ld
1.1 an almos symme ic wo ld
In 1918, he ma hema ician Emmy Noe he ’s p oo , which showed ha e e y di e -
en iable symme y o he ac ion o a physical sys em subjec ed o conse a i e o ces
co esponds o a conse a ion law, was published. She had o iginally p o ed his
h ee yea s ea lie [62].
A e Emmy Noe he ’s g oundb eaking wo k on symme ies and conse a ion
laws, physicis s began o del e deepe in o unde s anding he undamen al symme ies
inhe en in pa icle in e ac ions. These symme ies a e c ucial o unde s anding he
laws ha go e n he suba omic wo ld. They o igina e he conse a ion p inciples
we obse e, such as conse a ion o ene gy, momen um, and angula momen um.
Howe e , pa icle physics also in oduces o he symme ies, bo h exac and b oken,
ha a e no ob ious a mac oscopic scales.
Some o hese symme ies a e e med "Disc e e Space-Time Symme ies", such as
cha ge conjuga ion (C), pa i y (P), ime (T), CP, and CPT. O he s all unde "Numbe
Conse a ion Laws", including lep on, ba yon, la o , and cha ge conse a ion.
In quan um ield heo ies o pa icle physics, a cha ge conjuga ion ans o ma-
ion (C) is a undamen al ope a ion ha ans o ms a pa icle in o i s an ipa icle.
Meanwhile, a pa i y ans o ma ion (P) ep esen s he in e sion o spa ial coo dina es,
equi alen o a poin e lec ion.
The disco e y ha weak in e ac ions do no conse e pa i y symme y was
shocking. This obse a ion was i s made by Chien-Shiung Wu in 1956 du ing he
expe imen on he be a decay o cobal -60 [79]. Addi ionally, weak in e ac ions also
maximally iola e C symme y. This is because he cha ge conjuga ion does no
change he chi ali y o pa icles. Fo ins ance, a le -handed neu ino, when subjec ed
o cha ge conjuga ion, becomes a le -handed an ineu ino, which does no pa icipa e
in cha ged weak in e ac ions acco ding o he S anda d Model.
To econcile hese obse a ions, i was p oposed ha weak in e ac ions would
conse e he combined CP symme y, jus as he s ong and elec omagne ic in e ac-
ions do. In o he wo ds, i was belie ed ha i all pa icles in a p ocess we e swapped
wi h hei an ipa icles, i would mi o he ini ial p ocess, he eby conse ing he
combined CP-symme y in weak in e ac ions. None heless, subsequen expe imen s
e ealed ha his symme y is sligh ly iola ed in speci ic weak decay p ocesses.
CP- iola ion is esponsible o he ma e -an ima e imbalance in ou uni e se. How-
e e , he deg ee o CP iola ion obse ed wi hin he SM so a is no la ge enough o
explain he obse ed ma e -an ima e asymme y [74].
In a iance unde he combined ans o ma ion CPT is equi ed by gene al p inci-
ples o ela i is ic ield heo y and implies ha masses and li e imes o a pa icle and
i s an i-pa icle mus be equal. As as consequence, CP and T iola ion a e equi alen .
1.2 la o s uc u e o he s anda d model
As i can be seen in Fig. 1.1, he e a e six ypes o qua ks and six ypes o lep ons.
Each ype is conside ed a di e en " la o ". Fla o is conse ed in s ong and elec o-
magne ic in e ac ions. Bu , h ough cha ged cu en weak in e ac ions, qua ks and
3
chap e 1. in oduc ion
lep ons can change om one la o o ano he . A e y well known example is he
be a decay in a omic nuclei, whe e a neu on decays in o a p o on, an elec on and
an elec on neu ino. In ac , he undamen al p ocess ha is going on is
𝑑→𝑢 𝑒−𝜈𝑒(1.1)
whe e he d qua k decays o an up ype qua k ia he exchange o a
𝑊−
boson. A
common way o isualize i is using a Feynman diag am:
uu
u
d
dd
W−e−
νe
Figu e 1.2: Feynman diag am o a neu on be a decay.
No ice ha his decay is comple ely analogous o he semilep onic hype on decay
ha we aim o s udy, deno ed as
Λ→𝑝𝜇−¯
𝜈𝜇
. The only di e ences a e ha in ou
case we s udy an
𝑠→𝑢
ansi ion and ha he lep ons in he inal s a e belong o he
second gene a ion. To cla i y, "semilep onic" means ha in he inal s a e we ha e a
lep on, i s associa ed neu ino, and a had on. A hype on is any ba yon con aining
one o mo e s ange qua ks, bu no cha m, bo om, o op qua k, being he
Λ
he
ligh es o hem.
The SM lag angian can be spli ed in wo e ms:
LSM =LGauge(𝐴𝑎,Ψ𝑖) +LHiggs(𝐻, 𝐴𝑎,Ψ𝑖)(1.2)
In he gauge pa , we iden i y 3 iden ical eplica o he basic e mion amily
[Ψ=𝑄𝐿,𝑢𝑅,𝑑𝑅, 𝐿𝐿, 𝑒𝑅] and we obse e a huge la o degene acy.
LGauge =∑︁
𝑎−1
4𝑔2
𝑎(𝐹𝑎
𝜇𝜈 )2+∑︁
Ψ∑︁
𝑖=1,2,3
Ψ𝑖𝑖/
𝐷Ψ𝑖(1.3)
The Gauge lag angian is in a ian unde 5 independen U(3) global o a ions o
each o he independen e mion ields:
𝑄𝑖
𝐿→𝑈𝑖 𝑗𝑄𝑗
𝐿(1.4)
Wi hin he SM, he la o -degene acy is b oken only by he Yukawa in e ac ion.
In he qua k sec o
L𝑌=−𝑌𝑑
𝑖 𝑗𝑄𝐼
𝐿𝑖 𝜙 𝑑𝐼
𝑅𝑗 −𝑌𝑢
𝑖 𝑗𝑄𝐼
𝐿𝑖𝜖 𝜙∗𝑢𝐼
𝑅𝑗 +ℎ.𝑐. (1.5)
4
1.2. la o s uc u e o he s anda d model
whe e
𝑌𝑢,𝑑
a e 3
×
3 complex ma ices,
𝜙
is he Higgs ield,
𝑖, 𝑗
a e he gene a ion
labels,
𝜖
is he 2
×
2 an i-symme ic enso and "h.c." s ands o he He mi ian conjuga e,
which gi es he co esponding e m o he𝑊−boson [73].
The esidual la o symme y allows us o choose a gauge-in a ian la o basis
whe e only one o he wo Yukawa couplings is diagonal. We can choose
𝑌𝑑=
𝑑𝑖𝑎𝑔(𝑦𝑑,𝑦𝑠,𝑦𝑏)
and
𝑌𝑢=𝑉+×𝑑𝑖𝑎𝑔(𝑦𝑢,𝑦𝑐,𝑦𝑡)
o
𝑌𝑑=𝑉×𝑑𝑖𝑎𝑔(𝑦𝑑,𝑦𝑠,𝑦𝑏)
and
𝑌𝑢=
𝑑𝑖𝑎𝑔(𝑦𝑢,𝑦𝑐,𝑦𝑡), whe e V is a uni a y ma ix.
To diagonalize also he second ma ix we need o o a e sepa a ely
𝑢𝐿
and
𝑑𝐿
, so
we do no ha e a gauge-in a ian basis. This V ma ix appea s in cha ged-cu en
gauge in e ac ions.
This cha ged-cu en in e ac ions, media ed by a 𝑊±boson can be w i en as
𝐽𝜇
𝑊=−𝑔
√2𝑢𝐿𝛾𝜇𝑊+
𝜇𝑉𝐶𝐾𝑀 𝑑𝐿+ℎ.𝑐. (1.6)
which basically means ha he weak in e ac ions couples o pai s
𝑢
𝑑′
,
𝑐
𝑠′
and
𝑡
𝑏′, whe e d’, s’ and b’ a e linea combina ions o he physical d, s, b:
©«
𝑑′
𝑠′
𝑏′ª®¬=©«
𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏
𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏
𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏 ª®¬©«
𝑑
𝑠
𝑏ª®¬(1.7)
This non- i ial mixing a ises solely om he Higgs sec o . Only in e ac ions
media ed by
𝑊±
and h in e ac ions a e la o physics. No e ha he o a ion o he
igh -handed sec o is no obse able and neu al cu en s emain la o diagonal.
The 3
×
3 qua k-mixing uni a y ma ix in ques ion is e med he CKM ma ix,
named a e Cabibbo, Kobayashi, and Maskawa. O iginally, Cabibbo p oposed his
ma ix s uc u e o wo gene a ions in 1963. A decade la e , Kobayashi and Maskawa
ex ended his o mula ion o accommoda e h ee gene a ions. Essen ially, he CKM
ma ix encapsula es in o ma ion ega ding he s eng h o la o -changing weak
in e ac ions. Each elemen o he ma ix signi ies he p obabili y ampli ude o a
ansi ion om one qua k la o
𝑗
o ano he qua k la o
𝑖
. The p obabili ies o hese
ansi ions a e p opo ional o |𝑉𝑖 𝑗 |2.
Up o his poin , we ha e consis en ly obse ed ha he lep onic gene a ion
numbe (o en simply e e ed o as he lep on numbe ) is conse ed in pa icle
decays. Fo ins ance, in ou
Λ→𝑝𝜇−¯
𝜈𝜇
decay, we do no need o iden i y he speci ic
la o o he an i-neu ino in he inal s a e o asce ain ha i ’s an an i-muon neu ino,
since he muonic lep on numbe in he ini ial s a e is
0
. In a hypo he ical scena io
whe e c oss-gene a ional qua k ansi ions do no occu , quan i ies such as ’upness’
plus ’downness’ would be conse ed, simila o how he elec on numbe is conse ed.
Likewise, ’s angeness’ plus ’cha m’ and ’ opness’ plus ’bo omness’ would also be
conse ed. Such a wo ld would be desc ibed by a CKM ma ix ha is simply he
iden i y ma ix.
In ac , he CKM ma ix is e y close o he iden i y ma ix, being he numbe s in
he diagonal ex emely close o 1. The wo ld a e age o he CKM elemen s is [78]:
5
chap e 1. in oduc ion
o his ela i e heo e ical p ecision (
O((𝑀1−𝑀2)2
𝑀2
1)
) he a io does no depend on o m
ac o s.
A p ecise measu emen o
𝑅𝜇𝑒
implies a cons ain on he Wilson coe icien s,
since he men ioned new physics scala and enso ope a o s will con ibu e o he
a io in he ollowing way [26]:
𝑅𝜇𝑒
NP =𝜖𝑆𝑓𝑆(0)
𝑓1(0)+12𝜖𝑇𝑔1(0)
𝑓1(0)
𝑓𝑇(0)
𝑓1(0)
(1−3
2𝛿)1+3𝑔1(02)
𝑓1(0)2Π(Δ,𝑚𝜇)(1.27)
whe e he phase-space in eg al Π(Δ,𝑚𝜇)is
Π(Δ,𝑚𝜇)=5
2
𝑚𝜇
Δh(2+13𝑚2
𝜇
Δ2)√︄1−𝑚2
𝜇
Δ2−34𝑚2
𝜇
Δ2+𝑚4
𝜇
Δ4a c anh(√︄1−𝑚2
𝜇
Δ2))i(1.28)
I is use ul o exp ess he a io o
𝑅𝜇𝑒
NP
and
𝑅𝜇𝑒
SM
encapsula ing he scala and enso
ela ed dimensionless con ibu ions in
𝑟𝑆
and
𝑟𝑇
in o de o exp ess he sensi i i y o
he Wilson coe icien s [26]:
𝑅𝜇𝑒
NP
𝑅𝜇𝑒
SM
=1+𝑟𝑆𝜖𝑆+𝑟𝑇𝜖𝑇(1.29)
being he SHD sensi i i y o he Wilson coe icien s e y channel-dependen [26].
Gi en ha he SM-NLO p edic ions,
𝑅𝜇𝑒
SM
, o he a ious SHD modes a e p ecise,
hese decays a e excellen candida es o pe o ming es s o LFU.
Combining Eq. 1.26 and Eq. 1.20 we a i e o he SM p edic ion o he muon
mode b anching a io.
ΓSM(𝐵1→𝐵2𝜇−¯
𝜈𝜇) ≃ 𝐺2
𝐹|𝑉𝑢𝑠 𝑓1(0)|2Δ5
60𝜋3h1−3
2𝛿+31−3
2𝛿𝑔1(0)2
𝑓1(0)2−4𝛿𝑔2(0)
𝑓1(0)
𝑔1(0)
𝑓1(0)i
√︄1−𝑚2
𝜇
Δ21−9
2
𝑚2
𝜇
Δ2−4𝑚4
𝜇
Δ4+15
2
𝑚4
𝜇
Δ4a c anh√︄1−𝑚2
𝜇
Δ2!
(1.30)
1.4.2 𝑉𝑢𝑠 om B(Λ→𝑝𝜇−¯
𝜈𝜇)
Condensing he
𝑅𝜇𝑒
e m in Eq. 1.30 and conside ing no BSM con ibu ions, we can
w i e 𝑉𝑢𝑠 in e ms o he o m ac o s p edic ed by heo y and he decay a es a io.
|𝑉𝑢𝑠 |2≃
ΓSM(𝐵1→𝐵2𝜇−¯
𝜈𝜇)60𝜋3
𝑅𝜇𝑒𝐺2
𝐹𝑓1(0)2Δ5h1−3
2𝛿+31−3
2𝛿𝑔1(0)2
𝑓1(0)2i(1.31)
whe e he - 4𝛿𝑔2(0)
𝑓1(0)
𝑔1(0)
𝑓1(0) e m is no being conside ed, since i is O(𝛿).
12
1.5. mo i a ion o his measu emen
Fo he
Λ→𝑝𝜇−¯
𝜈𝜇
case, using he cu en PDG measu emen s and heo e ical
compu a ion, he alues o he pa ame e s in ol ed in his exp essions a e
Δexp =
177.4110 ±0.0060
,
𝛿exp =0.1590160 ±0.0000050
,
𝑓1(0)=−√︃3
2
,
𝑔1(0)
𝑓1(0)=0.718 ±0.015
,
𝑅𝜇𝑒 =0.153 ±0.008 [26] and 𝐺𝐹
(ℏ𝑐)3=1.1663787(6) ×10−5𝐺𝑒𝑉 −2[78].
Conside ing ha we aim o measu e
B(Λ→𝑝𝜇−¯
𝜈𝜇)
, we should ew i e he decay
a e
Γ(Λ→𝑝𝜇−¯
𝜈𝜇)=Γ(Λ) B(Λ→𝑝𝜇−¯
𝜈𝜇)(1.32)
whe e he
Γ(Λ)
can be ob ained om he pa icle li e- ime (
𝜏(Λ)=(2.632 ±
0.020) ×10−10 [78]) using
Γ(Λ)=ℏ
𝜏(Λ)=(2.501 ±0.019) ×10−15 [𝐺𝑒𝑉 ](1.33)
Including he alues in GeV uni s in Eq. 1.31, we ob ain:
|𝑉𝑢𝑠 |2≃BSM(𝐵1→𝐵2𝜇−¯
𝜈𝜇) (4.652 ±0.035) ×10−12
(1.06 ×0.06) ×10−14 =BSM(𝐵1→𝐵2𝜇−¯
𝜈𝜇)·(437±26)
(1.34)
Using he cu en
B(Λ→𝑝𝜇−¯
𝜈𝜇)
PDG alue [78] we ob ain
𝑉𝑢𝑠 ≃0.257 ±0.018
,
wi h a la ge unce ain y compa ed o ou cu en knowledge on his CKM ma ix
elemen ,
𝑉𝑢𝑠 =0.22500 ±0.00067
. On op o his, his
𝑉𝑢𝑠
p edic ion was done wi hin
a heo e ical p ecision o O(𝛿2), es ima ed o be be ween 1 o 5 %.
E en ha ing a la ge unce ain y using he cu en a ailable alues o he
B(Λ→
𝑝𝜇−¯
𝜈𝜇)
and he heo e ical p edic ion, his unce ain y can be educed pe o ming a
p ecise measu emen o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
in LHCb, as we plan o do in his hesis.
Mo eo e , as i is explained in de ail in he nex sec ion, he wo mos p ecise
𝑉𝑢𝑠
mea-
su emen s exhibi a 3
𝜎
disc epancy. In his con ex , p ecise SHD
𝑉𝑢𝑠
measu emen s
a e equi ed o pu ligh in his puzzle.
Despi e he conside able unce ain y in he cu en alues o he b anching a io
(
B(Λ→𝑝𝜇−¯
𝜈𝜇)
) and he heo e ical p edic ion, his unce ain y can be mi iga ed wi h
heo e ical e o s and by conduc ing a p ecise measu emen o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
a
LHCb, which is a key objec i e o his hesis. Fu he mo e, as de ailed in he ollowing
sec ion, he wo mos p ecise measu emen s o
𝑉𝑢𝑠
cu en ly show a 3
𝜎
disc epancy.
In his con ex , accu a e measu emen s o
𝑉𝑢𝑠
om SHD a e essen ial o shed ligh on
his puzzle
1.5 mo i a ion o his measu emen
In he las decades he ocus was in he highe mass sec o o he CKM ma ix.
Howe e i is he low mass sec o ,
𝑉𝑢𝑑
and
𝑉𝑢𝑠
, whe e is i possible o ob ain he
highes p ecision and he mos sensi i e es o he uni a y o he CKM ma ix.
One o he s onges es s o he uni a i y o he CKM ma ix can be achie ed by
accu a ely measu ing |𝑉𝑢𝑠 |. This is because eq. 1.14, implies ha :
13
chap e 1. in oduc ion
|𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2≡1(1.35)
Gi en ha he con ibu ion om
|𝑉𝑢𝑏 |2
elemen is almos en i ely negligible
(app oxima ely
1.3×10−5
[78]), his ela ion is educed o he Cabibbo uni e sali y
(|𝑉𝑢𝑑 | ≈𝑐𝑜𝑠 𝜃12,|𝑉𝑢𝑠 | ≈𝑠𝑖𝑛 𝜃12).
Since
|𝑉𝑢𝑑 |
has al eady been measu ed wi h g ea p ecision, wi h a alue o
|𝑉𝑢𝑑 |=0.97436 ±0.00016 [78], he ocus shi s o 𝑉𝑢𝑠 .
In ac , using ou cu en bes measu emen s o 𝑉𝑢𝑑 ,𝑉𝑢𝑠 and 𝑉𝑢𝑏 we ob ain
|𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2=0.9985 ±0.0007 (1.36)
showing a 2.2
𝜎
ension wi h he expec ed uni a i y in he i s CKM ow. Cu en ly,
enhanced p ecision in heo e ical unce ain ies when es ima ing
|𝑉𝑢𝑑 |
and
|𝑉𝑢𝑠 |
is
unco e ing po en ial anomalies. These anomalies migh indica e he p esence o NP
phenomena a he TeV scale [47].
Mo eo e , he measu emen s o
𝑉𝑢𝑠
in lep onic (
𝐾𝜇2
) and semilep onic (
𝐾𝑙3
) kaon
decays exhibi a 3
𝜎
disc epancy. Such a disag eemen can hin owa ds wo po en ial
scena ios: he exis ence o physics beyond he S anda d Model o a signi ican , ye
uniden i ied, sys ema ic e ec wi hin he S anda d Model i sel [72].
Gi en his con ex , i becomes pa amoun o explo e o he a enues o measu e
𝑉𝑢𝑠
wi h high p ecision. In his ega d, semilep onic hype on decays eme ge as a
p omising al e na i e. I hese decays yield alues o
𝑉𝑢𝑠
consis en wi h one se
o kaon decays and no he o he , i could po en ially pinpoin he o igin o he
a o emen ioned disc epancy. On he o he hand, i he alue om hype on decays
s ands in con as o bo h kaon measu emen s, i would u he complica e ou
unde s anding and sugges deepe unde lying issues.
Thus, in ensi ying he ocus on measu ing
𝑉𝑢𝑠
om semilep onic hype on decays
could be ins umen al in shedding ligh on his puzzle. Whe he i ends up ein o cing
he S anda d Model, iden i ying sys ema ic laws, o poin ing owa ds new physics,
he endea o will undoub edly p o ide aluable insigh s in o he ealm o pa icle
physics.
I is also na u al o in es iga e i con ibu ions in cha ged-cu en qua k decays
b eaking LFU can be ound in s
→
u since his can open a doo o physics BSM.
Especially aking in o accoun he esul s coming om b
→
c ansi ions ha poin
in his di ec ion [30].
F om a heo e ical pe spec i e, hype on semilep onic decays ha e been iden i ied
as po en ially sensible o BSM mechanisms ha b eak lep on uni e sali y. These
decays a e go e ned by a mino SU(3) la o symme y b eaking pa ame e , enabling
sys ema ic expansions and p ecise o ecas s wi h minimal eliance on had onic o m
ac o s. The muonic decay channels a e pa icula ly ecep i e o non-s anda d scala
and enso con ibu ions, po en ially o e ing a signi ican complemen a y app oach
o di ec new physics sea ches a he LHC [26].
In he
Λ→𝑝𝑙−¯
𝜈𝑙
case, he LFU es obse able de ined in 1.15 is p edic ed by
heo y o be
𝑅𝜇𝑒 =0.153 ±0.008
wo king a nex - o-leading o de [26]. Cu en
bes measu en o his obse able was pe o med by BESIII in 2021, ob aining 𝑅𝜇𝑒 =
0.178 ±0.028, consis en wi hin unce ain ies wi h he p edic ed alue [6].
14
1.5. mo i a ion o his measu emen
Howe e , since he decay mode in ol ing he elec on is measu ed wi h g ea e
p ecision,
B(Λ→𝑝𝑒−¯
𝜈𝑒)=(8.34 ±0.14) ×10−4
[78], mos o he unce ain y a ises
om he BESIII measu emen o he muonic mode, gi en by
B(Λ→𝑝𝜇−¯
𝜈𝜇)
=
[1.48 ±0.21,(s a ) ±0.08,(sys )] ×10−4.
Inc easing he p ecision in he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
is essen ial o es lep on uni e -
sali y in 𝑠→𝑢 ansi ions.
15
chap e 2
EXPERIMENTAL CONDITIONS
2.1 he lhc
The La ge Had on Collide (LHC) is he mos powe ul and he la ges pa icle accel-
e a o o he wo ld. I began ope a ions on Sep embe 10, 2008. I is he mos ecen
expansion o CERN’s complex o accele a o s. This accele a o ea u es a 27-kilome e
ing equipped wi h supe conduc ing magne s, along wi h se e al accele a ing s uc-
u es designed o inc emen ally inc ease he ene gy o he pa icles as hey a el
h ough he ing [45].
Wi hin he accele a o , wo beams o high-ene gy pa icles a e accele a ed o
nea ly he speed o ligh and a e hen di ec ed o collide wi h each o he . These beams
mo e in opposi e di ec ions, each con ained wi hin i s own beam pipe – a pai o
ubes main ained unde ul a-high acuum condi ions. A powe ul magne ic ield,
gene a ed by supe conduc ing elec omagne s, main ain he beams a ound he ing
o he accele a o .
The pa icle beams wi hin he LHC a e made o collide a ou speci ic poin s
along he accele a o ’s ing. These collision poin s align wi h he loca ions o ou
majo pa icle de ec o s: A To oidaL Apa a uS (ATLAS), Compac Muon Solenoid
(CMS), A La ge Ion Collide Expe imen (ALICE), and LHCb.
2.2 he lhcbde ec o
LHCb is one o he ou big de ec o s collec ing da a in he LHC, a CERN. The name
comes om i s pu pose o de ec ing he decay o pa icles ha con ain b qua ks.
These pa icles, o med in pp collisions, and he pa icles in which hey decay, do no
mo e away oo much om he di ec ion o incidence o he beam. This is e lec ed
in he o wa d design o he de ec o [58] which, unlike o he LHC de ec o s which
17
chap e 2. expe imen al condi ions
CMS
ATLAS
LHCb
ALICE
LHC
SPS
PS
Lei
27 km
628 m
78 m
Linac 2
Boos e
157 m
Linac 3
Lead ions, …
P o ons
7 km
Figu e 2.1: Display o he CERN accele a o complex, including he LHC and i s ou
expe imen s.
co e he en i e solid angle a ound he collision o he p o ons, p esen s i s mul iple
subde ec o s a anged in he o wa d di ec ion
The LHCb, one o he ou majo de ec o s a he LHC loca ed a CERN, is speci i-
cally designed o he de ec ion o decays in ol ing b qua ks. O igina ing om pp
collisions, hese pa icles and hei decay p oduc s end o a el close o he inciden
beam’s di ec ion. This cha ac e is ic is he basis o he o wa d design o he LHCb
de ec o , as de ailed in [58]. Unlike o he de ec o s a he LHC, which co e he en i e
solid angle a ound he p o on collisions, he LHCb has i s subde ec o s on he o wa d
di ec ion [37] wi h an accep ance o 1.6≤𝜂≤4.9, whe e 𝜂is he pseudo apidi y
𝜂=1
2ln 𝑝+𝑝𝑧
𝑝−𝑝𝑧
=−ln an 𝜃
2(2.1)
In his exp ession p is he magni ude o he pa icle momen um,
𝑝𝑧
he magni ude
in he di ec ion o he colliding p o ons and
𝜃
is he angle be ween he pa icle’s
pa h and he ajec o y o he colliding p o ons. This accep ance is equi alen o an
angula accep ance o 10 m ad ≤𝜃≤300 m ad.
The LHCb de ec o was speci ically designed o he accu a e measu emen o CP
symme y iola ion and he a e decay o mesons, pa icula ly hose comp ising b
qua ks o hei an ipa icles (
𝑏
). I s unique design is ailo ed o e icien ly s udy hese
speci ic p ocesses. This op imiza ion has acili a ed signi ican disco e ies, including
he de e mina ion o he b anching a io o he a e decay o he
𝐵𝑠
meson in o a
muon-an imuon pai , as well as he measu emen o he CP iola ion phase in he
18
2.2. he lhcbde ec o
VELO RICH1 TT Imán T1 T2 T3 RICH2 M5M4M3M2M1 HCALECAL
Ve ex
Loca o
Rich1
TT
Magne
T1 T2 T3
Rich2
M1
ECAL HCAL M2 M3
M4 M5
Figu e 2.2: The LHCb de ec o acco ding o he plane o cu a u e o he ajec o y o he
cha ged pa icles.
decay o
𝐵𝑠→
J/
Ψ𝜙
. Examples o he key physics measu emen s by LHCb can be
ound in [7].
The LHCb expe imen is designed o ope a e a a educed ins an aneous luminosi y
o 2 - 5
·1032 𝑐𝑚−2·𝑠−1
, which is lowe han he nominal LHC luminosi y o
1034 𝑐𝑚−2·
𝑠−1
. This is achie ed by employing la ge
𝛽∗
(which deno e he ampli ude modula ion
o he beam a he in e ac ion poin and a e di ec ly ela ed o he beam size) compa ed
o o he LHC de ec o s, esul ing in less ocused beams.
The idea behind his app oach is o simpli y he ask o accu a ely pinpoin ing
he loca ion o he ini ial p o on-p o on collision P ima y Ve ex (PV) and he subse-
quen decay poin s o o he sho -li ed pa icles Seconda y Ve ex (SV). Accu a ely
iden i ying hese e ices is c ucial o he physics objec i es o he LHCb expe imen .
The LHCb expe imen adop s a coo dina e sys em consis en ly u ilized h oughou
his hesis. The o igin is designa ed a he pp in e ac ion poin , ex ending he 𝑧axis
along he beam di ec ion owa ds he emainde o he de ec o appa a us. O ien ed
e ically upwa ds, in luenced by g a i y, he
𝑦
axis is es ablished, while he
𝑥
axis
main ains he sys em’s “ igh -handedness” (
ˆ
𝑥׈
𝑦=ˆ
𝑧
), posi ioned ho izon ally, acing
he de ec o ’s le when obse ed om he nega i e
𝑧
side. A p e alen me ic,
“ ans e se momen um” (
𝑝𝑇
), e e encing a pa icle, is de ined wi hin his pa icula
coo dina e amewo k as
𝑝𝑇=√︃𝑝2
𝑥+𝑝2
𝑦(2.2)
The i s pe iod o da a aking, Run I, ook place om 2009 o 2012. Run II e e s
o he second da a- aking un o he LHCb expe imen , ha ook place om 2015 o
2018. In Run II, he LHC ope a ed a a highe ene gy, wi h p o on-p o on collision
ene gies eaching 13 TeV and a luminosi y o almos 6 𝑓 𝑏−1was eco ded.
19
chap e 2. expe imen al condi ions
Table 2.1: Ene gy in he cen e o mass (s) and in eg a ed luminosi y eco ded o each
yea o da a aking du ing Run1 and Run2.
Yea Ene gy (TeV) In eg a ed Luminosi y (𝑓 𝑏−1)
2010 7 0.04
2011 7 1.11
2012 8 2.08
2015 13 0.33
2016 13 1.67
2017 13 1.71
2018 13 2.19
This analysis uses Run II LHCb da a. As a consequence, he de ec o desc ibed is
he one ha ook da a om 2015 o 2018 and no he upg aded one ha is aking da a
cu en ly [48].
2.2.1 echnical speci ica ions.
LHCb ea u es a single-a m spec ome e design, p o iding o wa d angula co e age
anging om oughly 10 m ad o 300 m ad in he bending plane and up o 250
m ad in he non-bending plane. This speci ic geome y is chosen because, a high
ene gies, bo h b and
¯
𝑏
had ons a e p edominan ly p oduced wi hin he same o wa d
o backwa d di ec ional cone.
The basic cha ac e is ics o LHCb a e:
Dimensions: 21 me e s long, 13 me e s wide and 10 me e s high.
Weigh : 5 600 ons.
2.3 subde ec o s
We essen ially ha e a Ve ex Loca o (
VELO
) ( o de e mine he ajec o y o he
pa icles nea he poin o in e ac ion, wi h he main objec i e o sepa a ing he
p ima y e ices whe e, o example, he B-mesons a e p oduced and he seconda y
ones, whe e hey decay),
RICH
( o iden i y he pa icles p oducing each ack by
ob aining hei mass and cha ge),
T-s a ions
(gi e he ajec o ies and momen um
o cha ged pa icles),
ECAL
(de ec elec ons and pho ons),
HCAL
(de ec had ons),
Muon Chambe s (de ec muons).
2.3.1 magne :
The LHCb dipole magne [59] p o ides a magne ic ield o 4 T.m ha cu e he
cha ged pa icles in he ho izon al plane o he de ec o wi h he idea o allowing he
20
2.3. subde ec o s
measu emen o hei momen a. The measu emen co e s he o wa d accep ance o
±250 m ad e ically and o ±300 m ad ho izon ally.
To accoun o po en ial sys ema ic e ec s, he o ien a ion o he magne ic ield is
al e na ed pe iodically be ween upwa d and downwa d di ec ions.
The magne ic ield p o ided by he dipole mus be known wi h excellen p ecision,
in o de o yield a momen um esolu ion as good as possible. The p ecision o he
measu emen ob ained o he ield mapping in he acking olume is abou
4·10−4
.
The ajec o y o beams ci cula ing wi hin he LHC is in luenced by he exis ence o
he LHCb dipole magne . To mi iga e his impac , h ee compensa o y magne s a e
s a egically posi ioned a ound he de ec o [45].
2.3.2 e ex loca o :
The Ve ex Loca o (VELO) [[37],[36],[35]] is he subde ec o placed close o he
p o on in e ac ion poin (p ima y e ex). I is designed o loca e he p ima y and
seconda y e ices, ocusing in b and c-had ons decays.
The VELO also p o ides an excellen ime esolu ion o measu e he li e imes o his
pa icles, some hing c ucial o in es iga e CP iola ion e ec s.
The Run 2 VELO con ains wo hal es wi h 21 s a ions each, posi ioned along and pe -
pendicula o he beam axis. Two ypes o silicon senso s a e used: one measu es he
coo dina e wi h ci cula s ips cen e ed a ound he beam axis, he o he measu es
he
𝜙
coo dina e wi h s aigh , almos adial s ips (including a s e eo-angle buil in).
The VELO is e ac able, which allows o inc ease he sepa a ion be ween he wo
hal es du ing injec ion and o adjus i (±5mm) o he posi ion o he beam.
The senso s a e housed in a acuum, isola ed om he LHC acuum by a slende ,
co uga ed aluminum shee . The design geome y enables he wo hal es o he VELO
o o e lap when comple ely closed, educing he ma e ial a cha ged pa icle a e ses
om he in e ac ion poin o he senso s.
The unce ain y in he p ima y e ex’s posi ion p ima ily depends on he numbe
o acks gene a ed du ing a p o on-p o on collision. On a e age, he esolu ion is
42 𝜇𝑚
in he
𝑧
-di ec ion and
10 𝜇𝑚
in he di ec ion pe pendicula o he beam. The
esolu ion o he impac pa ame e is
20 𝜇𝑚
, excluding he in luence o he p ima y
e ex, o acks exhibi ing he maximum ans e se momen um. The accu acy o
he decay leng h measu emen a ies be ween
220 𝜇𝑚
and
370 𝜇𝑚
, con ingen on he
speci ic decay channel. Fo he
𝐵0
𝑠→𝐷−
𝑠𝜋+
decay channel, a li e ime esolu ion o
40 𝑓 𝑠
has been a ained, enabling a
5𝜎
measu ing o
Δ𝑚𝑠
up o
54𝑝𝑠−1
a e a yea o
da a collec ion [36].
2.3.3 acking sys em:
In LHCb acks a e econs uc ed o ming pa icle ajec o ies om he hi s ha
he acking sys em collec s. Appa om he VELO, he LHCb acking sys em is
composed by he T acke Tu icensis (TT) [35], a single s a ion igh ups eam he
magne , and by h ee acking s a ions downs eam he magne and be o e RICH2.
The acking s a ions ha e wo di e en subs uc u es: he inne acke (IT) [14]
21
chap e 2. expe imen al condi ions
2.4.4 is / os de ini ion
The LHCbIDs
1
associa ed wi h he inal s a e pa icles o an o line candida e can be
c oss- e e enced wi h hose a chi ed by he High-Le el T igge (HLT) o asce ain
i he o line candida e ecei ed app o al by he igge . This compa a i e analysis
yields a classi ica ion e med TISTOS (T igge independen o Signal / T igge on
Signal).
An o line candida e is ca ego ized as TOS ela i e o a igge selec ion i i gains
accep ance by he espec i e igge selec ion. To a icula e his mo e o mally, an
o line candida e is Tos i he LHCbIDs o each o i s inal s a e pa icles coincide by
o e 70% wi h he LHCbIDs o he inal s a e pa icles o a igge -accep ed candida e.
Con e sely, an o line candida e achie es a TIS classi ica ion ela i e o a igge
selec ion i i s emo al om he e en doesn’ impede he igge selec ion’s accep-
ance o he e en . This implies he p esence o an al e na i e pa icle wi hin he
e en ha also secu es accep ance by he igge selec ion. Fo mally, his is alida ed
when he LHCbIDs o all inal s a e pa icles o any accep ed candida es exhibi less
han a 1% o e lap wi h he LHCbIDs o he inal s a e pa icles o he o line candida e.
Fo example, an e en is iden i ied as TISTISIS i i is TIS o he h ee igge le els:
L
0
, HLT1 and HLT2. The s a egy o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
measu emen in ol es
using TISTISTIS Da a bo h o measu ing he
Λ→𝑝𝜇−¯
𝜈𝜇
and
Λ→𝑝𝜋−
yields o
educe unce ain ies as much as possible, since any igge equi emen will imply an
ex a sys ema ic unce ain y. This is possible due o he la ge
Λ
p oduc ion a io a
LHCb.
2.5 lhcbupg ade
A e he Run 2 da a aking, LHC s opped o 4 yea s (Long Shu down 2). Du ing
his pe iod, he de ec o unde wen a comp ehensi e upg ade, wi h many signi ican
enhancemen s being made. These imp o emen s enable LHCb o ope a e a an
ins an aneous luminosi y i e imes g ea e han du ing Run 1 and Run 2 and o
econs uc da a a 40 MHz LHC c ossing a e, wi h he goal o accumula ing a o al
in eg a ed luminosi y o app oxima ely
50 b−1
by he end o LHC Run 4 [34]. A side
iew o he upg aded de ec o can be seen in 2.5.
The VELO unde wen a o al eno a ion, wi h he main echnology now cen e ed
a ound hyb id silicon pixel de ec o s. The in eg a ion o pixel-based geome y, cou-
pled wi h a educed p oximi y o he ini ial measu ed poin and minimized ma e ial
usage, has ma kedly enhanced he VELO’s pe o mance [32].
The Ups eam T acke (UT) is si ua ed be ween RICH1 and he Magne and
enables a signi ican enhancemen in accep ance compa ed o i s p edecesso , he
TT. As cha ged pa icles a e se his acking sys em, hey p oduce hi s; hese UT
hi s a e c ucial o he ini ial s ages o he so wa e igge . When combined wi h
VELO hi s, VELO-UT acks a e o med. The p esence o a magne ic ield in he
1
The LHCbID class se es as a uni e sal channel iden i ie ac oss he LHCb amewo k. I s p ima y
unc ion is wi hin he upda ed ack model, ensu ing each measu emen con ibu ing o a ack’s cons uc-
ion is dis inc ly ma ked. By ha ing access o a se o LHCbIDs and hei associa ed measu emen s, one
should be able o eplica e he ack i ing ou comes.
28
2.6. lhcbda a low
VELO RICH1 TT Imán T1 T2 T3 RICH2 M5M4M3M2M1 HCALECAL
Ve ex
Loca o
RICH1
UT
Magne SciFi
T acke
RICH2 ECAL HCAL M2 M3
M4 M5
Figu e 2.5: The LHCb upg aded de ec o acco ding o he plane o cu a u e o he ajec-
o y o he cha ged pa icles.
UT egion enables an ini ial es ima ion o pa icle momen um wi h app oxima ely
15%
unce ain y. Addi ionally, UT hi s subs an ially educe he a e o ake acks
and can ma kedly boos he s a is ics o long-li ed pa icles such as
𝐾0
𝑆
o
Λ
, by
p o iding measu emen s o he seconda y e ex o pa icles ha decay a e passing
he VELO [34].
The h ee acking s a ions downs eam he magne and be o e RICH2 (T1, T2 and
T3) we e eplaced by he Scin illa ing Fib e acke (SciFi), asked wi h acking
cha ged pa icles and de e mining hei momen um. The sys em mus a ain a mo-
men um esolu ion and ack e iciency o b- and c-had ons ha is on pa wi h he
pe o mance om Run 1 and Run 2, despi e ope a ing unde condi ions o inc eased
pa icle densi y [34].
The RICH de ec o s and calo ime e s we e also upg aded, while main aining he
undamen al design p inciples o hei p edecesso s.
Conce ning he muon sys em, he
𝑀1
s a ion was emo ed as i was p e iously
u ilized o he Le el-0 ha dwa e igge , which is no longe necessa y. A de ailed
accoun o he igge sys em implemen ed in he upg ade is p o ided in Sec ion 3.4.
2.6 lhcbda a low
The i s s ep in he da a low in ol es da a collec ion using he LHCb subde ec o s
o ac ual da a and he simula ion and digi isa ion p ocesses o he Mon e Ca lo
simula ion (MC).
The simula ion o e en s un olds in h ee dis inc phases: he gene a ion o
pa icles, acili a ed by Py hia [19]; he decay o pa icles, managed by E Gen [56];
and he p opaga ion o pa icles h ough he de ec o , o ches a ed by Gean 4 [8].
29
chap e 2. expe imen al condi ions
The Gauss so wa e package o e sees he en i e simula ion p ocess. Subsequen ly,
he digi isa ion p ocess is simula ed using Boole.
The emaining s ages o he da a low a e consis en o bo h Mon e Ca lo (MC)
and ac ual da a. Ini ially, he e a e h ee igge s eps ( e e o Sec ion 2.4), supe ised
by he Moo e so wa e package. This is ollowed by he econs uc ion p ocess,
conduc ed by B unel, and ul ima ely, he s ipping p ocess, managed by DaVinci. The
s ipped da a is s o ed and made accessible o analys s, who can u ilize DaVinci o
gene a e da a and MC NTuples o hei analyses.
A comp ehensi e depic ion o he LHCb da a low is a ailable in Figu e 2.6.
T igge
Moo e
Recons uc ion
B unel
S ipping
DaVinci
Digi isa ion
Boole
Simula ion
Gauss
S o age
NTuple Making
Analysis
Lep onic.ds , …
DaVinci
ROOT, Numpy,..
Gene a ion Decay P opaga ion
Py hia E Gen Gean 4
LHCb
Da a Taking
MC
MC
S o age S o age
FULLSTREAM FULLSTREAM
ReS ipping
Re- econs uc ion
VELO RICH1 TT Imán T1 T2 T3 RICH2 M5M4M3M2M1 HCALECAL
Ve ex
Loca o
Rich1
TT
Magne
T1 T2 T3
Rich2
M1
ECAL HCAL M2 M3
M4 M5
Figu e 2.6: LHCb Da a low.
2.7 s ipping
The s ipping p ocess ollows he igge sys em and econs uc ion in he da a selec-
ion hie a chy. I is an so wa e o line selec ion ha il e s speci ic decay channels o
e en s o in e es .
In he s ipping p ocess, p ede ined selec ion c i e ia, known as "lines," a e applied.
Each line co esponds o a speci ic decay channel o a se o equi emen s. Mul iple
lines collec i ely o m a "s ipping e sion" o "s ipping con igu a ion".
This selec ion is based on pa icle iden i ica ion, kinema ics, o o he e en cha -
ac e is ics. The cu s a e op imized o e ain as many signal e en s as possible while
educing he backg ound.
E en s ha pass he s ipping c i e ia a e e ained o u he analysis. These
e en s a e s o ed in a mo e accessible o ma , allowing physicis s o analyze hem in
de ail.
30
2.8. simula ion so wa e and amewo ks
2.8 simula ion so wa e and amewo ks
Simula ion plays a pi o al ole in high-ene gy physics expe imen s such as hose
conduc ed a LHCb. I in ol es he use o compu a ional models o mimic he physical
p ocesses occu ing du ing pa icle collisions and hei in e ac ions wi h he de ec o .
Simula ions p o ide a heo e ical amewo k ha aids in he in e p e a ion and
unde s anding o he expe imen al da a, helping physicis s o un a el he mys e ies
o undamen al pa icles and hei in e ac ions.
In he ealm o LHCb expe imen s, a ious sophis ica ed so wa e and amewo ks
play an indispensable ole in he gene a ion o accu a e and eliable simula ions. A
no able men ion is Gauss, he o icial LHCb so wa e o e en simula ion. Gauss
allows o he me iculous modeling o p o on-p o on collisions, subsequen pa icle
decays, and hei in e ac ions wi h he de ec o ’s ma e ial, based on he p e ailing
heo e ical models and Mon e Ca lo echniques. I is complemen ed by he Gaudi
amewo k [17], a e sa ile and obus en i onmen used o da a p ocessing and
analysis wi hin LHCb. Gaudi acili a es he e icien handling o e en da a, ensu ing
ha bo h simula ed and eal da a a e p ocessed h ough iden ical econs uc ion and
analysis chains. This cong uence ensu es a cohe en and s aigh o wa d compa i-
son be ween expe imen al obse a ions and heo e ical expec a ions, ensu ing he
in eg i y o he esul s.
2.8.1 e en gene a ion
E en gene a ion is a key pa o simula ing physical p ocesses, like hose happening
in expe imen s a LHCb. I helps u n heo e ical physics ideas in o a i ual o m
ha can be s udied and analyzed in de ail. In LHCb expe imen s, e en gene a o s
help simula e he i s p o on-p o on collisions and he ollowing se ies o pa icle
decays and in e ac ions.
These gene a o s use Mon e Ca lo me hods, c ea ing many possible e en s ha
show he andom na u e o quan um p ocesses. This allows o a de ailed s udy o
all possible ou comes. The e en gene a o s wo k based on a gi en pa icle physics
heo y (no only he SM, BSM models can also be conside ed), helping he simula ions
closely ma ch wha we expec o see in he eal wo ld unde he co esponden heo y.
E en gene a o s a e especially impo an o simula ing a e pa icle decays,
which a e c ucial o LHCb’s mission o s udy he beha iou o pa icles. The e en s
c ea ed by hese gene a o s ac as a base, allowing us o compa e eal-li e expe imen al
esul s wi h heo e ical expec a ions, helping us o unde s and he physics in ol ed.
Py hia is a powe ul ool used in he ield o pa icle physics o simula e he
gene a ion o e en s in high-ene gy in e ac ions, such as p o on-p o on collisions
[19]. I p o ides de ailed models o high-ene gy eac ions, allowing us o unde s and
he p oduc ion and decay o pa icles and an ipa icles. In he con ex o he LHCb
expe imen , Py hia is used by Gauss o accu a ely simula e he pa icles p oduced
immedia ely a e p o on-p o on collisions.
E Gen is ano he essen ial ool used in pa icle physics simula ions, specializing
in he simula ion o he decay o hea y pa icles, like hose p oduced in p o on-p o on
collisions [56]. A e Py hia simula es he ini ial collision and p oduc ion o pa icles,
31
chap e 2. expe imen al condi ions
E Gen akes o e o handle he de ailed simula ion o how hese gene a ed pa icles
decay in o ligh e pa icles. Gauss, he o e a ching simula ion so wa e used in he
LHCb expe imen , o ches a es his p ocess.
2.8.2 de ec o simula ion
De ec o simula ion is a c ucial pa o analyzing esul s in high-ene gy physics,
helping o connec heo y wi h ac ual expe imen esul s. In he LHCb expe imen ,
de ec o simula ion ca e ully mimics he pa hs o pa icles as hey mo e h ough
he de ec o , in e ac wi h i s pa s, and lea e behind elec onic aces ha we can
measu e. Specialized so wa e helps o ec ea e he physical happenings inside he
de ec o , cap u ing de ails like pa icle in e ac ions and ene gy le behind. This helps
us unde s and how he de ec o esponds o a ious pa icles and e en s, making i
easie o pull ou use ul in o ma ion om he aw da a.
De ec o simula ion c ea es a i ual model o he de ec o ’s ac ions, imp o ing
he eliabili y and p ecision o he expe imen ’s analysis. This ensu es ha he
conclusions d awn a e based on a de ailed unde s anding o how he de ec o wo ks
and pe o ms.
Gean 4 is a powe ul so wa e ool used o simula e how pa icles mo e h ough
and in e ac wi h de ec o s in expe imen s [8] like hose conduc ed a LHCb. Gauss
is a p og am ha uses a ious ools, including Gean 4, o simula e he en i e jou ney
o pa icles p oduced in high-ene gy collisions.
A e he ini ial collision is simula ed, and he pa icles a e p oduced and decayed
using ools like Py hia and E Gen, Gauss uses Gean 4 o simula e he nex pa o he
pa icles’ jou ney. Gean 4 helps Gauss o c ea e a i ual eplica o he LHCb de ec o .
I ca e ully simula es how he pa icles a el h ough he de ec o , how hey in e ac
wi h he ma e ials in he de ec o , and how hese in e ac ions lea e behind signals
ha can be measu ed.
Gean 4 is e y de ailed and can mimic he eal physical p ocesses happening
inside he de ec o , like how pa icles lose ene gy and how hey sca e . This makes
he simula ion e y ealis ic, helping esea che s o be e unde s and and in e p e
he ac ual expe imen al da a collec ed by he LHCb de ec o . By using Gean 4, Gauss
ensu es ha he simula ions a e as accu a e and use ul as possible, helping scien is s
o make sense o hei expe imen s and explo e he mys e ies o pa icle physics.
2.8.3 econs uc ion and analysis
Recons uc ion and analysis a e key s eps in u ning aw da a om expe imen s
o compu e simula ions in o use ul scien i ic indings. In he LHCb expe imen ,
econs uc ion means aking he basic elec onic signals om he de ec o and u ning
hem in o a clea pic u e o each e en . This includes igu ing ou which pa icles
a e p esen and de e mining hei pa hs, speeds, and ene gy. Bo h eal expe imen
da a and simula ed da a go h ough he same econs uc ion p ocess, making su e
he esul s a e consis en and us wo hy.
Du ing he analysis pa , he e ined da a is closely s udied o ind impo an
in o ma ion abou physical p ope ies and beha io s. Di e en s a is ical me hods and
32
2.8. simula ion so wa e and amewo ks
da a selec ion c i e ia a e used o ocus on speci ic pa icles o decay ypes. Insigh s
om bo h eal and simula ed da a wo k oge he o imp o e ou unde s anding o
he physics in ol ed. This collabo a ion helps o make su e ha he expe imen
esul s a e accu a e and can be con iden ly compa ed wi h heo e ical expec a ions.
O e all, his p ocess helps o ca e ully assess he expe imen ’s me hods and esul s,
suppo ing de ailed and eliable disco e ies abou pa icle beha io s.
2.8.4 alida ion and calib a ion
Valida ion and calib a ion a e impo an s eps ha make simula ions in he LHCb
expe imen mo e accu a e and us wo hy. Valida ion means ca e ully checking ha
he simula ed da a ma ches up wi h he eal expe imen esul s. This makes su e
ha he simula ions a e a eliable ool o es ing ideas and unde s anding da a. Any
di e ences ound du ing alida ion a e s udied closely o imp o e he simula ions,
making hem be e a p edic ing wha will happen.
Calib a ion is abou adjus ing he simula ions o make su e hey ma ch he ac ual
esponses o he de ec o and he eal expe imen al condi ions. Since expe imen s
can be complica ed and changeable, calib a ion helps keep he simula ions up- o-da e
and accu a e in e lec ing wha is ac ually happening in he expe imen s.
Toge he , alida ion and calib a ion help make su e ha he simula ions a e
s ong and dependable, accu a ely showing wha happens in high-ene gy physics
expe imen s. This helps inc ease us in he esul s om he simula ions, making
hem use ul o planning expe imen s, unde s anding esul s, and disco e ing new
hings abou he basic pa icles and how hey in e ac .
2.8.5 use o simula ion in his esea ch
In his hesis, simula ion has been ins umen al in e ining he analysis s a egy
and enhancing he obus ness o he esul s. Using he Gauss and Gaudi so wa e
amewo ks, a de ailed simula ion o he signal and backg ound p ocesses was con-
duc ed. This allowed o a me iculous e alua ion o he de ec o ’s esponse, enabling
a comp ehensi e compa ison be ween he simula ed and eal da a, he eby acili-
a ing a mo e accu a e ex ac ion o he physical pa ame e s unde s udy. Fo he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
measu emen , we gene a ed speci ic
Λ→𝑝𝜇−¯
𝜈𝜇
and
Λ→𝑝𝜋−
simula ion samples (using a speci ic E Gen model o he
Λ→𝑝𝜇−¯
𝜈𝜇
) passing he
Λ→𝑝𝜇−¯
𝜈𝜇
s ipping line. Fo he no maliza ion, we used MinBias MC (see nex
sec ion) samples o compu e he e iciencies needed o compu e he o al amoun o
Λpa icles in he da a sample.
2.8.6 minimum bias simula ion
A minimum bias (MinBias) simula ion aims o esemble as close as possible ypical
LHCb e en s wi hou in oducing any bias. A comple e lis o he Py hia p ocesses
ha a e included in he MinBias MC can be ound in [33]. This kind o simula ion
will be used in he no maliza ion p ocess in ou case.
33
chap e 2. expe imen al condi ions
When no malizing agains modes ha exhibi high yields in Minimum Bias
e en s (such as
Λ→𝑝𝜋−
,
𝐾0
𝑆→𝜋+𝜋−
), u ilizing speci ic Decay Files wi h imposed
gene a o -le el cu s o hese modes o e s no pa icula ad an age. No e ha such
wo-body decays do no equi e a dedica ed E Gen model. In p ac ice, one is likely
o encoun e a g ea e numbe o hese decays in he unde lying e en . Implemen ing
gene a o -le el cu s complica es ma e s, as i becomes challenging o asce ain which
decay he cu s ha e impac ed, making e iciency calcula ions inc easingly complex.
Op ing o Minimum Bias allows o a s aigh o wa d calcula ion o he combined
gene a ion-le el and econs uc ion e iciencies in a single s ep. Wi h an adequa ely
sized Minimum Bias sample, s a is ical conce ns should no a ise.
34
chap e 3
STRANGE PHYSICS AT LHCb
P ecise measu emen s o he
𝑏→𝑐
ansi ion p o ide hin s o Lep on Fla o Uni-
e sali y (LFU) b eaking [30], which could poin o physics Beyond he S anda d
Model (BSM). I is na u al o in es iga e whe he simila beha io occu s in o he
cha ged-cu en decays o d- ype qua ks, namely 𝑠→𝑢.
The LHCb expe imen has shown i s capabili y o ob ain leading s ange physics
measu emen s, pa icula ly sea ching o hei a e decays. In ac , he LHCb col-
labo a ion has published he wo ld’s mos p ecise measu emen in
𝐾0
𝑆→𝜇+𝜇−
,
𝐾0
𝑆→𝜇+𝜇−𝜇+𝜇−, and Σ+→𝑝𝜇+𝜇−[2] [4], [3].
In he las decades he ocus was in he highe mass sec o o he CKM ma ix.
Howe e i is he low mass sec o ,
𝑉𝑢𝑑
and
𝑉𝑢𝑠
, whe e is i possible o ob ain he
highes p ecision and he mos sensi i e es o he uni a y o he CKM ma ix [23].
Fo he CKM ma ix o be uni a y,
|𝑉𝑢𝑑 |2
+
|𝑉𝑢𝑠 |2
+
|𝑉𝑢𝑏 |2≡1
. Since
|𝑉𝑢𝑏 |
has been
measu ed o be
0.00369 ±0.00011
[78],
|𝑉𝑢𝑏 |2
is almos negligible and he uni a y es
educes o
|𝑉𝑢𝑑 |2
+
|𝑉𝑢𝑠 |2
= 1, which can be exp essed in e ms o he Cabibbo angle
(
𝜃𝑐
) as
cos2𝜃𝑐+sin2𝜃𝑐=1
. Expe imen ally,
|𝑉𝑢𝑑 |
can be de e mined om nuclea
be a decay [53], and
|𝑉𝑢𝑠 |
can be measu ed in s angeness-changing semilep onic
decays [20]. P ecise de e mina ion o he
𝑠→𝑢
ansi ion is he e o e an impo an
componen o alida ing he uni a i y o he CKM ma ix.
As i was explained in he In oduc ion, a 2.2
𝜎
ension wi h he expec ed uni a i y
was obse ed in he i s CKM ow uni a i y es . The measu emen s o
𝑉𝑢𝑠
in lep onic
(𝐾𝜇2) and semilep onic (𝐾𝑙3) kaon decays exhibi also a 3𝜎disc epancy [72].
Taking his in o accoun , i is necessa y o measu e
𝑉𝑢𝑠
wi h high p ecision and
Semilep onic Hype on Decays (SHD) a e he na u al al e na i e.
F om a heo e ical s andpoin , s udies ha e demons a ed ha he SHD ( e e
o Fig. 3.1 o a lis o hype ons) can po en ially de ec speci ic BSM dynamics ha
b eak lep onic uni e sali y. These decays a e go e ned by a mino SU(3) la o
b eaking pa ame e , enabling sys ema ic expansions and p ecise p edic ions in e ms
o a educed dependence on had onic o m ac o s. Muonic decays a e pa icula ly
35
chap e 3. s ange physics a lhcb
Figu e 3.1: A hype on is any ba yon con aining one o mo e s ange qua ks, bu no cha m
bo om, o op qua k, being he
Λ
he ligh es o hem. The expec ed yields o semilep onic
hype on decays in LHCb a e la ge.
sensi i e o scala and enso de ia ion con ibu ions. Such pa e ns could complemen
di ec sea ches o new physical phenomena a he LHC [26].
The LFU es obse able de ined as he a io be ween muon and elec on modes
𝑅𝜇𝑒 =
Γ(𝐵1→𝐵2𝜇−¯
𝜈𝜇)
Γ(𝐵1→𝐵2𝑒−¯
𝜈𝑒)(3.1)
is sensi i e o non s anda d scala and enso con ibu ions [26] . Mo eo e , in he
SM, he dependency on he o m ac o s is an icipa ed o simpli y when conside ing
he a io. Indeed, by ope a ing a Nex - o-Leading O de (NLO), we achie e:
𝑅𝜇𝑒
SM =√︄1−𝑚2
𝜇
Δ2 1−9
2
𝑚2
𝜇
Δ2−4𝑚4
𝜇
Δ4!+15
2
𝑚4
𝜇
Δ4a c anh √︄1−𝑚2
𝜇
Δ2!
whe e Δ=𝑀2−𝑀1.
This p edic ion is ema kable, since up o his ela i e heo e ical p ecision
(O((𝑀1−𝑀2)2
𝑀2
1)) he a io does no depend on o m ac o s [26].
In 2019 we published a pape , Re . [10] desc ibing some p ospec s o measu e-
men s wi h s ange had ons a LHCb. A able wi h he accep ance e iciencies and
in a ian mass esolu ions o he s udied s ange had on decays can be ound in Tab.
3.1. The p oduc ion a e in LHCb, compa ed o he
𝐾0
𝑆
one, was also compu ed (see
Fig. 3.2).
36
3.1. Λ→𝑝𝜇−¯
𝜈𝜇
Table 3.1: In his s udy, he accep ances and in a ian mass esolu ions o key s ange
channels we e e alua ed using a simula ion based on he upg aded acking o he LHCb.
The calcula ed accep ances we e hen no malized wi h espec o he ully econs uc ed
𝐾0
𝑆→𝜇+𝜇−
, which has been de e mined o be
1%
. The e iciency has been p esen ed o
bo h long and downs eam acks, and he in a ian mass esolu ion has been shown o
each econs uc ion me hod, as de ailed in [10]. He e,
R
ep esen s he p oduc ion a io
ela i e o he 𝐾0
𝑆one.
Channel R𝝐𝑳𝝐𝑫𝝈𝑳𝝈𝑫
(𝑀𝑒𝑉
𝑐2) (𝑀𝑒𝑉
𝑐2)
𝐾0
𝑆→𝜇+𝜇−1 1.0 (1.0) 1.8 (1.8) ∼3.0 ∼8.0
𝐾0
𝑆→𝜋+𝜋−1 1.0 (0.30) 1.9 (0.91) ∼2.5 ∼7.0
𝐾0
𝑆→𝜋0𝜇+𝜇−1 0.93 (0.93) 1.5 (1.5) ∼35 ∼45
𝐾0
𝑆→𝛾𝜇+𝜇−1 0.85 (0.85) 1.4 (1.4) ∼60 ∼60
𝐾0
𝑆→𝜇+𝜇−𝜇+𝜇−1 0.37 (0.37) 1.1 (1.1) ∼1.0 ∼6.0
𝐾0
𝐿→𝜇+𝜇−∼1 2.7 (2.7) ×10−30.014 (0.014) ∼3.0 ∼7.0
𝐾+→𝜋+𝜋+𝜋−∼2 9.0 (0.75) ×10−341 (8.6) ×10−3∼1.0 ∼4.0
𝐾+→𝜋+𝜇+𝜇−∼2 6.4 (2.3) ×10−30.030 (0.014) ∼1.5 ∼4.5
Σ+→𝑝𝜇+𝜇−∼0.13 0.28 (0.28) 0.64 (0.64) ∼1.0 ∼3.0
Λ→𝑝𝜋−∼0.45 0.41 (0.075) 1.3 (0.39) ∼1.5 ∼5.0
Λ→𝑝𝜇−¯
𝜈𝜇∼0.45 0.32 (0.31) 0.88 (0.86) - -
Ξ−→Λ𝜇−¯
𝜈𝜇∼0.04 39 (5.7) ×10−30.27 (0.09) - -
Ξ−→Σ0𝜇−¯
𝜈𝜇∼0.04 24 (4.9) ×10−30.21 (0.068) - -
Ξ−→𝑝𝜋+𝜋−∼0.04 0.41 (0.05) 0.94 (0.20) ∼3.0 ∼9.0
Ξ0→𝑝𝜋−∼0.03 1.0 (0.48) 2.0 (1.3) ∼5.0 ∼10
Ω−→Λ𝜋−∼10−395 (6.7) ×10−30.32 (0.10) ∼7.0 ∼20
3.1 Λ→𝑝𝜇−¯
𝜈𝜇
Among he s udied channels,
Λ→𝑝𝜇−¯
𝜈𝜇1
is one o he mo e in e es ing SHD due o
i s high econs uc ion e iciency and because, being he ligh es hype on, i is he
mos abundan in LHCb. The pu pose o he main analysis in his hesis is o measu e
i s b anching a io using he LHCb Run2 da a sample.
In [10] we p oposed a s a egy o sepa a e
Λ→𝑝𝜇−¯
𝜈𝜇
om he main backg ound,
Λ→𝑝𝜋−
, using he missing pe pendicula momen um in he
Λ
di ec ion o ligh s
𝑀(𝑝𝜇)plane.
1
F om now on, when discussing he decay modes such as
Λ→𝑝𝜇−¯
𝜈𝜇
,
Λ→𝑝𝜋 −
, among o he s, we
will always implici ly include he cha ge-conjuga e modes as well.
37
chap e 3. s ange physics a lhcb
VELO
UT
SciFi
Magne
RICH1
RICH2, ECAL, HCAL
M2 M3 M4 M5
z Δ x
x
Figu e 3.3: Simpli ied side iew o he LHCb de ec o and a g aphic ep esen a ion o he
VELO-UT muon ma ching algo i hm. The implied subde ec o s a e highligh ed in blue.
The GPU-based implemen ed echnology o Allen con ibu ed o make possible
he emo al o he ha dwa e igge . This ha dwa e igge , based on selec ing only
high-ene gy pa icles, educed signi ican ly he s ange physics s a is ics du ing Run
2.
As a consequence, Allen’s lexibili y makes possible o de elop di e en s a egies
o igge on s ange pa icles. Fo ins ance, he HLT now enables igge ing based
on displacemen , which is ad an ageous o he s ange physics p og am, as pa icles
wi h lowe mass end o a el u he wi hin he de ec o .
The upda ed econs uc ion sequence deli e s ema kable esul s o he decay
p oduc s o low-momen um signals, pa icula ly o Kaons and o he s ange pa icles.
The o e all e iciency o Fo wa d- acking acks o igina ing om s ange pa icle
decays s ands a 76.5% o ene gies abo e 3 GeV and 81.4% o ene gies abo e 5 GeV.
This ep esen s an imp o emen o mo e han double pe ack compa ed o he HLT1
Fo wa d- acking econs uc ion u ilized in Run 2. Consequen ly, he e is no longe a
equi emen o dis inc econs uc ion p ocesses o low-momen um pa icles a he
HLT1 le el. This no only s eamlines he econs uc ion sequence bu also ensu es
uni o mi y in he HLT1 Fo wa d- acking econs uc ion [60].
44
chap e 4
OBJECTIVES AND
METHODOLOGY
This hesis
has clea goals ha aim o help us lea n mo e abou lep on la ou
uni e sali y. The main goal is o add new knowledge o wha we al eady know
and o check i wha we hink we know is eally ue by ca e ully looking a
he da a and wha i shows us.
4.1 objec i es
The p ima y goal o his hesis is o measu e p ecisely
B(Λ→𝑝𝜇−¯
𝜈𝜇)
, su passing all
exis ing measu emen s o se a new wo ld eco d o p ecision. Since he
Λ→𝑝𝑒−¯
𝜈𝑒
elec on mode has al eady been measu ed e y p ecisely (
B(Λ→𝑝𝑒−¯
𝜈𝑒)=(8.34 ±
0.14) ×10−4
[78]) and he SM gi es us a clean p edic ion o he a io be ween he
muonic and elec on modes, a imp o ed measu emen o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
can
di ec ly ansla es in o a sea ch o BSM dynamics ha can modi y he b anching
ac ion.
As a esul , his measu emen will imply new cons ain s in LFU in
𝑠→𝑢
qua k
ansi ions.
4.2 me hodology
Fi s o all, i is impo an o men ion ha his is no a di ec
B(Λ→𝑝𝜇−¯
𝜈𝜇)
mea-
su emen . The b anching ac ion will be measu ed using
Λ→𝑝𝜋−
as no maliza ion
channel, and inco po a ing B(Λ→𝑝𝜋−) as an inpu .
The unde lying p inciple is o i he amoun o
Λ→𝑝𝜇−¯
𝜈𝜇
and
Λ→𝑝𝜋−
e en s
in he Run 2 LHCb da ase (using TISTISTIS da a) and, di iding hose ex ac ed yields
by he e iciencies compu ed wi h ou MC, ex ac he o al amoun o
Λ→𝑝𝜇−¯
𝜈𝜇
and Λ→𝑝𝜋−gene a ed a LHCb du ing he 2016-2018 pe iod.
45
chap e 4. objec i es and me hodology
Di iding he numbe o
Λ→𝑝𝜋−
by he
B
(
Λ→𝑝𝜋−
) we can compu e he o al
amoun o
Λ
pa icles. A e wa ds, we can di ide his numbe by he o al
Λ→𝑝𝜇−¯
𝜈𝜇
yield o compu e B(Λ→𝑝𝜇−¯
𝜈𝜇).
The no maliza ion i will be pe o med o a double sided c ys al ball + an expo-
nen ial PDF using he M(p
𝜋
) a iable whe e
Λ→𝑝𝜋−
peaks. The c ys al ball ail
pa ame e s will be ex ac ed by i ing he
Λ→𝑝𝜋−
MC. P e iously some cu s will
be in oduced o emo e he 𝐾0
𝑆→𝜋+𝜋−componen .
The signal yield will be de e mined h ough a binned wo-dimensional (2D) i
in a plane ha easonably sepa a es
Λ→𝑝𝜋−
and
Λ→𝑝𝜇−¯
𝜈𝜇
. This i will u ilize
Poisson s a is ics and employ he MC dis ibu ions as empla es. The adop ion o a
2D i aids in managing he challenge posed by low backg ound MC s a is ics.
Va ious sys ema ic unce ain ies will be conside ed and calcula ed. Mos will
pe ain o disc epancies be ween da a and Mon e Ca lo beha io s, wi h he mos
signi ican a ising om he choice o binning scheme and modes in he 2D i .
The
Λ→𝑝𝜇−¯
𝜈𝜇
MC u ilized is gene a ed wi h a speci ic E Gen model o e i y
i s di e en ial decay a e, and bo h
Λ→𝑝𝜇−¯
𝜈𝜇
and
Λ→𝑝𝜋−
MC samples a e
p oduced using LHCb’s ull simula ion, passing h ough all he s eps o he LHCb
da a- low. Minimum Bias (MinBias) MC is employed o de e mine he e iciency and
beha io o Λ→𝑝𝜋− o he no maliza ion channel.
46
chap e 5
ANALYSIS
The
main challenge associa ed o he
B(Λ→𝑝𝜇−¯
𝜈𝜇)
measu emen a LCHb
will be disc imina ing he signal om peaking backg ound, p ima ily om
Λ→𝑝𝜋−
decays, bu also om
𝐾0
𝑆→𝜋+𝜋−
decays. In addi ion, emo ing
he combina o ial backg ound can be challenging due o he p esence o a neu ino
in he
Λ→𝑝𝜇−¯
𝜈𝜇
inal s a e, which esul s in missing momen um ha we ha e o
accoun o .
Only long acks will be used in his analysis. As we a e no domina ed by
s a is ical unce ain ies, he e is no p essing need o include downs eam acks, whose
esolu ion could ad e sely a ec he measu emen . This is because ou kinema ic
s a egies hea ily ely on ha ing a good esolu ion.
To gene a e simula ed e en s ha ep oduce he heo e ical kinema ic dis i-
bu ions, a new E Gen [56] model will be necessa y. The nex s ep will in ol e
s udying he signal p ope ies and compa ing hem wi h hose o he backg ound.
Subsequen ly, we will de elop selec ion c i e ia o e ec i ely sepa a e he signal om
he backg ound and, ul ima ely, ob ain an es ima ed alue o he expec ed yield o
Λ→𝑝𝜇−¯
𝜈𝜇decays a LHCb.
The b anching a io can be exp essed as he numbe o
Λ
decaying o
𝑝𝜇−¯
𝜈𝜇
in
ou da ase o e he o al amoun o Λpa icles in ou da ase :
B(Λ→𝑝𝜇−¯
𝜈𝜇)=𝑁(Λ→𝑝𝜇−¯
𝜈𝜇)
𝑁(Λ)(5.1)
being
𝑁(Λ→𝑝𝜇−¯
𝜈𝜇)=𝑁 eco
𝑝𝜇𝜈
𝜖𝑝𝜇𝜈
(5.2)
whe e
𝑁 eco
𝑝𝜇𝜈
is he numbe o
Λ→𝑝𝜇−¯
𝜈𝜇
e en s econs uc ed and selec ed as signal
and
𝜖𝑝𝜇𝜈
is he e iciency o his p ocess, ex ac ed om Mon e Ca lo (MC) s udies.
Applying Eq. 5.1 and Eq. 5.2 o he Λ→𝑝𝜋−case, is easy o ob ain
47
chap e 5. analysis
B(Λ→𝑝𝜋−)=𝑁 eco
𝑝𝜋
𝜖𝑝𝜋 𝑁(Λ)(5.3)
and combining p e ious equa ions a i e o:
B(Λ→𝑝𝜇−𝜈𝜇)=B(Λ→𝑝𝜋−)𝜖𝑝𝜋
𝜖𝑝𝜇𝜈
𝑁 eco
𝑝𝜇𝜈
𝑁 eco
𝑝𝜋
(5.4)
So, we can de ine an
𝛼
pa ame e ha ela es he
Λ→𝑝𝜇−𝜈
b anching a io and
he numbe o econs uc ed signal e en s 𝑁 eco
𝑝𝜇𝜈 ,
B(Λ→𝑝𝜇−𝜈𝜇)=𝛼𝑁 eco
𝑝𝜇𝜈 (5.5)
being
𝛼=B(Λ→𝑝𝜋−)
𝑁 eco
𝑝𝜋
𝜖𝑝𝜋
𝜖𝑝𝜇𝜈
(5.6)
Once we calcula e he
𝛼
pa ame e , using he PDG alue o he
B
(
Λ→𝑝𝜋−
),
we will be able o ob ain he expec ed yield.
Two S ipping Lines wi h aligned cu s ha e been c ea ed, as will be explained
in he nex sec ion. The i s one is o no maliza ion, whe e we can i he yield o
Λ→𝑝𝜋−decays, while he o he one aims o maximize signal pu i y.
Du ing he Run2, LHCb had 3 igge le els (L
0
, HLT1 and HLT2). As cla i ica ion,
an o line candida e is conside ed o be TIS wi h espec o a igge selec ion i
emo ing i om he e en would s ill cause he igge selec ion o accep he e en .
TISTISTIS means ha he e en is TIS o he L0, he HLT1 and he HLT2 T igge .
Bo h i s will be pe o med o TISTISTIS Da a, o educe sys ema ic unce ain ies
o he minimum.
5.1 analysis s a egy
The
Λ→𝑝𝜇−¯
𝜈𝜇
b anching a io will be ob ained using as inpu he
B(Λ→𝑝𝜋−)
.
Two S ipping Lines ha e been w i en wi h his pu pose, he no maliza ion one
(No mLine) o selec
Λ→𝑝𝜋−
and measu e i s yield and he signal one (SignalLine)
o selec
Λ→𝑝𝜇−¯
𝜈𝜇
and measu e i s yield. Cu s in bo h lines a e aligned o educe
sys ema ic e o s, being he pa icle ID cu s and he mass window he only di e ence
be ween hem.
In addi ion, we ha e a MinBias MC Sample o 2018 MD and 2018 MU, and a
S ipping Fil e ed P oduc ion o bo h
Λ→𝑝𝜋−
and
Λ→𝑝𝜇−¯
𝜈𝜇
channels passing
SignalLine o 2016, 2017 and 2018 wi h Magne Up and Magne Down con igu a ions.
Taking ha in o accoun , he analysis s a egy can be summa ized in he ollowing
s eps:
1.
Add Common Cu s o MC and Da a passing No mLine. The idea is o emo e
he 𝐾0
𝑆→𝜋+𝜋−componen .
48
5.1. analysis s a egy
2.
Fi
Λ→𝑝𝜋−
om MinBias MC passing No mLine, selec ed wi h he TRUE ID
1, o ob ain he ail pa ame e s o he Lppi peak.
3.
Fi TISTISTIS Da a passing No mLine o each yea and pola i y, se ing he ail
pa ame e s ob ained in he TRUE ID MinBiasMC Fi . By doing his, we ob ain
he amoun o
Λ→𝑝𝜋−
in Da a passing he No maliza ion S ippingLine
(𝑁No mLine
Λ→𝑝𝜋 −).
4.
Ob ain he e iciency o he
Λ→𝑝𝜋−
passing No mLine (
𝜖No mLine
Λ→𝑝𝜋 −
). This
will be ob ained by i ing he MinBiasMC passing No mLine se ing he ail
pa ame e s ex ac ed in poin 2 o ob ain he amoun o
Λ→𝑝𝜋−
in ha sample
and di iding his numbe by he o al amoun o Λ→𝑝𝜋−in he MinBiasMC
sample (be o e he econs uc ion and he s ipping).
5.
The amoun o
Λ→𝑝𝜋−
in Da a be o e he s ipping (
𝑁Λ→𝑝𝜋 −
) will be ob-
ained di iding he ou pu o s ep numbe 3,
𝑁No mLine
Λ→𝑝𝜋 −
, by he ou pu o s ep 4,
𝜖No mLine
Λ→𝑝𝜋 −.
𝑁Λ→𝑝𝜋 −=
𝑁No mLine
Λ→𝑝𝜋 −
𝜖No mLine
Λ→𝑝𝜋 −
(5.7)
6.
Nex s ep will be o pe o m a i o measu e he amoun o Signal in TISTISTIS
Da a passing he SignalLine, 𝑁SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇.
7.
Using he
Λ→𝑝𝜇−¯
𝜈𝜇
s ipping il e ed MC p oduc ion we can ob ain he
selec ion e iciency o signal,
𝜖𝑆𝑒𝑙
Λ→𝑝𝜇−¯
𝜈𝜇
. F om he p oduc ion logs we can
also ob ain he e iciency o he signal passing he SignalLine,
𝜖SignalLine
Λ→𝑝𝜇−¯
𝜈𝜇
. The
p oduc o bo h e iciencies is 𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇.
8.
The e iciencies
𝜖SignalLine
Λ→𝑝𝜇−¯
𝜈𝜇
and
𝜖No mLine
Λ→𝑝𝜋 −
a e co ec ed using PidCalib2 and T ack-
Calib2.
9. The inal s ep, will be o ob ain he B(Λ→𝑝𝜇−¯
𝜈𝜇)appliyng he equa ion
B(Λ→𝑝𝜇−¯
𝜈𝜇)=𝑁SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇B(Λ→𝑝𝜋−)
𝑁No mLine
Λ→𝑝𝜋 −
𝜖No mLine
Λ→𝑝𝜋 −
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇
(5.8)
Ob iously, in he p e ious analysis desc ip ion we will be aking in o conside a ion
also he cha ge conjuga ed modes.
Ob iously, ollowing he oo no e 1 p esc ip ion, in he p e ious analysis desc ip-
ion we will be aking in o conside a ion also he cha ge conjuga ed modes.
A diag am o he Analysis wo k low can be ound in Fig. 5.1.
1
The
TRUE ID
a iable p o ides he ID o he pa icle esponsible o p oducing a ack, wi h he ID
numbe ing ollowing he PDG Mon e Ca lo numbe ing scheme [63]. This a iable is exclusi ely de ined in
MC samples, whe e he ue in o ma ion o he e en is accessible.
49
chap e 5. analysis
Figu e 5.1: Analysis wo k low. Blue colo indica es p ocesses ela ed o no malisa ion and
ed ones o he signal measu emen . Black colo is associa ed o MC and yellow o MC
co ec ions. Do ed lines show he sys ema ic unce ain y sou ces.
50
5.2. s ipping lines
5.2 s ipping lines
E en hough in LHCb an e en is only eco ded i i passes a T igge Line, we ha e
a huge amoun o e en s in LHCb Da a. As a consequence, speci ic s ipping lines
(o line selec ion) a e w i en o educe he amoun o e en s, selec ing only hose
ha e i y some cu s.
In gene al, a S ipping Line is designed o selec a ce ain decay channel. In ou
case we designed wo S ipping Lines, one o selec he Signal (
Λ→𝑝𝜇−¯
𝜈𝜇
) and he
o he o selec he no maliza ion channel (Λ→𝑝𝜋−).
F om now on we will call he S ipping Line w i en aiming o selec
Λ→𝑝𝜇−¯
𝜈𝜇
SignalLine and he S ipping Line w i en o selec Λ→𝑝𝜋−No mLine.
Bo h T igge Line Cu s (see Tab. 5.1) a e aligned o educe he sys ema ic e o s
associa ed o he Λ→𝑝𝜇−¯
𝜈𝜇b anching ac ion measu emen as much as possible.
No ice he acciden ally missing cu in he pion Impac Pa ame e . This cu will be
added in No mLine Da a a e he s ipping p ocess o align bo h S ipping Lines.
Table 5.1: This able compa es he cu s applied in he SignalLine and No mLine side-by-side
o each ca ego y. No e ha o he Daugh e Cu s (Muon/Pion), he cu s a e compa ed
be ween he muon in he SignalLine and he pion in he No mLine.
Ca ego y Va iable SignalLine Cu No mLine Cu
Combina ion Cu s DOCA 1[mm] <0.3 <0.3
Mo he Mass [𝑀𝑒𝑉 /𝑐2]<1141 <1141
Mo he Cu s
𝜏[ps] >9>9
Mo he Mass [𝑀𝑒𝑉 /𝑐2]<1141 <1141
𝑉𝜒22<9<9
𝜒2dis ance o PV >50 >50
IP 3[mm] >0.2 >0.2
P o on Cu s
P o on P obNN >0.3 >0.3
Muon P obNN <0.7 <0.7
Kaon P obNN <0.7 <0.7
Ghos P obNN <0.2 <0.2
𝐼𝑃𝜒2>16 >16
T ack 𝜒2/d.o. . <3<3
Muon/Pion Cu s
Pion P obNN <0.7 >0.4
Muon P obNN >0.3 <0.7
Kaon P obNN <0.7 <0.7
Ghos P obNN <0.2 <0.2
ISMUON TRUE FALSE
IP >1×Missing
𝐼𝑃𝜒2>60 >60
T ack 𝜒2/d.o. . <3<3
51
chap e 5. analysis
5.2.1 de ini ion o s ipping a iables
5.2.1.1 p obnn
This a iables, used o pa icle iden i ica ion, a e de i ed om Neu al Ne wo ks
(NNs). To ob ain hese a iables, da a om a ious subde ec o s a e u ilized, aking
hei co ela ions in o accoun . The objec i e is o de e mine a alue ha co ela es
wi h he p obabili y o each ack being p oduced by a speci ic ype o pa icle.
5.2.2 ismuon
The p ocess o spo muons begins by linking he hi s in he muon de ec o s wi h each
ack. This in ol es ex ending he acks in a s aigh line owa ds he de ec o s. An
a ea called he Field o In e es (FoI) is hen es ablished a ound he p ojec ed spo . The
size o his a ea a ies based on he ack’s momen um, he speci ic muon chambe ,
and i s loca ion. Wi hin hese FoIs, he sea ch o de ec ions occu s, wi h he numbe
o de ec o s in ol ed depending on he ack’s momen um.
The nea es hi s a e selec ed o u he conside a ion, and only acks wi h
hese con i med hi s go on o he subsequen s eps in he iden i ica ion p ocess. The
ini ial ou come o his me hod is a simple yes-o -no indica o , known in he LHCb
communi y as IsMuon which signi ies he mos elemen a y le el o iden i ying a
muon.
5.2.2.1 doca
The Dis ance O Closes App oach (DOCA) o he wo daugh e s. This ep esen s he
minimal leng h ha sepa a es wo acks.
5.2.2.2 ip
The impac pa ame e is he pe pendicula dis ance be ween he ajec o y o a
pa icle and he e ex om which i o igina es o a which i decays.
5.2.2.3 ip𝜒2
The impac pa ame e signi icance in uni s o 𝜒2.
5.2.2.4 𝜒2dis ance o p
This a iable is ela ed o he mo he pa icle dis ance o ligh , since includes he
di e ence be ween he p ima y and seconda y e ices.
1Dis ance O Closes App oach.
2Ve ex 𝜒2/d.o. .
3Impac Pa ame e .
52
5.2. s ipping lines
5.2.2.5 𝜏
Measu ed li e ime o he mo he pa icle.
5.2.2.6 𝜒2
The e ex
𝜒2
e lec s he quali y o i o he es ima ed posi ion o he decay e ex.
53
chap e 5. analysis
5.4 backg ound sou ces
Ha ing he MinBias MC passing he SignalLine sample p o ides us wi h an o e iew
o wha we can expec o obse e in he Da a.
Al hough he a e age con ibu ion o each decay in he MC may no be en i ely
eliable, s udying i se es as a help ul exe cise and can p o ide a ough es ima e. Fo
ins ance, i is c ucial o no e ha e en ha ing a SignalLine wi h igh cu s designed
o selec Λ→𝑝𝜇−¯
𝜈𝜇, he signal pu i y in his MinBias MC sample is only 3.48 %.
The e o e, i is necessa y o analyze he composi ion o he MinBias MC sample
ha passes he SignalLine. This analysis was conduc ed by applying he co espon-
den u h-ma ching condi ions o each channel, ha a e de ailed in he appendices
A.3. Resul s can be ound in Tab 5.9. An addi ional check was pe o med o en-
su e he absence o peaking backg ounds by eplacing he mass hypo hesis o he
combina o ial backg ound e en s (see Appendix A.6)
Table 5.9: A e age con ibu ion o each decay channel o he MinBias MC sample a e
he S ipping p ocess in SignalLine. In he non-ob ious cases, econs uc ed pa icles a e
w i en in bold symbols. A s udy o he a e age con ibu ion a e applying igh e PID
cu s was pe o med, and he esul s can be seen in Appendix A.5.
Decay Con ibu ion
Λ→𝑝𝜋−(42.7 ±1.5) %
Combina o ial Backg ound and O he s (35.4 ±1.4) %
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)(14.7 ±1.1) %
Λ→𝑝𝜇−¯
𝜈𝜇(3.48 ±0.56) %
𝐾0
𝑆→𝜋+𝜋−(2.20 ±0.44) %
Ξ−→ (Λ→𝒑𝜋−)𝝅+(1.28 ±0.34) %
Ξ−→ (Λ→𝒑𝜋−)(𝜋+→𝝁¯
𝜈𝜇)(0.275 ±0.16) %
Taking his esul s in o accoun is ob ious ha Misiden i ied
Λ→𝑝𝜋−
and
ea ly Decays In Fligh (eDIF) a e he main backg ounds in his analysis, wi h a o al
expec ed con ibu ion close o 60 %o he SignalLine sample.
The ea ly decays in ligh (Fig. 5.3), wi h he pion decaying ea ly o a muon and a
neu ino, may be eally ha d o sepa a e om signal, since we ha e he same inal
s a e in bo h channels wi h almos indis inguishable kinema ic p ope ies.
The good news is ha we ha e a dedica ed LHCb p oduc ion o simula e
Λ→𝑝𝜋−
passing SignalLine, which will be c ucial o unde s and how o selec he signal and
how o disc imina e hese backg ound sou ces.
On he o he hand,
𝐾0
𝑆→𝜋+𝜋−
is an easie backg ound o kill, since we can
design a speci ic cu in he A men e os-Podolanski plo o kill mos o he
𝐾0
𝑆→𝜋+𝜋−
p ese ing almos all he signal.
60
5.4. backg ound sou ces
Figu e 5.3: A ep esen a ion o an ea ly decay in ligh (eDIF).
5.4.1 misiden i ied Λ→𝑝𝜋−
This decay, wi h a pion misiden i ied as muon, is he main backg ound con ibu ion
o he MinBias MC SignalLine sample. E en hough ha ing c ea ed he SignalLine
s ipping line speci ically o educe his con ibu ion, he di e ence in he b anching
a ios o
Λ→𝑝𝜋−
and
Λ→𝑝𝜇−¯
𝜈𝜇
is so la ge ha we s ill a e domina ed by
Λ→𝑝𝜋−
.
Despi e ha , i should be ela e ely easy o design some selec ion cu s o emo e
mos o MisID
Λ→𝑝𝜋−
. The A men e os-Podolanski plo [66] should also be a good
plane o impose selec ion equi emen s [42].
The A men e os-Podolanski plo has as Y-axis he QPT a iable, he ans e se
momen um o any o he daugh e s wi h espec o he mo he di ec ion o ligh
(in a 2-body decay bo h mus be equal) and as X-axis he longi udinal momen um
asymme y,
𝛼=𝑝+
𝐿−𝑝−
𝐿
𝑝+
𝐿+𝑝−
𝐿
(5.15)
whe e
𝑝+
𝐿
and
𝑝−
𝐿
a e
𝑝+𝑐𝑜𝑠(𝜃1)
and
𝑝−𝑐𝑜𝑠(𝜃2)
espec i ely, supposing ha he pa icle
1 is he posi i e in Fig. 5.4. The mo he di ec ion o ligh can be ob ained om he
p ima y and second e ex posi ions.
Signal and
Λ→𝑝𝜋−
MC beha iou in he A men e os-Podolanski plo can be
ound in Fig. 5.5.
In P ospec s o measu emen s wi h s ange had ons a LHCb [10] ano he wo
dimensional plane was sugges ed o sepa a e
Λ→𝑝𝜋−
and
Λ→𝑝𝜇−¯
𝜈𝜇
. This wo
dimensional plane has as x-axis he missing ans e se momen um in he plane ha
is pe pendicula o he he mo he pa icle di ec ion o ly (
/
𝑝𝑇
2
), and as y-axis he
𝑀(𝑝𝜇)
( econs uc ed mass wi h he p o on-muon hypo hesis). Fig. 5.6 shows he
ull-simula ed beha iou in he plane.
2
This a iable ep esen s he missing ans e se momen um in he plane ha is pe pendicula o
he he mo he pa icle di ec ion o ly, calcula ed using econs uc ed in o ma ion. Fo a mo e de ailed
explana ion, see subsec ion 5.5.1.1.
61
chap e 5. analysis
Figu e 5.4: 2-Body decay scheme in he labo a o y ame o e e ence.
Figu e 5.5: A men e os-Podolanski plo o SignalMC and
Λ→𝑝𝜋 −
MC passing Sig-
nalLine.
Some conclusions can be ex ac ed om Fig. 5.5 and Fig. 5.6. Fo example, i
we compa e he Λ→𝑝𝜋−MC passing he SignalLine beha iou in he A men e os-
Podolanki plo wi h a ypical
Λ→𝑝𝜋−
domina ed A men e os-Podolanki plo , as
he one in Fig. 5.7, we ind ele an di e ences.
Fo example, in Fig. 5.5, e en ha ing he usual
Λ→𝑝𝜋−
ellipse isible, he
misiden i ied
Λ→𝑝𝜋−
passing No mLine p esen s a highly popula ed egion unde
he ellipse. This is because i he pion decays o a muon and a neu ino a enough
om he p ima y e ex i will be econs uc ed as pion, bu he econs uc ed pa icle
will ha e less momen um han he o iginal pion, since he missing momen um is
ca ied by he neu ino.
On ano he hand, i d aws a en ion an emp y space unde an ellipse cen e ed
in
𝛼≈
0.82 wi h i s maximum QPT alue in QPT
≈
60
𝑀𝑒𝑉 /𝑐
. An ellipse in he
A men e os-Podolanksi plo is equi alen o a speci ic mo he mass. Taking his in o
accoun , he ac o no ha ing misiden i ied
Λ→𝑝𝜋−
decays alling below his
62
5.4. backg ound sou ces
Figu e 5.6: Missing momen um in he plane ans e se o he
Λ
ligh di ec ion (
/
𝑝𝑇
) s.
econs uc ed mass M(𝑝𝜇) o Λ→𝑝𝜇−¯
𝜈𝜇in blue and misiden i ied Λ→𝑝𝜋 −in ed.
Figu e 5.7: A men e os-Podolanski plo o a 10000 en ies subsample o he MinBiasMC
passing No mLine, whe e he Λ→𝑝𝜋−ellipse is ema kable.
elipse indica es ha he e is a minimum mass ha can be econs uc ed wi h a p o on
and muon, whe e he muon comes om an o iginal pion om he
Λ→𝑝𝜋−
decay. I
is also ema kable ha his does no happen in he Λ→𝑝𝜇−¯
𝜈𝜇case.
I his explana ion is ue, we should see he e ec in he M(p
𝜇
) dis ibu ion o
he
Λ→𝑝𝜋−
passing SignalLine. The esul an no malised his og ams a e in Fig. 5.8,
e i ying ou deduc ion.
63
chap e 5. analysis
1040 1060 1080 1100 1120 1140
M
(
p
)
MeV
/
c
2
0.000
0.005
0.010
0.015
0.020
0.025
0.030 Signal MC
MisID
p
MC
Figu e 5.8: No m. M(p𝜇) dis ibu ion o Λ→𝑝𝜇−¯
𝜈𝜇in blue and MisID Λ→𝑝𝜋 −in ed.
As a c oss-check, Fig. 5.9 displays hose e en s wi h low
𝑀(𝑝, 𝜇)
, se ing as a
epe i ion o Fig. 5.5 and con i ming he in e p e a ion.
Figu e 5.9: A men e os-Podolanski plo o
Λ→𝑝𝜋 −
MC passing SignalLine, showing in
blue hose e en s wi h
𝑀(𝑝, 𝜇)<1070
Me /
𝑐2
and in black hose wi h
𝑀(𝑝, 𝜇)<1060
Me /𝑐2.
Conce ning he
/
𝑝𝑇
s. M(
𝑝𝜇
) plane (Fig. 5.5), we can also ex ac some conclusions
om he 2-dimensional dis ibu ions. Fo example he highe minimum mass in he
Λ→𝑝𝜋−
is e iden he e. Bu he e is also a di e en co ela ion be ween he
/
𝑝𝑇
and
he M(
𝑝𝜇
) in bo h cases. This would allow o a possible selec ion cu in his plane o
selec a egion wi h high signal pu i y.
64
5.4. backg ound sou ces
5.4.2 ea ly decays in ligh (Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇))
I in a
Λ→𝑝𝜋−
decay he pion decays o a muon and a neu ino close enough o he
seconda y e ex, mo e han he 70 % o he ack hi s will be om he muon, and he
ack will be co ec ly ma ched o a muon. This ca ego y p esen some cha ac e is ic
ea u es, making i ha de o dis inguish om he signal.
1080 1090 1100 1110 1120 1130 1140 1150 1160
M
(
p
)
MeV
/
c
2
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08 MisID
p
MC
eDIF
p
( ) MC
Figu e 5.10: No malised M(p
𝜋
) dis ibu ion o eDIF in g een and MisID
Λ→𝑝𝜋 −
in ed.
Fo ins ance, he eDIF ca ego y M(p
𝜋
) dis ibu ion does no peak clea ly in he
Λ
mass, whe eas he MisID
Λ→𝑝𝜋−
p esen s a na ow peak cen e ed in he
Λ
mass
(see Fig. 5.10).
As we can see in Fig. 5.11, he z-componen o he muon o igin e ex has a
maximum alue a ound 650 mm in he MisID
Λ→𝑝𝜋−
, whe eas he eDIF ca ego y
p esen s highe z- alues o he muon o igin e ices. So i he pion decays o a muon
a e his maximum alue, which implies ew VELO hi s, i will ne e be econs uc ed
as a pion.
Being he
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)
decays he ha des o sepa a e om signal, ha ing
he same inal s a e and simila kinema ic p ope ies, we ha e designed some a iables
ha will help in his ask. Those a iables a e p esen ed in Sec ion 5.5.1.
5.4.3 𝐾0
𝑆→𝜋+𝜋−
Ano he p oblema ic backg ound sou ce is 𝐾0
𝑆→𝜋+𝜋−wi h one pion misiden i ied
as a p o on an he o he as muon o decaying in ligh o a muon and a neu ino.
This is he only peaking backg ound an icipa ed o con ibu e o SignalLine e en s,
excluding
Λ→𝑝𝜋−
. Ha ing mul iple peaking modes complica es he i ing o he
signal yield. Hence, i ’s c ucial o elimina e i . Addi ionally, his decay channel also
con amina es he No maliza ion sample.
E en being a channel e y di e en om signal, he
𝐾0
𝑆→𝜋+𝜋−
p oduc ion yield
is so high in LHCb ha i s con ibu ion o he SignalLine is ele an (see Tab. 5.9).
65
chap e 5. analysis
0 2000 4000 6000 8000 10000
T ue Muon O igin Ve ex Z [mm]
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030 MisID
p
MC
0 2000 4000 6000 8000 10000
T ue Muon O igin Ve ex Z [mm]
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
eDIF p
( ) MC
Figu e 5.11: No malised dis ibu ion o he ue o igin e ex z-componen o he pa icle
econs uc ed as a muon o MisID
Λ→𝑝𝜋 −
(le ) and o eDIF ( igh ). No ice ha he
O igin Ve ex Z e e s o a di e en e ex o each channel. In he MisID Λ→𝑝𝜋 −case,
whe e he pa icle econs uc ed as a muon is ac ually a pion, i s ue o igin e ex is he
Λ
decay e ex, whe eas in he eDIF case, he ue muon o igin e ex is he pion decay
e ex.
The good news a e ha he
𝐾0
𝑆→𝜋+𝜋−
alls inside a speci ic egion in he
A men e os-Podolanksi plo . In gene al,
𝐾0
𝑆→𝜋+𝜋−
decays should co espond o
a na ow elipse in his plane. See o example Fig. 5.12, whe e we a e selec ing
𝐾0
𝑆→𝜋+𝜋−
om he MinBias MC sample passing No mLine and he
𝐾0
𝑆→𝜋+𝜋−
ellipse is clea ly isible.
On he o he hand, he
𝐾0
𝑆→𝜋+𝜋−
MC in he SignalLine is also, as i happens
wi h he
Λ→𝑝𝜋−
channel, blu ed a ound he usual
𝐾0
𝑆→𝜋+𝜋−
ellipse, because
o he missing momen um when he pion decays o a muon and a neu ino. The
co esponden A men e os-Podolanksi plo is depic ed in Fig. 5.13.
0.5 0.6 0.7 0.8 0.9
0
20
40
60
80
100
120
140
QPT
[
MeV
/
c
]
K
0
S
+ MC No mLine
Figu e 5.12: A men e os-Podolanski plo o
𝐾0
𝑆→𝜋+𝜋−
om he MinBias MC sample
passing No mLine, whe e he ypical 𝐾0
𝑆→𝜋+𝜋−ellipse is ema kable.
66
5.4. backg ound sou ces
Figu e 5.13: A men e os-Podolanski plo o 𝐾0
𝑆→𝜋+𝜋−MC passing SignalLine.
E en being less concen a ed a ound he usual
𝐾0
𝑆→𝜋+𝜋−
ellipse, i is easy o
c ea e a selec ion cu o emo e his backg ound. This will be explained in de ail in
he Selec ion sec ion 5.5.
67
chap e 5. analysis
5.5 selec ion and new a iables
5.5.1 a iables
Ha ing backg ound sou ces almos iden ical o ou signal, he de elopmen o new
a iables was manda o y o be able o sepa a e bo h. The idea is o use he kine-
ma ic p ope ies o each decay channel o design speci ic a iables ha allow us o
dis inguish ha channel. Being he
Λ→𝑝𝜇−¯
𝜈𝜇
case he mos p oblema ic o us,
we s a ed by sepa a ing hose decays in o wo ca ego ies. I he pion decays ea ly
enough, we will ha e a muon in he e ex loca o . I he pion decays in o a muon
and a neu ino a e passing he VELO, hen we will obse e a pion a he VELO
le el. Those wo ca ego ies and he s a egies o eco e he missing in o ma ion
a e de ailed in Fig. 5.14. I is impo an o no e ha hese new a iables a e only
compu ed o he SignalLine e en s, as hey a e no equi ed o he no maliza ion
p ocess.
Figu e 5.14: In he muon a VELO le el case, he neu ino
𝑃𝑇
can be ob ained om p o on
and muon momen um componen s and he neu ino
𝑃𝐿
by impossing
Λ
mass. In he pion
a VELO le el case, i he measu ed
|®
𝑝𝜋|
is no he co ec one,
Λ
will no poin o he
p ima y e ex. Imposing Λ o poin o PV allows o sol e o |®
𝑝𝜋|.
5.5.1.1 missing pe pendicula momen um (/
𝒑𝑻)
In he muon a VELO le el, when he pion decays o a muon and a neu ino wi hin he
Ve ex Loca o , he neu ino
𝑃𝑇
can be ob ained om p o on and muon momen um
componen s.
This can be done using he
Λ
ligh di ec ion
−−−−−−−−−→
(𝑆𝑉 −𝑃𝑉 )
and using he G am-
Schmid idea [70] o ind wo o hogonal ec o s o ha ligh di ec ion. Fi s we
should ob ain he ligh di ec ion ec o (
−→
𝑓
) using he P ima y Ve ex and he
Λ
Decay
Ve ex, and hen compu e he co esponden uni ec o , di iding each componen by
|−→
𝑓|.
I he mo he ligh di ec ion uni ec o is called
ˆ
𝑓
, he i s pe pendicula uni
ec o will be ob ained by cons uc ing a ec o
𝑥𝑢=(− ˆ
𝑓𝑦,−ˆ
𝑓𝑥,0)
and hen ob aining
a co esponden uni ec o
ˆ
𝑥𝑢
. Finally, he second uni pe pendicula momen um
will be he c oss p oduc ˆ
𝑦𝑢=ˆ
𝑓׈
𝑥𝑢.
68
5.5. selec ion and new a iables
Ha ing his o hogonal base allows us o ob ain he missing pe pendicula mo-
men um in he mo he ligh di ec ion. Fo example, we can add he wo daugh e s
momen um o ob ain he −−→
𝑝𝑝𝜇 and hen p ojec i s componen s o he new base:
−−→
𝑝𝑝𝜇′=(−−→
𝑝𝑝𝜇 .ˆ
𝑥𝑢,−−→
𝑝𝑝𝜇 .ˆ
𝑦𝑢,−−→
𝑝𝑝𝜇 .ˆ
𝑓)=(𝑝′
𝑝𝜇𝑥, 𝑝′
𝑝𝜇𝑦, 𝑝′
𝑝𝜇𝑧)(5.16)
Taking his in o accoun , he missing pe pendicula momen um in he mo he
ligh di ec ion will be
/
𝑝𝑇=√︃𝑝′2
𝑝𝜇𝑥+𝑝′2
𝑝𝜇𝑦(5.17)
5.5.1.2 longi udinal neu ino momen um (/
𝒑𝑻)
In he muon a VELO le el case, he neu ino
𝑃𝑇
can be ob ained om p o on and
muon momen um componen s and he neu ino 𝑃𝐿by impossing Λmass.
We can s a by ob aining he pe pendicula componen s o he neu ino momen-
um as i was explained in p e ious subsec ion. A e ha he e will be only one
piece missing, he longi udinal componen o he neu ino momen um, ha can be
ob ained imposing he Λmass.
𝑀2
Λ=(𝐸𝑝𝜇 +𝐸𝜈)2− |−−→
𝑝𝑝𝜇 +−→
𝑝𝜈|2=𝑀2
𝑝𝜇 +0+2.(𝐸𝑝𝜇 .𝐸𝜈−−−→
𝑝𝑝𝜇 .−→
𝑝𝜈)(5.18)
whe e
𝐸𝑝𝜇 =√︃𝑀2
𝑝𝜇 + |−−→
𝑝𝑝𝜇′|2(5.19)
and
𝐸𝜈=√︃/
𝑝2
𝑇+𝑝𝐿(𝜈𝜇)2(5.20)
Taking in o accoun ha
−−→
𝑝𝑝𝜇 .−→
𝑝𝜈=−/
𝑝2
𝑇+𝑝′
𝑝𝜇𝑧.𝑝𝐿(𝜈𝜇)(5.21)
we inally ob ain he exp ession o compu e he 𝑝𝐿(𝜈𝜇):
𝑝𝐿(𝜈𝜇)=
𝐸𝑝𝜇 .√︃𝐴2−2𝐴./
𝑝2
𝑇+/
𝑝2
𝑇.𝑝′2
𝑝𝜇𝑧+/
𝑝4
𝑇−/
𝑝2
𝑇.𝐸2
𝑝𝜇 −𝐴.𝑝′
𝑝𝜇𝑧+𝑝′
𝑝𝜇𝑧./
𝑝2
𝑇
(𝑝′
𝑝𝜇𝑧)2−𝐸2
𝑝𝜇
(5.22)
whe e
𝐴=𝑀2
Λ−𝑀2
𝑝𝜇
2(5.23)
69
chap e 5. analysis
Table 5.11: Sel1 e iciencies o Signal, Lppi and eDIF MC.
Sel1 E iciency
Signal MC 𝜖Sel1
Λ→𝑝𝜇−¯
𝜈𝜇0.63656 ±0.00065
Lppi MC 𝜖Sel1
Λ→𝑝𝜋 −0.3175 ±0.0060
eDIF MC 𝜖Sel1
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)0.325 ±0.011
5.5.2.3 selec ion 2 (a men e os-podolanski plo )
As men ioned ea lie , he A men e os-Podolanski plo can be use ul in enhancing
signal pu i y. In Fig. 5.23, possible selec ion cu s in his plane a e shown. The cen al
ellipse ep esen s he egion wi h highe signal densi y, while he egion below he
ellipse on he igh co esponds o he a ea wi h highe expec ed signal pu i y in he
da a.
Bo h cu s can be applied oge he o sepa a ely. Howe e , selec ing only e en s
unde he ellipse on he igh poses a challenge as we would ha e insu icien back-
g ound Mon e Ca lo (MC) s a is ics passing his cu . On he o he hand, choosing
o selec only e en s inside he cen al ellipse would esul in a loss o some signal
wi hou a subs an ial jus i ica ion.
The e o e, i appea s mo e a o able o selec e en s inside he yellow ellipse o
below he g een cu e in Fig. 5.23. This cu will be named Sel2.
Figu e 5.23: A men e os-Podolanski plane o Da a (le ) and MC ( igh ) wi h posi i e
𝑃𝐿(𝜈𝜇). Dashed lines ep esen possible selec ion cu s.
I is also ema kable ha he equi emen o a posi i e
𝑃𝐿(𝜈𝜇)
is an excep ionally
e ec i e cu o emo ing
𝐾0
𝑆→𝜋+𝜋−
backg ound. Ini ially, ou app oach in ol ed
applying a cu in he A men e os-Podolanski plo o elimina e his backg ound con i-
bu ion. Howe e , we ound ha he emo al powe o bo h selec ions was compa able,
wi h he posi i e longi udinal neu ino momen um equi emen o e ing he ad an-
age o p ese ing a la ge numbe o signal, Lppi, and eDIF decays. Bo h s a egies
76
5.5. selec ion and new a iables
Table 5.12: Sel2 e iciencies o Signal, Lppi and eDIF MC.
Sel2 E iciency
Signal MC 𝜖Sel2
Λ→𝑝𝜇−¯
𝜈𝜇0.54024 ±0.00065
Lppi MC 𝜖Sel2
Λ→𝑝𝜋 −0.3537 ±0.0061
eDIF MC 𝜖Sel2
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)0.3713 ±0.011
a e ep esen ed in Fig. 5.24. So, in summa y, we a e applying he Sel1 + Sel2 selec ion,
and he e is no need o any addi ional cu in he A men e os-Podolanski plo .
Figu e 5.24: A men e os-Podolanski plane o Da a and
𝐾0
𝑆→𝜋+𝜋−
MC p e iously o
any selec ion (le ) and equi ing posi i e
𝑃𝐿(𝜈𝜇)
( igh ). Solid and dashed lines ep esen
possible selec ion cu s.
5.5.2.4 signal selec ion summa y
In summa y, ou selec ion s a egy ocused on emo ing combina o ial backg ound
and
𝐾0
𝑆→𝜋+𝜋−
while p ese ing a subs an ial numbe o
Λ→𝑝𝜋−
decays and ea ly
decays in ligh o he pu pose o pe o ming a i .
The equi emen o
𝑃𝐿(𝜈𝜇)>0
, implici in Sel1, e ec i ely add essed mos o ou
conce ns. Bo h Sel1 and Sel2 cu s p o ed o be use ul in enhancing signal pu i y and
p e en ing any po en ially ha m ul backg ound om en e ing he selec ion.
An addi ional equi emen o
𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋)<
1160 and
𝑀(𝑝𝜋)<
1120 was applied.
Taking in o accoun ha :
77
chap e 5. analysis
Sel1 =/
𝑝𝑇>16&𝑀(𝑝, 𝜇)<(1116.3−1.03/
𝑝𝑇)
&𝑀(𝑝, 𝜇)>(1122.683 −2/
𝑝𝑇)
Sel2A =𝑄𝑃𝑇 <(√︄0.182−𝛼−0.7
0.52
×128 +60)
&𝑄𝑃𝑇 >(−√︄0.182−𝛼−0.7
0.52
×128 +60)
Sel2B = (𝑄𝑃𝑇 <((40 +√︃502−4× (252−372× (1− (𝛼−0.79)2
0.0852)))/2))
Sel2 = (Sel2A |Sel2B)
The inal selec ion applied is as ollows:
Sel = Sel1 &Sel2 &𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋)<1160 &𝑀(𝑝, 𝜋)<1120
The Selec ion E iciency o Signal o each yea and pola i y can be ound in Tab.
5.13.
Table 5.13: 𝜖Selec ion
Λ→𝑝𝜇−𝜈𝜇 o each yea and pola i y.
Magne Down Magne Up
𝜖Selec ion
Λ→𝑝𝜇−𝜈𝜇2018 0.3011 ±0.0015 0.3011 ±0.0015
𝜖Selec ion
Λ→𝑝𝜇−𝜈𝜇2017 0.3004 ±0.0015 0.3016 ±0.0015
𝜖Selec ion
Λ→𝑝𝜇−𝜈𝜇2016 0.3033 ±0.0015 0.2989 ±0.0015
Wi h his selec ion he signal pu i y in he MinBias MC passing SignalLine in-
c eases om 3.48 % o 9.82 %, wi h he addi ional ad an age o he s ong combina o ial
backg ound supp ession.
78
5.5. selec ion and new a iables
5.5.3 no malisa ion selec ion
The ini ial idea was o ha e wo s ipping lines wi h aligned cu s, excluding pa icle
iden i ica ion ones. Bu one o he cu s, he muon impac pa ame e equi ed in he
SignalLine, was no included in he No mLine, so he i s cu o add was o equi e
an impac pa ame e o he pion g ea e han one (𝜋𝐼𝑃 >1 mm).
Besides ha , ano he cu was designed o emo e he
𝐾0
𝑆→𝜋+𝜋−
componen ha
pollu es he No mLine Da a sample. This can easily be obse ed in he A men e os-
Podolanski plo (Fig. 5.25).
0.4 0.5 0.6 0.7 0.8 0.9
0
20
40
60
80
100
120
140
160
QPT [MeV/c]
KspipiMC No mLine
Figu e 5.25: A men e os-Podolanski plo o
𝐾0
𝑆→𝜋+𝜋−
MC passing No mLine (le )
and Da a passing No mLine ( igh ).
The cu is excluding e en s alling inside he egion bounded by he ed lines and
can be applied imposing (Cu 1 |Cu 2), whe e hese cu s a e:
Cu 1 :𝑄𝑃𝑇 >©«25.2+√︄(25.2)2−4.252−2002.1−𝛼2
0.8152ª®¬/2(5.25)
Cu 2 :𝑄𝑃𝑇 <©«25.2+√︄(25.2)2−4.252−1302.1−𝛼2
0.8152ª®¬/2(5.26)
The cu o kill he
𝐾0
𝑆→𝜋+𝜋−
componen was designed by s udying di e en
simula ion samples passing he No mLine.
This 𝐾0
𝑆→𝜋+𝜋−beha iou can be obse ed in Fig. 5.25.
79
chap e 5. analysis
5.6 no malisa ion
5.6.1 i minbias mc Λ→𝑝𝜋−peak
Ou i s s ep o i he No mLine
𝑀(𝑝𝜋)
is o ob ain he ail pa ame e s o he
Λ→𝑝𝜋−peak.
To ob ain hese pa ame e s, we should i a pu e sample o
Λ→𝑝𝜋−
MC passing
he No mLine. The sample is selec ed by applying o he MinBias MC ha passes he
No mLine u h-ma ching condi ions, which a e equi alen o hose used o selec ing
Λ→𝑝𝜋−
MC passing he SignalLine. The explici equi emen s can be ound in he
appendices, A.4.
The
𝑀(𝑝𝜋)
dis ibu ion was i ed o a double sided C ys al Ball pd , as can be
seen in Fig. 5.26.
0
500
1000
1500
2000
2500
3000
3500
4000 CB pd
LppiMC MD
M(p, ) [
MeV
/
c
2]
5
0
5
Pulls
0
500
1000
1500
2000
2500
3000
3500
4000 CB pd
LppiMC MU
M(p, ) [
MeV
/
c
2]
5
0
5
Pulls
Figu e 5.26:
𝑀(𝑝𝜋 )
i o he pu e
Λ→𝑝𝜋 −
MC passing No mLine. Magne Down (MD)
is depic ed on he le and Magne Up (MU) on he igh .
𝜒2
/ndo is 1.52 o MU and 1.16
o MD.
The double sided C ys al Ball ail pa ame e s ex ac ed om he i a e in able
5.14. These wo i s we e pe o med using z i .
Table 5.14: Tail pa ame e s o he double sided c ys al ball ha i s he
𝑀(𝑝𝜋 )
o he pu e
Λ→𝑝𝜋 −
MC passing No mLine.
Λ→𝑝𝜋 −
decays we e selec ed om a MinBias MC
LHCb p oduc ion o 2018MU and 2018MD.
𝛼𝐿𝛼𝑅𝑛𝐿𝑛𝑅
2018MU 1.046 ±0.027 1.025 ±0.026 3.43 ±0.14 3.30 ±0.13
2018MD 1.085 ±0.026 1.012 ±0.024 3.21 ±0.12 3.39 ±0.13
80
5.6. no malisa ion
5.6.2 i da a no mline
Ha ing he ail pa ame e s, we can pe o m a i o he Da a in No mLine. The
combina o ial backg ound can be pa ame e ized wi h an exponen ial unc ion and
he
Λ→𝑝𝜋−
componen wi h a double sided c ys al ball, whe e we se he ail
pa ame e s ob ained by i ing he pu e
Λ→𝑝𝜋−
MC No mLine sample in p e ious
subsec ion.
This p ocess should be epea ed o all yea s and pola i ies o measu e he o al
amoun o Λ→𝑝𝜋−in No mLine ( 𝑁No mLine
Λ→𝑝𝜋 −).
Fig. 5.27 shows he i esul o 2018MU and 2018MD, applying Common Cu s o
No mLine Da a. Only
𝛼𝐿
,
𝛼𝑅
,
𝑛𝐿
and
𝑛𝑅
we e se , whe eas we le he wid h and he
cen e o he double sided C ys al Ball and he exponen ial pa ame e o loa .
The i p ocess was epea ed o all yea s and pola i ies, and he numbe o
Λ→𝑝𝜋−decays measu ed in each case a e shown in Tab. 5.15.
0
5000
10000
15000
20000
25000
30000 o al
backg ound
Lppi
Da a
M(p, ) [MeV/
c
2]
5
0
5
Pulls
0
5000
10000
15000
20000 o al
backg ound
Lppi
Da a
M(p, ) [MeV/
c
2]
5
0
5
Pulls
Figu e 5.27:
𝑀(𝑝𝜋 )
i o he
Λ→𝑝𝜋 −
yield in Da a passing No mLine. Magne Up is
depic ed on he le and Magne Down on he igh .
𝜒2
/ndo is 2.54 o MU and 2.33 o
MD.
Table 5.15: Numbe o
Λ→𝑝𝜋 −
decays in No mLine Da a o each yea and pola i y.
𝑁No mLine
Λ→𝑝𝜋 −
was ex ac ed om he i o No mLine
𝑀(𝑝𝜋 )
wi h common cu s o an expo-
nen ial + a double sided C ys al Ball whe e he ail pa ame e s ha e been se o ma ch he
TRUE ID ones.
Magne Down Magne Up
2018 16080300 ±4900 17254500 ±5100
2017 14454500 ±4700 13933100 ±4600
2016 16527000 ±4900 14902400 ±4700
81
chap e 5. analysis
5.6.3 Λ→𝑝𝜋−e iciency passing no mline
Ou nex goal is o know how many
Λ→𝑝𝜋−
decays we ha e be o e he s ipping
p ocess. This can be compu ed once we ob ain he a e age o he
Λ→𝑝𝜋−
e en s
ha a e econs uc ed and pass he No mLine (𝜖No mLine
Λ→𝑝𝜋 −).
The e iciency can be compu ed pe o ming a i o he MinBias MC sample ha
passes he No mLine o a double sided C ys al Ball + a exponen ial, whe e we also
se he ail pa ame e s ob ained in he Fig. 5.14. Di iding he numbe o
Λ→𝑝𝜋−
e en s measu ed wi h he i in he MinBias MC No mLine sample by he o iginal
amoun o Λ→𝑝𝜋−in he sample be o e any econs uc ion o s ipping.
The o iginal amoun o
Λ→𝑝𝜋−
in he sample be o e any econs uc ion o
s ipping o each yea and pola i y can be ound in Tab. 5.16. These alues a e he
numbe o en ies in he MCDecayT ee, gene a ed in he same uple p ocessing ha
c ea ed he MinBias MC No mLine samples o ensu e ha we a e always compa ing
he same o iginal sample.
The i esul s o he MinBias MC sample passing No mLine can be ound in Fig.
5.28 and Tab. 5.17.
Table 5.16: Numbe o
Λ→𝑝𝜋 −
decays be o e he econs uc ion and s ipping p ocess
o each yea and pola i y in he MinBias MC sample.
Magne Down Magne Up
2018 294,890752 M 295,092897 M
0
1000
2000
3000
4000 o al
Lppi
backg ound
Da a
M(p, ) [MeV/
c
2]
5
0
5
Pulls
0
500
1000
1500
2000
2500
3000
3500
4000 o al
Lppi
backg ound
Da a
M(p, ) [MeV/
c
2]
5
0
5
Pulls
Figu e 5.28:
𝑀(𝑝𝜋 )
i o MinBias MC passing No mLine o an exponen ial + a double
sided C ys al Ball, we e he ail pa ame e s we e se o ma ch he TRUE ID i ones. Magne
Up is depic ed on he le and Magne Down on he igh .
𝜒2
/ndo is 1.20 o MU and 1.17
o MD.
Di iding he Tab. 5.17 esul s by he Tab. 5.16 ones, we ob ain he
𝜖No mLine
Λ→𝑝𝜋 −
(Tab.
5.18 ).
82
5.6. no malisa ion
Table 5.17: Numbe o
Λ→𝑝𝜋 −
decays in No mLine MinBias MC o each yea and
pola i y. Numbe s we e ex ac ed om he z i o No mLine
𝑀(𝑝𝜋 )
wi h common cu s o
an exponen ial + a double sided C ys al Ball whe e ail pa ame e s ha e been se o ma ch
he TRUE ID ones.
Magne Down Magne Up
2018 46590 ±250 46620 ±250
Table 5.18: Compu ed No mLine
Λ→𝑝𝜋 −
e iciencies o Magne Down and Magne Up.
Magne Down Magne Up
𝜖No mLine
Λ→𝑝𝜋 −(1.5799 ±0.0085) ×10−4(1.5798 ±0.0085) ×10−4
5.6.4 numbe o Λ→𝑝𝜋−be o e s ipping
Ha ing he amoun o
Λ→𝑝𝜋−
in No mLine and he e iciency
𝜖No mLine
Λ→𝑝𝜋 −
we can
compu e he amoun o Λ→𝑝𝜋−be o e S ipping using Eq. 5.7.
Table 5.19: Numbe o Λ→𝑝𝜋−decays be o e he s ipping o each yea and pola i y.
Magne Down Magne Up
2018 (101780 ±550) M (109220 ±590) M
2017 (91490 ±490) M (88200 ±480) M
2016 (104610 ±560) M (94330 ±510) M
5.6.5 numbe o Λpa icles be o e s ipping
Di iding
𝑁Λ→𝑝𝜋 −
by he b anching a io a io
B(Λ→𝑝𝜋−)
we will ob ain he
numbe o Λs be o e he s ipping, 𝑁Λ.
𝑁Λ=𝑁Λ→𝑝𝜋 −
B(Λ→𝑝𝜋−)(5.27)
In oducing he PDG
B(Λ→𝑝𝜋−)
in Eq. 5.27 we ob ain he numbe o
Λ
pa icles
be o e S ipping (Tab. 5.20).
83
chap e 5. analysis
Table 5.20: Numbe o Λpa icles be o e he s ipping o each yea and pola i y.
Magne Down Magne Up
2018 (159300 ±1500) M (170900 ±1600) M
2017 (143200 ±1400) M (138000 ±1300) M
2016 (163700 ±1600) M (147600 ±1400) M
5.6.6 no malisa ion
As usual, we can de ine an 𝛼pa ame e , being:
B(Λ→𝑝𝜇−¯
𝜈𝜇)=𝛼𝑁 SignalLine
Λ→𝑝𝜇−¯
𝜈𝜇(5.28)
whe e we ha e included all he e iciencies in he 𝛼pa ame e :
𝛼=B(Λ→𝑝𝜋−)
𝑁No mLine
Λ→𝑝𝜋 −
𝜖No mLine
Λ→𝑝𝜋 −
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇
(5.29)
and
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇
=𝜖SignalLine
Λ→𝑝𝜇−¯
𝜈𝜇. 𝜖Selec ion
Λ→𝑝𝜇−¯
𝜈𝜇(5.30)
Whe e he cu en PDG alue o he b anching a io o he No maliza ion Chan-
nel is
B(Λ→𝑝𝜋−)=64.1±0.5%
, he No mLine Sselec ion + S ipping e iciency
𝜖No mLine
Λ→𝑝𝜋 −
=
(1.5799±0.0085)×10−4
o Magne Down and
𝜖No mLine
Λ→𝑝𝜋 −
=
(1.5798±0.0085)×
10−4
o Magne Up pola i y, and
𝑁No mLine
Λ→𝑝𝜋 −
,
𝜖SignalLine
Λ→𝑝𝜇−¯
𝜈𝜇
and
𝜖Selec ion
Λ→𝑝𝜇−¯
𝜈𝜇
alues o each
yea and pola i y can be ound in Tab. 5.15, Tab. 5.5 and Tab. 5.13 espec i ely.
Table 5.21: 𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇 o each yea and pola i y.
Magne Down Magne Up
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇2018 (1.0810 ±0.0070) ×10−4(1.0860 ±0.0070) ×10−4
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇2017 (1.0870 ±0.0070) ×10−4(1.1030 ±0.0070) ×10−4
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇2016 (1.1020 ±0.0070) ×10−4(1.0820 ±0.0070) ×10−4
As explained in Subsec ion 5.6.3,
𝜖No mLine
Λ→𝑝𝜋 −
was compu ed by i ing he MinBias
MC sample passing he No mLine. This MinBias MC sample is only a ailable o
2018MD and 2018MU, and he esul s a e e y simila o bo h cases. We will use his
𝜖No mLine
Λ→𝑝𝜋 − alue also o 2017 and 2016.
84
5.6. no malisa ion
As we will i he Signal in all he Run II Da a, wi hou sepa a ing by yea and
pola i y, we should weigh he 𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇.
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇
=Í
Yea Pol(𝑁Yea PolNo mLine
Λ→𝑝𝜋 −. 𝜖Yea PolSignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇)
Í
Yea Pol(𝑁Yea PolNo mLine
Λ→𝑝𝜋 −)(5.31)
The esul is
𝜖SignalLineSel
Λ→𝑝𝜇−¯
𝜈𝜇
=
(1.0902 ±0.0027) ×10−4
. Wi h all his alues we can
inally compu e 𝛼:
𝛼=(1.073 ±0.011) ×10−8(5.32)
85
chap e 5. analysis
1040 1060 1080 1100 1120 1140
M(p, ) [
MeV
/
c
2]
0
100
200
300
400
500
600 CombBkg om SignalGen
SignalMC
1080 1100 1120 1140 1160 1180
M(p, ) [
MeV
/
c
2]
0
100
200
300
400
500
600
700
800 CombBkg om SignalGen
SignalMC
1040 1060 1080 1100 1120 1140
M(p, ) [
MeV
/
c
2]
0
20
40
60
80
100 CombBkg om BkgGen
BkgMC
1080 1100 1120 1140 1160 1180
M(p, ) [
MeV
/
c
2]
0
20
40
60
80
100
120
140 CombBkg om BkgGen
BkgMC
Figu e 5.31:
𝑀(𝑝𝜇)
and
𝑀(𝑝𝜋 )
dis ibu ions o "Comb Bkg MC " om Signal ( op) and
Lppi (bo om) s ipping il e ed MC samples whe e i is easy o see ha mos o e en s
iden i ied as combina o ial backg ound a e in ac misiden i ied signal o Lppi backg ound
e en s.
A sklea n G adien Boos ingClassi ie [64] was ained using as signal he
Λ→
𝑝𝜇−¯
𝜈𝜇MC and as backg ound he 𝜌𝑆𝑉 <2da a. The aining a iables we e 𝑀(𝑝𝜇),
APLA, A men e os 𝛼, Lambda ETA, Lambda PT and Lambda EndVe ex_Z.
0.0 0.2 0.4 0.6 0.8 1.0
BDT esponse
0
10
20
30
40
50
60 MC Signal
Combina o ial Bkg
1040 1060 1080 1100 1120 1140
M
(
p
, ) [
MeV
/
c
2]
0
100
200
300
400
500
600 CombBkg SignalGen
CombBkg SignalGen BDT<0.4
Figu e 5.32: The BDT esponse can be used o sepa a e
Λ→𝑝𝜋 −
and Signal om
combina o ial backg ound (le ). In he plo placed a he igh he e ec o selec ing e en s
wi h BDT esponse
<
0.8 in he e en s iden i ied as combina o ial backg ound om he
S ipping Fil e ed MC sample can be ound.
This p ocess se es wo pu poses. Fi s ly, i allows us o enhance he s a is ics o
ou combina o ial backg ound MC sample by sepa a ing he signal and combina o ial
92
5.8. signal yield i
backg ound componen s (see Fig. 5.32). Secondly, we can e alua e he BDT esponse
alues o combina o ial backg ound e en s om he MinBias MC sample ha sa is y
he
𝑃𝐿(𝜈𝜇)>0
cu . This enables us o de e mine whe he hese e en s a e genuine
combina o ial backg ound o po en ial misiden i ica ions as Signal o Lppi.
Figu e 5.33 demons a es ha a signi ican numbe o e en s iden i ied as combina-
o ial backg ound om he MinBias MC sample exhibi signal and peaking backg ound
cha ac e is ics. Mo e impo an ly, he e en s selec ed wi h
𝑃𝐿(𝜈𝜇)>0
a e highly
unlikely o be combina o ial backg ound. This indica es ha ou p e ious es ima ion
o 𝜖𝑃𝐿(𝜈𝜇)>0
CombBkg has g ea ly o e es ima ed i s alue.
Fu he mo e, i is no app op ia e o u ilize he e en s iden i ied as combina o ial
backg ound om he MinBias MC wi h a posi i e neu ino longi udinal momen um
as he combina o ial backg ound empla e in he signal yield i .This is because he
esul ing empla e would be comple ely domina ed by Lppi, as can be seen in he
bo om plo s o Figu e 5.33.
Since we ha e now ob ained he combina o ial backg ound om he signal s ip-
ping il e ed MC sample (selec ed using he BDT), we can compu e he e iciency
𝜖𝑃𝐿(𝜈𝜇)>0
CombBkg
o hose e en s wi h a BDT esponse
<
0.4. The esul is
𝜖𝑃𝐿(𝜈𝜇)>0
𝐶𝑜𝑚𝑏𝐵𝑘𝑔𝐵𝐷𝑇 <0.4=0
.
Howe e , his does no imply ha he e is no combina o ial backg ound in he da a
wi h
𝑃𝐿(𝜈𝜇)>0
, as he BDT does no selec e e y single combina o ial backg ound
e en and we canno di ec ly compu e he e iciency. Bu i is e iden ha he combi-
na o ial backg ound is e ec i ely supp essed when applying 𝑃𝐿(𝜈𝜇)>0.
0.0 0.2 0.4 0.6 0.8 1.0
BDT esponse
0
20
40
60
80
100
120 CombBkg MinBiasMC
0.0 0.2 0.4 0.6 0.8 1.0
BDT esponse
0
5
10
15
20
25
30
35
CombBkg MinBiasMC
PL
( ) > 0
1080 1090 1100 1110 1120 1130 1140
M
(
p
, ) [
MeV
/
c
2]
0.00
0.02
0.04
0.06
0.08
0.10
CombBkg MinBiasMC
PL
( ) > 0
Bkg MC
PL
( ) > 0
1080 1090 1100 1110 1120 1130 1140 1150
Co M
(
p
, ) [
MeV
/
c
2]
0.00
0.02
0.04
0.06
0.08
0.10
0.12
CombBkg MinBiasMC
PL
( ) > 0
Bkg MC
PL
( ) > 0
Figu e 5.33: Top plo s show BDT esponse o all e en s iden i ied as combina o ial
backg ound in he MinBias MC sample (le ) and o hose e en s passing he
𝑃𝐿(𝜈𝜇)>0
cu ( igh ). Bo om plo s a e
𝑀(𝑝𝜋 )
and
𝐶𝑜𝑟𝑟𝑀 (𝑝𝜋 )
dis ibu ions o "combina o ial
backg ound" om MinBias MC sample and o Lppi bkg MC, bo h passing 𝑃𝐿(𝜈𝜇)>0.
93
chap e 5. analysis
Taking all ha in o ma ion in o accoun , he bes op ion o selec ing a combi-
na o ial backg ound empla e is o combine he e en s iden i ied as combina o ial
backg ound om bo h he MinBias MC sample and he backg ound-s ipping il e ed
MC sample. Since we a e only in e es ed on he numbe o signal e en s, we a e no
conce ned by he ac ha mos e en s in ou combina o ial backg ound sample a e
in ac Λ→𝑝𝜋−ghos s.
5.8.2 mc weigh
To accoun o he disc epancies be ween he Mon e Ca lo (MC) and Da a, we pe -
o med a eweigh ing o he MC o align i s p ope ies wi h hose obse ed in he
Da a. The a iables ha we a e eweigh ing a e
Λ𝑃𝑇
and
𝜂
. By i ing he
Λ→𝑝𝜋−
con ibu ion in he No mLine egion o he Da a, we can ex ac he
𝑃𝑇
and
𝜂
dis i-
bu ions o
Λ→𝑝𝜋−
in he Da a and apply co esponding eweigh ing ac o s o he
MC.
The i s pa o he p ocess is analogous o he one ollowed when i ing he
No mLine o ex ac he yield o
Λ→𝑝𝜋−
e en s.(Subsec ion 5.6.2). In his case
we ob ained he sWeigh s using he heps a s package om he i esul s and hen
we passed hose sWeigh s o a GB eweigh e om he hep_ml package. So, he
GBReweigh e is ained using he whole
Λ→𝑝𝜋−
da a sample passing No mLine,
selec ed wi h he sWeigh s me hod, o co ec he di e ences be ween MC and Da a
in Λ𝑃𝑇and 𝜂dis ibu ions.
Figu e 5.34: Reweigh ing esul o
Λ→𝑝𝜋 −
MC passing No mLine.
Λ
ans e se
momen um is depic ed in he le plo and i s pseudo apidi y in he igh one.
This eweigh e , al eady ained o co ec he disc epancies be ween MC and
Da a, was used hen o p edic he co esponding eweighing o
Λ→𝑝𝜋−
MC passing
SignalLine. The eweigh ed his og ams can be ound in Fig. 5.34.
94
5.8. signal yield i
5.8.3 i
The 2D i e akes as inpu he numbe o en ies o each channel in each bin,
u ilizing he MC dis ibu ions as empla es, and ou pu s he co esponding numbe
o occu ences o each channel in he Da a. I pe o ms a log likelihood calcula ion
using Poisson s a is ics, add essing he low s a is ics issue.
The maximum likelihood wi h binned da a case p ocedu e [38] is ollowed o i
he con ibu ion o each channel o he selec ed da a. Fo each bin, he i e compu es
a
𝜒2=2(−OBS ·𝑙𝑜𝑔(EXP) + EXP)
, whe e OBS is he obse ed amoun o selec ed
da a in he bin and EXP is he expec ed sum o all he componen s in he bin:
EXP =𝑓Λ→𝑝𝜇−¯
𝜈𝜇·B(Λ→𝑝𝜇−¯
𝜈𝜇)
𝛼+𝑓Λ→𝑝𝜋 −·𝑁Λ→𝑝𝜋 −+𝑓𝑒𝐷𝐼𝐹 ·𝑁𝑒𝐷𝐼𝐹 +𝑓𝐶𝑜𝑚𝑏 ·𝑁𝐶𝑜𝑚𝑏
whe e he ac ions o each channel in each bin a e ex ac ed om he MC samples,
he
𝛼
pa ame e was al eady compu ed p e iously in his hesis and he
B(Λ→
𝑝𝜇−¯
𝜈𝜇)
and numbe o each backg ound channel a e being i ed. In he i ing
p ocess, a Gaussian cons ain o he no maliza ion pa ame e (
𝛼
) is inco po a ed.
This app oach e ec i ely in eg a es p io knowledge abou 𝛼in o he i .
Di e en binning schemes we e used and he blinded esul s a e p esen ed in
Tab. 5.22. Resul a e blinded by mul iplying he
𝛼
no malisa ion pa ame e by a
andom numbe be ween 0 and 3 (blinding cons an ). Th ee di e en modes we e
implemen ed, he i s one ( i s column) se s he
Λ→𝑝𝜋−
and
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)
a io o he one obse ed in he MinBias MC passing he selec ion, he second mode
(second column) le s his a io ee and he hi d one ( hi d column) conside s also
he combina o ial backg ound channel. As i was discussed in he sec ion 5.8.1, he
MC empla e o he combina o ial backg ound is e y likely misma ched
Λ→𝑝𝜋−
,
and he expec ed con ibu ion o combina o ial backg ound o he selec ed sample is
ex emely low.
Table 5.22: Blinded
B(Λ→𝑝𝜇−¯
𝜈𝜇)
i esul o di e en binning schemes and backg ound
empla es a e included.
Scheme Me ged Lppi+eDIF Lppi,eDIF Lppi,eDIF,CombBkg
Binning 1 (×10−4)B= 3.865 ±0.051 B= 3.913 ±0.068 B= 3.780 ±0.066
Binning 2 (×10−4)B= 3.793 ±0.052 B= 4.041 ±0.074 B= 3.734 ±0.067
Binning 3 (×10−4)B= 3.806 ±0.051 B= 3.965 ±0.072 B= 3.753 ±0.059
Binning 4 (×10−4)B= 3.865 ±0.049 B= 3.899 ±0.073 B= 3.845 ±0.059
Binning 5 (×10−4)B= 3.808 ±0.051 B= 3.964 ±0.070 B= 3.750 ±0.059
95
chap e 5. analysis
Binning Scheme 1 coincides wi h he one shown in Fig. 5.29, while he o he
binning schemes can be ound in Fig. 5.35. The selec ed cen al alue is
B(Λ→
𝑝𝜇−¯
𝜈𝜇)
=
(3.845 ±0.059 (s a )) × 10−4
(blinded) and he sys ema ic unce ain y is
de e mined by conside ing he la ges de ia ion om he esul s ob ained wi h o he
binning schemes and modes, ob aining 5.1 %.
Figu e 5.35: P oposed binnings o he
𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋 )
s
𝑀(𝑝𝜋 )
plane o pe o m a bi-
dimensional i . Top le is Binning Scheme 2, Top Righ Binning Scheme 3, Bo om le is
Binning Scheme 4 and Bo om Righ Binning Scheme 5. Binning Scheme 4 was selec ed o
be he de aul , since i s diagonal bin is igh e and mo e sensi i e o he Signal beha iou .
96
5.8. signal yield i
5.8.3.1 1-dimensional i check
E en hough he backg ound MC s a is ics a e insu icien o pe o m a ully alid i
in 1D, we can s ill conduc a i in
𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋)
as a check. This is possible because
he backg ound dis ibu ion in ha a iable exhibi s a sa is ac o y ag eemen wi h a
double-sided C ys al Ball PDF, allowing us o model he backg ound accu a ely.
The blinded b anching a io esul wi h he signal yield ex ac ed om his i is
B(Λ→𝑝𝜇−¯
𝜈𝜇)
=
(4.02 ±0.18) ×10−4
, in good ag eemen wi h he 2-dimensional i
esul .
The 1D i o he 𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋)dis ibu ion can be seen in Fig. 5.36.
1080 1090 1100 1110 1120 1130 1140 1150 1160
0
1000
2000
3000
4000
5000
6000
Co M(p,pi) [MeV/c^2]
o al
Signal
Bkg CB
Da a
Figu e 5.36: A 1D i o he
𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋 )
dis ibu ion is pe o med o ex ac he signal
yield in he Signal Line egion a e he selec ion. The backg ound componen is i ed
using a double-sided C ys al Ball PDF, while he signal componen is modeled using a
Ke nel Densi y Es ima ion (KDE).
97
chap e 5. analysis
5.9 sys ema ic unce ain ies
The en i e analysis was s uc u ed wi h he p ima y goal o minimizing sys ema ic
unce ain ies. I employs TISTISTIS Da a o bo h he No mLine and SignalLine,
ensu ing ha he cu s used in he S ipping lines a e consis en ac oss bo h lines. The
only di e ence lies in he PID c i e ia o muons and pions. Fu he mo e, hese PID
cu s ha e been minimized o he ex en possible, wi h he selec ion comple ely basaed
on kinema ic equi emen s. As a esul , his app oach should lead o he cancella ion
o mos sys ema ic unce ain ies.
As we a e using
Λ→𝑝𝜋−
as no malisa ion, we should include i s b anching a io
unce ain y as sys ema ic unce ain y.
Rega ding PidCalib2 and T ackCalib2, he so wa e packages used o co ec he
MC e iciencies o he S ipping lines PID and acking cu s, esul s a e a ec ed by
he chosen binning. To ake in o accoun his sys ema ic sou ce o unce ain y, we
can es ima e how he ob ained e iciency a ies by changing he binning scheme. The
choosen binning schemes and esul s can be ound in he appendices (A.11).
The sys ema ic unce ain y associa ed wi h he signal yield i , which is he p e-
dominan ac o , was p e iously de ailed in Sec ion 5.8.3. This unce ain y, 5.1 %,
could po en ially be educed o 3.64 % i he hi d mode, accoun ing o he p esence
o combina o ial backg ound, we e excluded. As discussed ea lie , he expec ed con-
ibu ion o combina o ial backg ound is minimal. Howe e , we chose o inco po a e
a "combina o ial backg ound" sample in o he i ing p ocess. This sample, despi e
being domina ed by misma ched
Λ→𝑝𝜋−
, was he unique me hod o assess he
impac o his backg ound.
I ’s impo an o no e ha he p esence o
Λ→𝑝𝜋−
wi hin he combina o ial
backg ound sample is no inhe en ly p oblema ic. In p inciple, he e is no issue in
i ing he
Λ→𝑝𝜋−
con ibu ion o he selec ed da a using one sample ins ead o
he o he , as he o al
Λ→𝑝𝜋−
coun will ul ima ely be de e mined by combining
bo h samples. The issue p ima ily a ises om i ing a po ion o he
Λ→𝑝𝜋−
con ibu ion using a sample wi h signi ican ly ewe s a is ics. This disc epancy
leads o a mo e p onounced di e ence in he esul s and con ibu es o an inc eased
sys ema ic unce ain y..
The de e mina ion o he inal sys ema ic unce ain y o T ackCalib2 is cu en ly
a Wo k In P og ess (WIP). Addi ionally, o he po en ial sou ces o sys ema ic unce -
ain y a e unde conside a ion ( e e o Table 5.23). Howe e , hei con ibu ion o
he o e all sys ema ic unce ain y is an icipa ed o be minimal.
The o al sys ema ic unce ain y is an icipa ed o be app oxima ely 6.0 %, wi hou
any signi ican a ia ions expec ed.
98
5.9. sys ema ic unce ain ies
Table 5.23: Sys ema ic unce ain ies ha a ec he B(Λ→𝑝𝜇−¯
𝜈𝜇)measu emen .
Sou ce Rela i e Unce ain y (%)
B(Λ→𝑝𝜋−)0.78 %
No mLine Fi expec ed o be negligible
PidCalib Signal Line 1.61 %
PidCalib No mLine 1.04 %
T acking ≈1.0 % (WIP)
Λ→𝑝𝜇−¯
𝜈𝜇yield ( i ) 5.1 %
Signal i empla e expec ed o be negligible
O he sou ces -
99
chap e 6
RESULTS AND CONCLUSIONS
The aim o his hesis
is o p ecisely measu e
B(Λ→𝑝𝜇−¯
𝜈𝜇)
and es lep on
la ou uni e sali y in
𝑠→𝑢
ansi ions. Any de ia ion om LFU would
indica e he p esence o new beyond he S anda d Model physics. Wi h his
pu pose, da a om he LHCb, p oduced h ough p o on-p o on collisions a he LHC
wi h a cen e-o -mass ene gy o 13 TeV, collec ed du ing i s second da a aking pe iod
(2016-2018), is analyzed.
6.1 esul s
In 2021, BESIII published he i s measu emen o he absolu e b anching ac ion
o
Λ→𝑝𝜇−¯
𝜈𝜇
, ob aining he bes b anching ac ion measu emen ill he da e,
B(Λ→𝑝𝜇−¯
𝜈𝜇)) = (1.48 ±0.21) ×10−4[6].
Ou measu ed blinded esul ,
B(Λ→𝑝𝜇−¯
𝜈𝜇)
=
(3.485±0.059(s a )±0.23(sys ))×
10−4
, shows a signi ican ly educed unce ain y. We should conside ha his blinded
esul ough o be di ided by he blinding cons an , which is expec ed o be app oxi-
ma ely equal o he a io o ou alue o he measu ed
B(Λ→𝑝𝜇−¯
𝜈𝜇)
esul . I should
also be no ed ha he calcula ion o he sys ema ic unce ain y is no comple ely
inalized, so he inal esul o his unce ain y may a y sligh ly.
6.2 conclusions
The BESII esul has an unce ain y o
14.19%
. Wi h his selec ion and he i esul ,
we an icipa e a s a is ical unce ain y o
1.5%
and a sys ema ic unce ain y o
6.0%
.
This implies a o al unce ainy o
6.2%
and aligns wi h ou goal o achie ing he mos
p ecise measu emen o he B(Λ→𝑝𝜇−¯
𝜈𝜇)using LHCb da a.
Rega ding 𝑉𝑢𝑠 , we ha e de i ed i s dependence on B(Λ→𝑝𝜇−¯
𝜈𝜇)
101
chap e 7. esumo
|𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2≡1
Dado que a con ibución do elemen o
|𝑉𝑢𝑏 |2
é p ac icamen e desp ezábel (ap-
p oximadamen e
1.3×10−5
), es a elación edúcese á uni e salidade de Cabibbo
(|𝑉𝑢𝑑 | ≈𝑐𝑜𝑠 𝜃12,|𝑉𝑢𝑠 | ≈𝑠𝑖𝑛 𝜃12).
Xa que
|𝑉𝑢𝑑 |
oi medido xa con g ande p ecisión, cun alo de
|𝑉𝑢𝑑 |=0.97436 ±
0.00016, o oco mó ese a 𝑉𝑢𝑠 .
De ei o, emp egando as mello es medidas de 𝑉𝑢𝑑 ,𝑉𝑢𝑠 e𝑉𝑢𝑏 ob emos
|𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2=0.9985 ±0.0007
mos ando unha ensión de 2.2
𝜎
ca uni a iedade na p imei a inglei a da ma iz
CKM.
Ademais, as medidas de
𝑉𝑢𝑠
en decaemen os lep ónicos (
𝐾𝜇2
) e semilep ónicos
(
𝐾𝑙3
) de kaóns mos an unha disc epancia de 3
𝜎
. Es a di e enza pode se un indicio
de BSM. Tendo is o en con a, ó nase i al a opa ou os xei os de medi
𝑉𝑢𝑠
de o ma
p ecisa. Os SHD son unha al e na i a p ome edo a.
Pe o o maio in e ese dos SHD é que son un excelen e ma co de es udo p a
in es iga a LFU. Desde un pun o de is a eó ico, demos ouse que os SHD poden se
sensíbeis a dinámicas BSM que ompen a uni e salidade lep ónica. Es es decaemen os
es án con olados po un pequeno pa áme o de up u a de sime ía
𝛿
que pe mi e
expansións sis emá icas e p ediccións p ecisas. Os modos muónicos son especialmen e
sensíbeis a con ibucións BSM.
No caso de
Λ→𝑝𝜇−¯
𝜈𝜇
, o obse ábel de LFU es es á p edi o pola eo ía como
𝑅𝜇𝑒 =0.153 ±0.008
aballando a nex - o-leading o de . A mello medida des e
obse ábel oi ealizada po BESIII no 2021, ob endo
𝑅𝜇𝑒 =0.178 ±0.028
, consis en e
den o das ince ezas ca p edicción.
aínda así, conside ando que o modo elec ónico oi medido cunha maio p ecisión
B(Λ→𝑝𝑒−¯
𝜈𝑒)=(8.34 ±0.14) ×10−4
, a maio pa e da ince eza en da medida de
BESIII do modo muónico,
B(Λ→𝑝𝜇−¯
𝜈𝜇)
=
[1.48 ±0.21,(s a ) ±0.08,(sys )] ×10−4
.
Aumen a a p ecisión en
B(Λ→𝑝𝜇−¯
𝜈𝜇)
é esencial pa a p oba a uni e salidade
lep ónica en ansicións 𝑠→𝑢.
7.2 condicións expe imen ais
O LHC é o maio e máis po en e acele ado de pa ículas do mundo. Consis e nun
anel de 27 km de ci cun e encia, compos o dunha se ie de elemen os p a acele a e
man e en ó bi a as pa ículas. Den o do acele ado , dous eixes de pa ículas de
al a ene xía iaxan en di eccións opos as. Os eixes anse colidi en ca o pun os de
in e acción co esponden es a ca o de ec o es ATLAS, CMS, ALICE e LHCb.
LHCb é un dos ca o g andes de ec o es ecollendo da os no LHC. O seu nome
p o én do p incipal p opósi o p a o que oi pensado, de ec a os decaemen os de
pa ículas con endo qua ks b. Es as pa ículas, o madas nas colisións de p o óns do
LHC, enden a xe a se e a decae sen alonxa se moi o da di ección de incidencia do
eixe. Is o e léxase na o ma do de ec o que non cub e odo o ángulo sólido ao edo
108
7.3. análise
da in e acción, senón que se ex ende na di ección "ca a adian e" cunha acep ancia en
pseudo apidi y de 1.6≤𝜂≤4.9.
LHCb es á compos o de di e en es subde ec o es. Basicamen e dispomos dun
localizado de é ices (
VELO
) (p a de e mina a axec o ia das pa ículas pe o
do pun o de in e acción co obxe i o de sepa a os pun os onde as pa ículas son
xe adas (PV) de onde decaen (SV), un de ec o chamado
RICH
(p a iden i ica que
ipo de pa ícula p oduce cada aza a pa i da súa masa e ca ga),
T-s a ions
(que nos
pe mi en ob e a axec o ia e momen o das pa ículas ca gadas),
ECAL
(que de ec a
elec óns e o óns e mide a súa ene xía),
HCAL
(que mide a ene xía deposi ada dos
had ons e Muon Chambe s (si uadas ao inal do de ec o p a de ec a muóns).
Es a análise emp ega da os ecollidos no LHCb du an e o Run 2 (2016-2018).
7.3 análise
A análise p incipal des a ese é a medida do
B(Λ→𝑝𝜇−¯
𝜈𝜇)
. O maio desa ío
elacionado con es a medida en LHCb é disc imina o sinal de ou as canles que
pican en ce as masas, p incipalmen e
Λ→𝑝𝜋−
e
𝐾0
𝑆→𝜋+𝜋−
. Ademais des es
ondos, o ondo combina o io amén nos c ea p oblemas, xa que no sinal emos un
neu ino e polo an o momen o pe dido no es ado inal. Is o ai que as dis ibucións
de
Λ→𝑝𝜇−¯
𝜈𝜇
poden esul a pa ecidas ás do ondo combina o io. Na análise
emp éganse só azas ipo long, xa que non es amos limi ados pola es a ís ica e es as
p esen an unha mello esolución.
O
B(Λ→𝑝𝜇−¯
𝜈𝜇)
ob e ase emp egando como inpu o
B(Λ→𝑝𝜋−)
.
Λ→𝑝𝜋−
se á a súa ez a canle de no malización.
Polo an o, podemos de ini un pa áme o
𝛼
que elaciona o
B(Λ→𝑝𝜇−¯
𝜈𝜇)
co
núme o de e en os de sinal econs uídos 𝑁𝑟𝑒𝑐𝑜
𝑝𝜇𝜈 ,
B(Λ→𝑝𝜇−𝜈𝜇)=𝛼𝑁𝑟𝑒𝑐𝑜
𝑝𝜇𝜈
sendo
𝛼=B(Λ→𝑝𝜋−)
𝑁𝑟𝑒𝑐𝑜
𝑝𝜋
𝜖𝑝𝜋
𝜖𝑝𝜇𝜈
Dúas S ipping lines (selección o line) o on esc i as con es e p opósi o, a de
no malización (No mLine) p a selecciona
Λ→𝑝𝜋−
e medi a súa p oducción en
LHCb e a de sinal (SignalLine) p a ace o mesmo co
Λ→𝑝𝜇−¯
𝜈𝜇
. Ambas seleccións
compa en o mesmos co es p a educi os sis emá icos, ca única di e enza nos co es
de ID e na xanela de masas.
Dispomos de simulación (MC) de MinBias p a 2018 MD and 2018 MU, e p oduc-
cións de
Λ→𝑝𝜋−
e
Λ→𝑝𝜇−¯
𝜈𝜇
MC pasando a SignalLine p a 2016, 2017 e 2018 cas
con igu acións Magne Up e Magne Down. A p oducción de
Λ→𝑝𝜇−¯
𝜈𝜇
oi xe ada
emp egando un modelo de E Gen desen ol o como pa e des a ese e que en en
con a a axa de decaemen o di e encial do sinal. O modelo oi esc i o de xei o que
poida se emp egado no u u o p a calque a SHD.
109
chap e 7. esumo
7.3.1 i da canle de no malización
O p imei o paso é elimina a con aminación de
𝐾0
𝑆→𝜋+𝜋−
p esen e na No mLine.
P a is o podemos aplica o seguin e co e (Cu 1
|
Cu 2) no plano de A men e os-
Podolanski, onde os co es son:
Cu 1 :𝑄𝑃𝑇 >©«25.2+√︄(25.2)2−4.252−2002.1−𝛼2
0.8152ª®¬/2
Cu 2 :𝑄𝑃𝑇 <©«25.2+√︄(25.2)2−4.252−1302.1−𝛼2
0.8152ª®¬/2
Unha ez eliminado o
𝐾0
𝑆→𝜋+𝜋−
(es e co e aplícase a MC e da os pasando a
No mLine a pa i des e momen o), podemos p ocede co i , onde a pd o al es á
compos a dunha double sided c ys al ball + exponencial. Comezamos cun i do
Λ→𝑝𝜋−
MC pu o, p a ex ae os ca o alo es das colas da unción double sided
c ys al ball.
A con inuación p ocedemos a ace o i dos da os da No mLine, onde se aplicou
o co e p a elimina
𝐾0
𝑆→𝜋+𝜋−
p e iamen e, ixando os alo es das colas ob idos no
paso an e io . Is o danos o núme o de Λ→𝑝𝜋−nos da os que pasa on a No mLine.
Po úl imo, epe imos es e i a odo o MinBias MC que pasa a No mLine, p a
ob e a e iciencia do
Λ→𝑝𝜋−
de econs ucción + pasa a No mLine (
𝜖𝑁𝑜𝑟𝑚𝐿𝑖𝑛𝑒
Λ→𝑝𝜋 −
),
di idindo o núme o de
Λ→𝑝𝜋−
no i en e o núme o o al de
Λ→𝑝𝜋−
no MC
sample p e io á econs ucción.
Di idindo o núme o de
Λ→𝑝𝜋−
nos da os que pasa on a No mLine en e
𝜖𝑁𝑜𝑟𝑚𝐿𝑖𝑛𝑒
Λ→𝑝𝜋 −
ob emos o núme o de sucesos de
Λ→𝑝𝜋−
en LHCb no Run 2. Podemos
di idi es e nume o en e
B
(
Λ→𝑝𝜋−
) p a sabe o núme o o al de pa ículas
Λ
xe adas en LHCb no Run2.
7.3.2 e iciencia de selección do sinal
O seguin e paso se á ob e a e iciencia do sinal, o úl imo alo que p ecisamos p a
calcula o pa áme o
𝛼
. Es a e iciencia encapsula os p ocesos de econs ucción,
s ipping e selección.
Nes e caso a selección es á baseada nun co e no plano momen o ans e so pe -
dido s masa ca hipó ese p o ón-muón (
/
𝑝𝑇
s
𝑀(𝑝𝜇)
, mo i ados po unha es a exia
quinemá ica que pe mi e ecupe a a in o mación de momen o do neu ino:
Sel1 =/
𝑝𝑇>16&𝑀(𝑝, 𝜇)<(1116.3−1.03/
𝑝𝑇)
&𝑀(𝑝, 𝜇)>(1122.683 −2/
𝑝𝑇)
110
7.3. análise
e un co e seleccionando os e en os que caen nas exións do plano de A men e os
onde a sinal p esen a maio pu eza.
A e iciencia des a selección ob ense aplicando os co es á simulación de
Λ→
𝑝𝜇−¯
𝜈𝜇
pasando a SignalLine. Es a e iciencia debe a se mul iplicada pola e iciencia de
xe ación, econs ucción e s ipping, que podemos ob e di ec amen e dos exis os
da p oducción o icial de LHCb.
Unha ez calculada es a e iciencia, dispomos de odos os elemen os p ecisos p a
calcula o pa áme o 𝛼.
7.3.3 co ección das e iciencias
O cálculo das e iciencias que en an no pa áme o
𝛼
pa en de supo que a simulación
ep oduce de o ma iabél os da os. Pe o is o pode non se así, especialmen e no
elacionado á espos a on e aos co es de PID e acking. Po es e mo i o, p ocedemos
a co exi es es alo es emp egando as e amen as de LHCb PidCalib e T ackCalib.
Unha ez aplicadas es as co eccións, an o ás e iencias de no malización como
de sinal, ob emos un alo de 𝛼co exido e iabél.
7.3.4 i pos selección do sinal
O úl imo paso é ob e o núme o de e en os de
Λ→𝑝𝜇−¯
𝜈𝜇
nos da os que pasan a
SignalLine seleccionados. Dada a di iculdade p a ob e MC de
Λ→𝑝𝜋−
e ondo
combina o io pasando a selección, decidimos ace un i 2D p a mi iga o p oblema
de baixa es a ís ica de MC.
Es e i aise no plano
𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋)
s
𝑀(𝑝, 𝜋)
, onde
𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋)
é unha a iable
c eada supondo que o pión decae pos e io men e a un muón e un an ineu ino.
Es e plano pe mi e sepa a de xei o sa is ac o io
Λ→𝑝𝜋−
,
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)
e
Λ→𝑝𝜇−¯
𝜈𝜇
. P a e i ica o esul ado e ob e a ince eza sis emá ica asociada,
emp egamos di e en es bineados e modos de i . Os esul ados mos an unha boa
compa ibilidade en e eles e cun i 1D na a iable
𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋)
. aínda así, a maio
pa e da ince eza sis emá ica da medida p o én des e i bidimensional.
7.3.5 sis emá icos
A análise oi pensada dende un comezo p a educi os sis emá icos odo o posibél,
escollendo un modo de no malización cunha quinemá ica moi simila , emp egando
da os TISTISTIS e ixando os mesmos co es en ambas seleccións o line. aínda así,
di e en es on es de e o sis emá ico son conside adas, especialmen e as elacionadas
ca co ección do pa áme o
𝛼
emp egando PIDCalib e T ackCalib. aínda así, o e o
sis emá ico es á dominado polo i do sinal (5.1 %).
7.3.6 conclusións
Es a medida do
B(Λ→𝑝𝜇−¯
𝜈𝜇)
es á aínda mul iplicada po un ac o de blinding, un
p ocedemen o habi ual no campo da ísica de al as ene xías. Ainda así, a ince eza
es a ís ica (1.5 %) e sis emá ica (6.0 %) acadada mello a signi ica i amen e a mello
111
chap e 7. esumo
medida de
B(Λ→𝑝𝜇−¯
𝜈𝜇)
ealizada a a o de ago a po BESIII, que p esen aba unha
ince eza do 14 %. A nosa medida e á impo an es consecuencias na comp ensión de
𝑅𝜇𝑒
, sendo sensíbel a des iacións signi ica i as do SM. Se á, polo an o, un impo an e
es da LFU en ansicións 𝑠→𝑢
Cabe des aca que es a é a p imei a ez que se mide a azón de ami icación dun
hype ón en LHCb e amén a p imei a ez que se mide un decaemen o semilep ónico
dunha pa ícula s ange en LHCb.
112
appendix a
APPENDIX
a.1 s ipping line e iciencies
a.1.1 signal passing signalline
This e iciencies can be ob ained by unning in lxplus lb-di ac di ac-bookkeeping-
ejec ion-s a s -P sample-numbe , whe e sample-numbe will ake he alues depic ed
on Tab. A.1.
Table A.1: P oduc ion sample codes o each yea and pola i y.
Magne Down Magne Up
Sample Code 2018 131673 131676
Sample Code 2017 131679 131682
Sample Code 2016 131685 131688
a.1.2 Λ→𝑝𝜋−passing no mline
The
Λ→𝑝𝜋−
S ipping Fil e ed P oduc ion Recons uc ion E iciency can be ob ained
by unning in lxplus lb-di ac di ac-bookkeeping- ejec ion-s a s -P sample-numbe ,
whe e sample-numbe will ake he alues depic ed on Tab. A.2.
a.2 igge lines i ing mo e o en in selec ed e en s
An in e es ing s udy is o check wich igge Lines a e i ing mo e o en in selec ed
e en s o No mLine and SignalLine. The esul can be seen in Figs. A.1, A.2, A.3.
113
appendix a. appendix
Table A.2: P oduc ion sample codes o each yea and pola i y.
Magne Down Magne Up
Sample Code 2018 131695 131698
Sample Code 2017 131701 131704
Sample Code 2016 131707 131710
102103104105106107108109
coun s
Coun e _ o _Lambda0_L0Global_TIS
Coun e _ o _Lambda0_L0Global_TOS
Coun e _ o _Lambda0_L0Pho onDecision_TIS
Coun e _ o _Lambda0_L0Pho onDecision_TOS
Coun e _ o _Lambda0_L0Elec onDecision_TIS
Coun e _ o _Lambda0_L0Elec onDecision_TOS
Coun e _ o _Lambda0_L0Had onDecision_TIS
Coun e _ o _Lambda0_L0Had onDecision_TOS
Coun e _ o _Lambda0_L0MuonDecision_TIS
Coun e _ o _Lambda0_L0MuonDecision_TOS
Coun e _ o _Lambda0_L0DiMuonDecision_TIS
Coun e _ o _Lambda0_L0DiMuonDecision_TOS
Coun e _ o _p_L0Global_TIS
Coun e _ o _p_L0Global_TOS
Coun e _ o _mu_L0Global_TIS
Coun e _ o _mu_L0Global_TOS
Coun e _ o _L0DUTCK
L0 Tis-Tos SignalLine
103105107109
coun s
Coun e _ o _Lambda0_L0Global_TIS
Coun e _ o _Lambda0_L0Global_TOS
Coun e _ o _Lambda0_L0Pho onDecision_TIS
Coun e _ o _Lambda0_L0Pho onDecision_TOS
Coun e _ o _Lambda0_L0Elec onDecision_TIS
Coun e _ o _Lambda0_L0Elec onDecision_TOS
Coun e _ o _Lambda0_L0Had onDecision_TIS
Coun e _ o _Lambda0_L0Had onDecision_TOS
Coun e _ o _Lambda0_L0MuonDecision_TIS
Coun e _ o _Lambda0_L0MuonDecision_TOS
Coun e _ o _Lambda0_L0DiMuonDecision_TIS
Coun e _ o _Lambda0_L0DiMuonDecision_TOS
Coun e _ o _p_L0Global_TIS
Coun e _ o _p_L0Global_TOS
Coun e _ o _pi_L0Global_TIS
Coun e _ o _pi_L0Global_TOS
Coun e _ o _L0DUTCK
L0 Tis-Tos No mLine
Figu e A.1: L0 T igge Lines i ing mo e o en in Selec ed E en s. SignalLine case is
depic ed in he le plo and No mLine in he igh one. Missing lines ha e coun e = 0
a.3 backg ound sou ces
a.3.1 pid and e ex eqi emen s o each channel (mc, signalline)
This appendix con ains he u h-ma ching and e ex equi emen s o each channel,
which a e de ailed below. As a eminde , 3122 is he nume ical code o
Λ
, 2212
o
𝑝
, 211 o
𝜋+
and 13 o
𝜇−
, whe e he nega i e numbe s a e associa ed o he
co esponden an ipa icles:
Selec ion equi emen s o he signal channel (Λ→𝑝𝜇−¯
𝜈𝜇)
The equi emen s o selec ing signal in he MC samples a e de ailed in Tab. A.3.
The TRUE ID o each pa icle should ma ch he co esponding numbe code o ensu e
co ec MC associa ion. Bo h he p o on and he muon a e equi ed o ha e a
Λ
as
hei mo he pa icle. These wo pa icles should o igina e om he same e ex,
which should also coincide wi h he
Λ
end e ex. Las ly, o con i m ha bo h pa icles
come om he same mo he , he MC key o hei espec i e mo he s mus ma ch.
Below is he explici code ha ensu es he sa is ac ion o he gi en condi ions:
((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=13) |
114
a.3. backg ound sou ces
101102103104105
coun s
Coun e _ o _Lambda0_Hl 1Global_TIS
Coun e _ o _Lambda0_Hl 1Global_TOS
Coun e _ o _Lambda0_Hl 1Phys_TIS
Coun e _ o _Lambda0_Hl 1Phys_TOS
Coun e _ o _Lambda0_Hl 1DiMuonHighMassDecision_TIS
Coun e _ o _Lambda0_Hl 1DiMuonLowMassDecision_TIS
Coun e _ o _Lambda0_Hl 1DiMuonLowMassDecision_TOS
Coun e _ o _Lambda0_Hl 1SingleMuonNoIPDecision_TIS
Coun e _ o _Lambda0_Hl 1SingleMuonHighPTDecision_TIS
Coun e _ o _Lambda0_Hl 1T ackMuonDecision_TIS
Coun e _ o _Lambda0_Hl 1T ackMuonDecision_TOS
Coun e _ o _p_Hl 1Global_TIS
Coun e _ o _p_Hl 1Global_TOS
Coun e _ o _p_Hl 1Phys_TIS
Coun e _ o _p_Hl 1Phys_TOS
Coun e _ o _mu_Hl 1Global_TIS
Coun e _ o _mu_Hl 1Phys_TIS
Hl 1 Tis-Tos SignalLine
100101102103104105106107
coun s
Coun e _ o _Lambda0_Hl 1Global_TIS
Coun e _ o _Lambda0_Hl 1Global_TOS
Coun e _ o _Lambda0_Hl 1Phys_TIS
Coun e _ o _Lambda0_Hl 1Phys_TOS
Coun e _ o _Lambda0_Hl 1DiMuonHighMassDecision_TIS
Coun e _ o _Lambda0_Hl 1DiMuonLowMassDecision_TIS
Coun e _ o _Lambda0_Hl 1SingleMuonNoIPDecision_TIS
Coun e _ o _Lambda0_Hl 1SingleMuonNoIPDecision_TOS
Coun e _ o _Lambda0_Hl 1SingleMuonHighPTDecision_TIS
Coun e _ o _Lambda0_Hl 1SingleMuonHighPTDecision_TOS
Coun e _ o _Lambda0_Hl 1T ackMuonDecision_TIS
Coun e _ o _Lambda0_Hl 1T ackMuonDecision_TOS
Coun e _ o _p_Hl 1Global_TIS
Coun e _ o _p_Hl 1Global_TOS
Coun e _ o _p_Hl 1Phys_TIS
Coun e _ o _p_Hl 1Phys_TOS
Coun e _ o _pi_Hl 1Global_TIS
Coun e _ o _pi_Hl 1Global_TOS
Coun e _ o _pi_Hl 1Phys_TIS
Coun e _ o _pi_Hl 1Phys_TOS
Hl 1 Tis-Tos No mLine
Figu e A.2: Hl 1 T igge Lines i ing mo e o en in Selec ed E en s. SignalLine case is
depic ed in he le plo and No mLine in he igh one. Missing lines ha e coun e = 0
100101102103104105
coun s
Coun e _ o _Lambda0_Hl 2Global_TIS
Coun e _ o _Lambda0_Hl 2Global_TOS
Coun e _ o _Lambda0_Hl 2Phys_TIS
Coun e _ o _Lambda0_Hl 2Phys_TOS
Coun e _ o _Lambda0_Hl 2DiMuonJPsiDecision_TIS
Coun e _ o _Lambda0_Hl 2DiMuonJPsiHighPTDecision_TIS
Coun e _ o _Lambda0_Hl 2DiMuonPsi2SDecision_TIS
Coun e _ o _Lambda0_Hl 2DiMuonBDecision_TIS
Coun e _ o _p_Hl 2Global_TIS
Coun e _ o _p_Hl 2Global_TOS
Coun e _ o _p_Hl 2Phys_TIS
Coun e _ o _p_Hl 2Phys_TOS
Coun e _ o _mu_Hl 2Global_TIS
Coun e _ o _mu_Hl 2Global_TOS
Coun e _ o _mu_Hl 2Phys_TIS
Hl 2 Tis-Tos SignalLine
101102103104105106107
coun s
Coun e _ o _Lambda0_Hl 2Global_TIS
Coun e _ o _Lambda0_Hl 2Global_TOS
Coun e _ o _Lambda0_Hl 2Phys_TIS
Coun e _ o _Lambda0_Hl 2Phys_TOS
Coun e _ o _Lambda0_Hl 2DiMuonJPsiDecision_TIS
Coun e _ o _Lambda0_Hl 2DiMuonJPsiHighPTDecision_TIS
Coun e _ o _Lambda0_Hl 2DiMuonPsi2SDecision_TIS
Coun e _ o _Lambda0_Hl 2DiMuonBDecision_TIS
Coun e _ o _p_Hl 2Global_TIS
Coun e _ o _p_Hl 2Global_TOS
Coun e _ o _p_Hl 2Phys_TIS
Coun e _ o _p_Hl 2Phys_TOS
Coun e _ o _pi_Hl 2Global_TIS
Coun e _ o _pi_Hl 2Global_TOS
Coun e _ o _pi_Hl 2Phys_TIS
Coun e _ o _pi_Hl 2Phys_TOS
Hl 2 Tis-Tos No mLine
Figu e A.3: Hl 2 T igge Lines i ing mo e o en in Selec ed E en s. SignalLine case is
depic ed in he le plo and No mLine in he igh one. Missing lines ha e coun e = 0
(Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=-13)) &
abs(mu_MC_MOTHER_ID)=3122 & abs(p_MC_MOTHER_ID)=3122 &
Lambda0_TRUEENDVERTEX_Z=mu_TRUEORIGINVERTEX_Z &
p_TRUEORIGINVERTEX_Z=mu_TRUEORIGINVERTEX_Z &
p_MC_MOTHER_KEY=mu_MC_MOTHER_KEY
Selec ion equi emen s o Λ→𝑝𝜋−
The equi emen s o selec ing
Λ→𝑝𝜋−
in he MC samples a e de ailed in Tab.
115
appendix a. appendix
Requi emen Λ𝑝 𝜇−
TRUE ID 3122 2212 13
TRUE ID CC -3122 -2212 -13
abs(MOTHER ID) 3122 3122
ORIGIN VERTEX ΛEnd Ve ex ΛEnd Ve ex
MOTHER KEY ΛKEY ΛKEY
Table A.3: Requi emen s o selec signal in he MC samples.
A.4. The TRUE ID o each pa icle should ma ch he co esponding numbe code o
ensu e co ec MC associa ion. Bo h he p o on and he pion a e equi ed o ha e
a
Λ
as hei mo he pa icle. These wo pa icles should o igina e om he same
e ex, which should also coincide wi h he
Λ
end e ex. Las ly, o con i m ha bo h
pa icles come om he same mo he , he MC key o hei espec i e mo he s mus
ma ch.
Requi emen Λ𝑝 𝜋−
TRUE ID 3122 2212 -211
TRUE ID CC -3122 -2212 211
abs(MOTHER ID) 3122 3122
ORIGIN VERTEX ΛEnd Ve ex ΛEnd Ve ex
MOTHER KEY ΛKEY ΛKEY
Table A.4: Requi emen s o selec
Λ→𝑝𝜋 −
in he MC samples.No e ha , in con as o
he muon, he sign o he nega i e pion is ’-’.
Below is he explici code ha ensu es he sa is ac ion o he gi en condi ions:
((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=-211) |
(Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=211)) &
abs(mu_MC_MOTHER_ID)=3122 & abs(p_MC_MOTHER_ID)=3122 &
Lambda0_TRUEENDVERTEX_Z=mu_TRUEORIGINVERTEX_Z &
p_TRUEORIGINVERTEX_Z=mu_TRUEORIGINVERTEX_Z &
p_MC_MOTHER_KEY=mu_MC_MOTHER_KEY
Selec ion equi emen s o eDIF (Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇))
The equi emen s o selec ing
Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇)
in he MC samples a e
de ailed in Tab. A.5. The TRUE ID o each pa icle should ma ch he co esponding
numbe code o ensu e co ec MC associa ion. The p o on is equi ed o ha e a
Λ
as i s mo he pa icle and he muon is equi ed o ha e a pion as mo he and a
Λ
as g andmo he . The muon should no o igina e om he
Λ
end e ex . Las ly, o
con i m ha bo h pa icles come om he same mo he , he MC key o he p o on
mo he and muon g andmo he mus ma ch.
Below is he explici code ha ensu es he sa is ac ion o he gi en condi ions:
116
a.3. backg ound sou ces
Requi emen Λ𝑝 𝜇−
TRUE ID 3122 2212 13
TRUE ID CC -3122 -2212 -13
abs(MOTHER ID) 3122 211
abs(GRANDMOTHER ID) 3122
ORIGIN VERTEX no ΛEnd Ve ex
KEY REQUIREMENT mo he = ΛKEY G andmo he = ΛKEY
Table A.5: Requi emen s o selec Λ→𝑝(𝜋−→𝜇−¯
𝜈𝜇).
((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=13) |
(Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=-13)) &
abs(p_MC_MOTHER_ID)=3122 & abs(mu_MC_MOTHER_ID)=211 &
abs(mu_MC_GD_MOTHER_ID)=3122 &
p_MC_MOTHER_KEY=mu_MC_GD_MOTHER_KEY &
Lambda0_TRUEENDVERTEX_Z≠mu_TRUEORIGINVERTEX_Z
Selec ion equi emen s o
𝐾0
𝑆→𝜋+𝜋−
The equi emen s o selec ing
𝐾0
𝑆→
𝜋+𝜋−
in he MC samples a e de ailed in Tab. A.6. The TRUE ID o each pa icle
should ma ch he co esponding numbe code o ensu e co ec MC associa ion. Bo h
pions a e equi ed o ha e a
𝐾0
𝑆
as hei mo he pa icle. These wo pa icles should
o igina e om he same e ex, which should also coincide wi h he
𝐾0
𝑆
end e ex.
This sample is only used o design he selec ion and ejec his channel and o emo e
his kind o e en s om he combina o ial backg ound sample. Requi emen s a e
loose o emo e also misma ched
𝐾0
𝑆→𝜋+𝜋−
om he combina o ial backg ound
sample.
Requi emen 𝐾0
𝑆𝜋+𝜋−
TRUE ID 310 211 -211
abs(MOTHER ID) 310 310
ORIGIN VERTEX 𝐾0
𝑆End Ve ex 𝐾0
𝑆End Ve ex
MOTHER KEY 𝐾0
𝑆KEY 𝐾0
𝑆KEY
Table A.6: Requi emen s o selec 𝐾0
𝑆→𝜋+𝜋−in he MC samples.
Below is he explici code ha ensu es he sa is ac ion o he gi en condi ions:
((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=13) |
(Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=-13)) &
abs(mu_MC_MOTHER_ID)=3122 & abs(p_MC_MOTHER_ID)=3122 &
Lambda0_TRUEENDVERTEX_Z=mu_TRUEORIGINVERTEX_Z &
p_TRUEORIGINVERTEX_Z=mu_TRUEORIGINVERTEX_Z &
p_MC_MOTHER_KEY=mu_MC_MOTHER_KEY
117
appendix a. appendix
T ig0x617d18a4/Reco18/30000000/LDST")
MU
DDDB: dddb-20170721-3 Condi ion DB: sim-20190430- c-mu100
BKQue y("MC/2018/Beam6500GeV-2018-MagUp-Nu1.6-25ns-Py hia8/ Sim09k/
T ig0x617d18a4/Reco18/30000000/LDST")
a.8.11 signal p i a e p oduc ion o co ec s ipping e :
YEAR: 2016 MD
E en Type=33512008
APPCONFIGOPTS_Gauss=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/AppCon ig/ 3 395/op ions
APPCONFIGOPTS_Boole=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/AppCon ig/ 3 374/op ions
APPCONFIGOPTS_Moo e_1=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/AppCon ig/ 3 297/op ions
APPCONFIGOPTS_Moo e_2=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/AppCon ig/ 3 297/op ions
APPCONFIGOPTS_Moo e_3=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/AppCon ig/ 3 355/op ions
APPCONFIGOPTS_B unel=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/AppCon ig/ 3 401/op ions
DECFILESROOT=
/c m s/lhcb.ce n.ch/lib/lhcb/DBASE/Gen/DecFiles/ 30 57
LBPYTHIA8ROOT=
/c m s/lhcb.ce n.ch/lib/lhcb/GAUSS/GAUSS_ 49 20/Gen/LbPy hia8
GAUSS:
sou ce /c m s/lhcb.ce n.ch/lib/LbEn .sh -c x86 _64-slc6-gcc48-op
lb- un Gauss/ 49 20 gaudi un.py ${APPCONFIGOPTS _Gauss}/Gauss/Beam6500GeV-
${magne }100-2016-nu1.6.py ${APPCONFIGOPTS _Gauss}/Gauss/EnableSpillo e -25ns.py
${APPCONFIGOPTS _Gauss}/Gauss/Da aType- ${yea }.py
${APPCONFIGOPTS _Gauss}/Gauss/RICHRandomHi s.py
${DECFILESROOT}/op ions/ ${E en Type}.py
$LBPYTHIA8ROOT/op ions/Py hia8.py
${APPCONFIGOPTS _Gauss}/Gauss/G4PL _FTFP _BERT _EmNoCu s.py
${mainDi }/ex aOp ionsGauss.py
BOOLE:
sou ce /c m s/lhcb.ce n.ch/lib/LbEn .sh -c x86 _64-slc6-gcc49-op
124
a.8. da inci e sions and ags
lb- un Boole/ 30 4 gaudi un.py ${APPCONFIGOPTS _Boole}/
Boole/De aul .py
${APPCONFIGOPTS _Boole}/Boole/EnableSpillo e .py
${APPCONFIGOPTS _Boole}/Boole/Da aType-2015.py
${APPCONFIGOPTS _Boole}/Boole/Boole-Se OdinRndT igge .py
${mainDi }/ex aOp ionsBoole.py
MOORE L0:
sou ce /c m s/lhcb.ce n.ch/lib/LbEn .sh -c x86 _64-slc6-gcc48-op
lb- un Moo e/ 25 4 gaudi un.py
${APPCONFIGOPTS _Moo e _1}/L0App/L0AppSimP oduc ion.py
${APPCONFIGOPTS _Moo e _1}/L0App/L0AppTCK-0x160F.py
${APPCONFIGOPTS _Moo e _1}/L0App/Fo ceLUTVe sionV8.py
${APPCONFIGOPTS _Moo e _1}/L0App/Da aType-2016.py
${APPCONFIGOPTS _Moo e _1}/Pe sis ency/Comp ession-ZLIB-1.py
${mainDi }/ex aOp ionsMoo eL0.py
MOORE HLT1:
sou ce /c m s/lhcb.ce n.ch/lib/LbEn .sh -c
x86 _64-slc6-gcc48-op pa
lb- un Moo e/ 25 4 gaudi un.py
${APPCONFIGOPTS _Moo e _2}/Moo e/
Moo eSimP oduc ionFo Sepa a eL0AppS ep2015.py
${APPCONFIGOPTS _Moo e _2}/Condi ions/TCK-0x5138160F.py
${APPCONFIGOPTS _Moo e _2}/L0App/Da aType-2016.py
${APPCONFIGOPTS _Moo e _2}/Pe sis ency/Comp ession-ZLIB-1.py
${APPCONFIGOPTS _Moo e _2}/Moo e/Moo eSimP oduc ionHl 1.py
${mainDi }/ex aOp ionsMoo eL1.py
MOORE HLT2:
sou ce /c m s/lhcb.ce n.ch/lib/LbEn .sh
-c x86 _64-slc6-gcc48-op
lb- un Moo e/ 25 4 gaudi un.p ${APPCONFIGOPTS _Moo e _3}/Moo e/
Moo eSimP oduc ionFo Sepa a eL0AppS ep2015.py
${APPCONFIGOPTS _Moo e _3}/Condi ions/TCK-0x6139160F.py
${APPCONFIGOPTS _Moo e _3}/L0App/Da aType-2016.py
${APPCONFIGOPTS _Moo e _3}/Pe sis ency/Comp ession-ZLIB-1.py
${APPCONFIGOPTS _Moo e _3}/Moo e/Moo eSimP oduc ionHl 2.py
${mainDi }/ex aOp ionsMoo eL2.py
125
appendix a. appendix
BRUNEL:
sou ce /c m s/lhcb.ce n.ch/lib/LbEn .sh
-c x86 _64-slc6-gcc49-op pa
lb- un B unel/ 50 7 gaudi un.py
${APPCONFIGOPTS _B unel}/B unel/Da aType-2016.py
${APPCONFIGOPTS _B unel}/B unel/MC-Wi hT u h.py
${APPCONFIGOPTS _B unel}/B unel/Spli RawE en Ou pu .4.3.py
${mainDi }/ex aOp ionsB unel.py
Whe e basically he ex aOp ions ile a e:
LHCbApp().DDDB ag = "dddb-20170721-3"
LHCbApp().CondDB ag = "sim-20170721-2- c-"+pol+"100"
DAVINCI:
DaVinci e sion: DaVinci/ 44 10p5
ags:
DaVinci().DDDB ag = "dddb-20170721-3"
DaVinci().CondDB ag = "sim-20170721-2- c-md100"
#dddb-20190206-3
#cond-20191004-1
Pa icles:
om S anda dPa icles impo
S dLooseP o ons, S dAllLooseMuons
#S dAllNoPIDsP o ons,S dAllNoPIDsMuons
We a e supposing ha
𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆
𝑳𝒑𝒎𝒖 =𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆
𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫 ×𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆
𝑪𝒖𝒕𝒔𝑷𝑰 𝑫
, so we ha e o
calcula e each e iciency sepa a ely.
The i s one,
𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆
𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫
, can be ob ained applying jus he NoPID S ipping
Line cu s:
i (((( Reco.Lambda0_TRUEID==3122) and
( Reco.p_TRUEID==2212) and ( Reco.mu_TRUEID==13)) |
(( Reco.Lambda0_TRUEID==-3122) and ( Reco.p_TRUEID==-2212)
and ( Reco.mu_TRUEID==-13))) and
( Reco.Lambda0_TRUEENDVERTEX_Z== Reco.mu_TRUEORIGINVERTEX_Z)
126
a.8. da inci e sions and ags
and (( Reco.p_TRUEORIGINVERTEX_Z== Reco.mu_TRUEORIGINVERTEX_Z))):
i Reco.Lambda0_M<1141 and Reco.mu_TRACK_CHI2NDOF<3
and Reco.mu_IPCHI2_OWNPV>60 and Reco.mu_IP_OWNPV>1 and
Reco.mu_TRACK_Ghos P ob<0.2 and
Reco.p_TRACK_Ghos P ob<0.2 and
Reco.p_TRACK_CHI2NDOF<3 and
Reco.p_IPCHI2_OWNPV>16 and
Reco.Lambda0_IP_OWNPV>0.2 and
Reco.Lambda0_VCHI2NDOF<9 and Reco.Lambda0_AMAXDOCA<0.3
and Reco.Lambda0_BPVLTIME>0.009
and Re co.Lambda0_BPVVDCHI2>50 and
Reco.Lambda0_MIPDV_PRIMARY>0.2:
coun e S ippingNoPID+=1
i Reco.mu_P obNNmu>0.3 and
Reco.mu_isMuon==T ue and
Reco.mu_P obNNpi<0.7 and
Reco.mu_P obNNk<0.7 and
Reco.p_P obNNp>0.3 and
Reco.p_P obNNmu<0.7 and
Reco.p_P obNNk<0.7:
coun e S ippingPID+=1
This can be done o Recons uc ed uples using as inpu o he CombinePa icles
S dLooseP o ons and S dAllLooseMuons o S dAllNoPIDsP o ons and S dAllNoPIDsMuons.
The esul s a e:
NoPIDsPa icles:𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆
𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫𝒔 =0.025189530
LoosePa icles:𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆
𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫𝒔 =0.0089420
127
appendix a. appendix
a.9 dec iles
a.9.1 lppi: igh cu (33102103)
# E en Type: 33102103
#
# Desc ip o : [Lambda0 -> pi- p+]cc
#
# NickName: Lambda_ppi=PHSP,Tigh Cu
#
# Cu s: LoKi::GenCu Tool/Tigh Cu
#
# Documen a ion: Lambda0 decay o p+ pi- wi h phase space model,
Tigh cu .
# * Lambda0 end e ex z in [-1m,0.8m]
# * Lambda0 end e ex adial cu a 38mm
# EndDocumen a ion
#
# CPUTime: < 1 min
#
# Inse Py honCode:
# #
# om Con igu ables impo LoKi__GenCu Tool
# om Gauss.Con igu a ion impo *
# gen = Gene a ion()
# gen.SignalPlain.addTool ( LoKi__GenCu Tool , 'Tigh Cu ')
# #
# igh Cu = gen.SignalPlain.Tigh Cu
# igh Cu .Decay = '[^(Lambda0 => ^p+ ^pi-)]CC'
# igh Cu .P eambulo += [
# " om GaudiKe nel.Sys emO Uni s impo me e , millime e , GeV, MeV" ,
# "inAcc = in_ ange ( 0.005 , GTHETA , 0.400 ) " ,
# "inE a = in_ ange ( 1.95 , GETA , 5.050 ) " ,
# "goodT ack = inAcc & inE a" ,
# "GVX = LoKi.GenVe ices.Posi ionX() " ,
# "GVY = LoKi.GenVe ices.Posi ionY() " ,
# "GVZ = LoKi.GenVe ices.Posi ionZ() " ,
# " x = GFAEVX ( GVX, 100 * me e ) " ,
# " y = GFAEVX ( GVY, 100 * me e ) " ,
# " ho2 = x**2 + y**2 " ,
# " hoK = ho2 < (38 * millime e )**2 " ,
# "decay = in_ ange ( -1 * me e , GFAEVX ( GVZ, 100 * me e ), 0.8 * me e ) ",
# "goodpion = (GPZ > 0) & (GPT > 100*MeV ) & (GP > 3.0*GeV)",
# "goodp o on = (GPT > 275*MeV ) & (GP > 12.25*GeV)"
# ]
128
a.9. dec iles
# igh Cu .Cu s = {
# "[Lambda0]cc" : "decay & hoK",
# "[p+]cc" : "goodT ack & goodp o on " ,
# "[pi-]cc" : "goodT ack & goodpion"
# }
# EndInse Py honCode
#
# PhysicsWG: RD
# Tes ed: Yes
# Responsible: Alexand e B ea Rod iguez
# Email: [email p o ec ed]
# Da e: 20201221
#
Decay Lambda0sig
1.000 p+ pi- PHSP;
Enddecay
CDecay an i-Lambda0sig
#
End
#
a.9.2 lpmunu: igh cu shd (33512008)
# E en Type: 33512008
#
# Desc ip o : [Lambda0 -> p+ mu- an i-nu_mu]cc
#
# NickName: Lambda_pmunuSHD=Tigh Cu
#
# Cu s: LoKi::GenCu Tool/Tigh Cu
#
# Documen a ion: Lambda0 decay o p+ mu- an i-nu_mu wi h SHD model.
p ob=0.615, p obcos=0.366001501202 igh gene a o cu
# * Lambda0 end e ex z in [-1m,0.8m]
# * Lambda0 end e ex adial cu a 38mm
# EndDocumen a ion
#
# CPUTime: < 1 min
#
# Inse Py honCode:
# #
# om Con igu ables impo LoKi__GenCu Tool
# om Gauss.Con igu a ion impo *
# gen = Gene a ion()
129
appendix a. appendix
# gen.SignalPlain.addTool ( LoKi__GenCu Tool , 'Tigh Cu ')
# #
# igh Cu = gen.SignalPlain.Tigh Cu
# igh Cu .Decay = '[^(Lambda0 => ^p+ ^mu- nu_mu~)]CC'
# igh Cu .P eambulo += [
# " om GaudiKe nel.Sys emO Uni s impo me e , millime e , GeV" ,
# "GY = LoKi.GenPa icles.Rapidi y () ## o be su e " ,
# "inY = in_ ange ( 1.9 , GY , 4.6 ) " ,
# "inAcc = in_ ange ( 0.005 , GTHETA , 0.400 ) " ,
# "inE a = in_ ange ( 1.95 , GETA , 5.050 ) " ,
# "goodT ack = inAcc & inE a" ,
# "GVX = LoKi.GenVe ices.Posi ionX() " ,
# "GVY = LoKi.GenVe ices.Posi ionY() " ,
# "GVZ = LoKi.GenVe ices.Posi ionZ() " ,
# " x = GFAEVX ( GVX, 100 * me e ) " ,
# " y = GFAEVX ( GVY, 100 * me e ) " ,
# " ho2 = x**2 + y**2 " ,
# " hoK = ho2 < (38 * millime e )**2 " ,
# "decay = in_ ange ( -1 * me e , GFAEVX ( GVZ, 100 * me e ), 0.8 * me e ) ",
# ]
# igh Cu .Cu s = {
# "[Lambda0]cc" : "decay & hoK",
# "[mu-]cc" : "goodT ack " ,
# "[p+]cc" : "goodT ack "
# }
# EndInse Py honCode
# PhysicsWG: RD
# Tes ed: Yes
# Responsible: Alexand e B ea Rod iguez
# Email: [email p o ec ed]
# Da e: 20190101
#
#Alias MyLambda0 Lambda0
#Alias Myan i-Lambda0 an i-Lambda0
#Cha geConj MyLambda0 Myan i-Lambda0
Decay Lambda0sig
1.000 p+ mu- an i-nu_mu SHD;
Enddecay
CDecay an i-Lambda0sig
#
End
130
a.10. pidcalib2
a.10 pidcalib2
a.10.1 signal line
In ou case we should un he ollowing commands:
pidcalib2.make_e _his s -c "B unel_InMuonAcc == 1.0" --sample Tu bo16
--magne down --pa icle Mu_nop --pid-cu "B unel_MC15TuneV1_P obNNmu>0.3
& B unel_MC15TuneV1_P obNNpi<0.7 & B unel_MC15TuneV1_P obNNk<0.7"
--cu "B unel_IsMuon & B unel_TRCHI2NDOF<3 & B unel_TRACK_GHOSTPROB<0.2
& B unel_IPCHI2>60" --bin- a B unel_P --bin- a B unel_ETA --bin- a
nSPDhi s --binning- ile binning- ile_noPT. x --ou pu -di pidcalib_ou pu /
pidcalib2.make_e _his s --sample Tu bo16 --magne down --pa icle P
--pid-cu "B unel_DLLp>-5 & B unel_MC15TuneV1_P obNNp > 0.3 &
B unel_MC15TuneV1_P obNNmu < 0.7 & B unel_MC15TuneV1_P obNNk < 0.7"
--cu "B unel_PT>250 & B unel_HasRich==1 & B unel_TRCHI2NDOF<3 &
B unel_TRACK_GHOSTPROB<0.2 & B unel_IPCHI2>16" --bin- a B unel_P
--bin- a B unel_ETA --bin- a nSPDhi s --binning- ile
p o on_binning- ile. x --ou pu -di pidcalib_ou pu /
Whe e he -c "InMuonAcc == 1.0" op ion was included because we wan o sepa a e
he e iciency ela ed o he Muon Sys em accep ance and he muon PID e iciency, so
he InMuonAcc cu was applied p e iously o he PIDCalib p ocess. In ou case we
should also use he Mu_nop ins ead o usual Mu, since he de aul muon calib a ion
sample has a ans e se momen um cu o 800
𝑴𝒆𝑽/𝒄
and a o al momen um cu o
3 GeV/c. The B unel p e ix o he a iables indica es ha we a e using he o line
a iables, since he aliases wi hou his p e ix a e used o alues a he igge s ages.
Conce ning he binning JSON ile indica ing he bin edges, i was designed aking
in o accoun he nSPDHi s and he muon and p o on ETA and P dis ibu ions a e
applying all he NoPID cu s de ailed be o e (A.5).
To compu e he co ec ed e iciencies o he p o on and he muon o he p i a e
Signal MC sample a e he non-PID selec ion Cu s, he applied commands we e:
pidcalib2. e _calib --sample Tu bo16 --magne down -- e - ile
da a/LambdapmunuSIM_2016MD_NoPIDS_ETA_Cu s. oo - "T"
--his o-di pidcalib_ou pu --bin- a s '{"B unel_P": "P",
"B unel_ETA": "ETA", "nSPDhi s": "nSPDHi s"}'-- e -pa s
'{"mu": ["Mu_nop ", "B unel_MC15TuneV1_P obNNmu>0.3 &
B unel_MC15TuneV1_P obNNpi<0.7 & B unel_MC15TuneV1_P obNNk<0.7"]}'
--ou pu - ile mu_md_n uple_PID_e . oo
131
appendix a. appendix
Figu e A.5: Dis ibu ions o he binning a iables a e he non-PID selec ion Cu s o
muon and p o on acks.
pidcalib2. e _calib --sample Tu bo16 --magne down -- e - ile
da a/LambdapmunuSIM_2016MD_NoPIDS_ETA_Cu s. oo - "T"
--his o-di pidcalib_ou pu --bin- a s '{"B unel_P": "P",
"B unel_ETA": "ETA", "nSPDhi s": "nSPDHi s"}'-- e -pa s '{"p": ["P",
"B unel__DLLp > -5 & B unel_MC15TuneV1_P obNNp > 0.3 &
B unel_MC15TuneV1_P obNNmu < 0.7 & B unel_MC15TuneV1_P obNNk < 0.7"]}'
--ou pu - ile p_md_n uple_PID_e . oo
a.10.2 no m line
In his case, he commands o c ea e he e iciency his og ams o he p o on and he
pion case should be:
pidcalib2.make_e _his s --sample Tu bo18 --magne down --pa icle Pi_KS
132
a.10. pidcalib2
Figu e A.6: Dis ibu ions o he binning a iables a e he non-PID selec ion Cu s o pion
and p o on acks.
--pid-cu "B unel_MC15TuneV1_P obNNpi > 0.4 & B unel_MC15TuneV1_P obNNmu <
0.7 & B unel_MC15TuneV1_P obNNk < 0.7" --cu "B unel_IsMuon!=1 &
B unel_TRCHI2NDOF<3 & B unel_TRACK_GHOSTPROB<0.2 & B unel_IPCHI2>60 &
B unel_HasRich==1" --bin- a B unel_P --bin- a B unel_ETA --bin- a
nSPDhi s --binning- ile Pi_KS_binning- ile_noPT. x --ou pu -di
pidcalib_ou pu /
pidcalib2.make_e _his s --sample Tu bo18 --magne down --pa icle P
--pid-cu "B unel_DLLp>-5 & B unel_MC15TuneV1_P obNNp > 0.3 &
B unel_MC15TuneV1_P obNNmu < 0.7 & B unel_MC15TuneV1_P obNNk < 0.7"
--cu "B unel_PT>250 & B unel_HasRich==1 & B unel_TRCHI2NDOF<3 &
B unel_TRACK_GHOSTPROB<0.2 & B unel_IPCHI2>16" --bin- a B unel_P
--bin- a B unel_ETA --bin- a nSPDhi s --binning- ile p o on_binning-
133
