Eu . Phys. J. C (2017) 77:812
h ps://doi.o g/10.1140/epjc/s10052-017-5178-x
Regula A icle - Expe imen al Physics
Upda ed sea ch o long-li ed pa icles decaying o je pai s
LHCb Collabo a ion
CERN, 1211 Gene a 23, Swi ze land
Recei ed: 23 May 2017 / Accep ed: 31 Augus 2017 / Published online: 29 No embe 2017
© CERN o he bene i o he LHCb collabo a ion 2017. This a icle is an open access publica ion
Abs ac A sea ch is p esen ed o long-li ed pa icles
wi h a mass be ween 25 and 50 GeV/c2and a li e ime
be ween 2 and 500 ps, using p o on–p o on collision da a
co esponding o an in eg a ed luminosi y o 2.0 b−1, col-
lec ed by he LHCb de ec o a cen e-o -mass ene gies o 7
and 8 TeV. The pa icles a e assumed o be pai -p oduced
in he decay o a 125 GeV/c2S anda d-Model-like Higgs
boson. The expe imen al signa u e is a single long-li ed pa -
icle, iden i ied by a displaced e ex wi h wo associa ed je s.
No excess abo e backg ound is obse ed and limi s a e se
on he p oduc ion c oss-sec ion as a unc ion o he mass and
li e ime o he long-li ed pa icle.
1 In oduc ion
Va ious ex ensions o he S anda d Model (SM) ea u e new
pa icles whose couplings o ligh e s a es a e su icien ly
small o esul in de ec able li e imes. In his pape we epo
on a sea ch o such long-li ed pa icles, which a e assumed
o be pai -p oduced in he decay o a S anda d-Model-like
Higgs boson, and subsequen ly decay in o a qua k–an iqua k
pai . Such a signa u e is p esen in models wi h a hidden-
sec o non-Abelian gauge g oup, whe e he S anda d Model
Higgs boson ac s as a po al [1–5]. The new scala pa i-
cle ep esen s he ligh es s a e in he hidden sec o and is
called a hidden- alley pion (π ) h oughou his pape . Expe -
imen al cons ain s on he p ope ies o he Higgs boson o
mass 125 GeV/c2obse ed by he ATLAS and CMS collab-
o a ions [6,7] s ill allow o b anching ac ions o non-SM
decay modes o up o 30% [8].
Da a collec ed wi h he LHCb expe imen in 2011 and
2012 a e used o his analysis, es ic ed o pe iods in
which sui able igge s we e a ailable. The da a sample anal-
ysed co esponds o 0.62 b−1a a cen e-o -mass ene gy o
√s=7 TeV and 1.38 b−1a √s=8 TeV. In simula ed
e en s wi h π pai s o igina ing om a Higgs boson decay i
e-mail: pie e .da[email p o ec ed]
is ound ha in mos cases no mo e han one o he wo π
decays occu s inside he LHCb accep ance. Consequen ly,
he expe imen al signa u e is a single π pa icle. The candi-
da e is iden i ied by i s decay o wo had onic je s o igina ing
om a displaced e ex, wi h a ans e se dis ance o he
p o on-p o on collision axis (Rxy)o a leas 0.4mm.The
e ex is equi ed o ha e a leas i e acks econs uc ed
in he LHCb e ex de ec o . The analysis is sensi i e o π
pa icles wi h a mass be ween 25 and 50 GeV/c2and a li e-
ime be ween 2 and 500 ps. The li e ime ange is limi ed due
o he p esence o la ge p omp backg ounds a sho decay
imes and he accep ance o he e ex de ec o o long decay
imes. The lowe bounda y on he mass ange a ises om he
equi emen o iden i y wo had onic je s while he uppe
bounda y is d i en by he geome ic accep ance o he de ec-
o .
This pape p esen s an upda e o an ea lie analysis, which
conside ed only he da a se co esponding o an in eg a ed
luminosi y o 0.62 b−1collec ed a √s=7TeV[9]. Simi-
la sea ches o hidden- alley pa icles decaying o je pai s
we e pe o med by he D0 [10], CDF [11], ATLAS [12–14]
and CMS [15] collabo a ions. Compa ed o hese analyses,
his sea ch is sensi i e o π pa icles wi h ela i ely low mass
and li e ime. The LHCb collabo a ion has also pe o med a
sea ch o e en s wi h wo displaced high-mul iplici y e -
ices [16] and a sea ch o e en s wi h a lep on om a high-
mul iplici y displaced e ex [17] in he con ex o SUSY
models, and se e al sea ches o so a unknown long-li ed
pa icles in B-meson decays [18–21].
2 De ec o and e en simula ion
The LHCb de ec o [22,23] is a single-a m o wa d spec-
ome e co e ing he pseudo apidi y ange 2 <η<5,
designed o he s udy o pa icles con aining bo cqua ks.
The de ec o includes a high-p ecision acking sys em con-
sis ing o a silicon-s ip e ex de ec o (VELO) su ounding
he pp in e ac ion egion, a la ge-a ea silicon-s ip de ec-
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812 Page 2 o 14 Eu . Phys. J. C (2017) 77 :812
o loca ed ups eam o a dipole magne wi h a bending
powe o abou 4 Tm, and h ee s a ions o silicon-s ip de ec-
o s and s aw d i ubes placed downs eam o he magne .
The acking sys em p o ides a measu emen o he momen-
um, p, o cha ged pa icles wi h a ela i e unce ain y ha
a ies om 0.5% a low momen um o 1.0% a 200 GeV/c.
The minimum dis ance o a ack o a p ima y e ex (PV),
he impac pa ame e (IP), is measu ed wi h a esolu ion o
(15+(29 GeV/c)/pT)μm, whe e pTis he componen o he
momen um ans e se o he collision axis. Di e en ypes
o cha ged had ons a e dis inguished using in o ma ion om
wo ing-imaging Che enko de ec o s. Pho ons, elec ons
and had ons a e iden i ied by a calo ime e sys em consis ing
o scin illa ing-pad (SPD) and p eshowe de ec o s, an elec-
omagne ic calo ime e and a had onic calo ime e . Muons
a e iden i ied by a sys em composed o al e na ing laye s o
i on and mul iwi e p opo ional chambe s.
The model o he p oduc ion o π pa icles h ough he
Higgs po al is ully speci ied by h ee pa ame e s: he mass
o he Higgs boson and he mass and li e ime o he π .The
Higgs boson mass is aken o be 125 GeV/c2, and i s p oduc-
ion h ough he gluon-gluon usion p ocess is simula ed wi h
he Py hia8 gene a o [24], wi h a speci ic LHCb con igu-
a ion [25] and using he CTEQ6 leading-o de se o pa on
densi y unc ions [26]. The in e ac ion o he gene a ed pa -
icles wi h he de ec o , and i s esponse, a e implemen ed
using he Gean 4 oolki [27,28] as desc ibed in Re . [29].
Signal samples wi h π masses o 25, 35, 43 and 50 GeV/c2
and li e imes o 10 and 100 ps a e gene a ed. In he sim-
ula ed e en s he long-li ed pa icles decay exclusi ely as
π →b¯
b, since his decay mode is gene ally p e e ed in he
Higgs po al model. Samples wi h decays o c- and s-qua k
pai s a e gene a ed as well, bu only in he scena io wi h a
mass o 35 GeV/c2and a li e ime o 10 ps.
3 E en selec ion
The expe imen al signa u e o his analysis is a single dis-
placed e ex wi h wo associa ed je s. Only decays ha p o-
duce a su icien numbe o acks in he VELO o a e ex o
be econs uc ed a e conside ed. Due o he geome y o he
e ex de ec o , his es ic s he sample o decay poin s up o
abou 200 mm om he nominal in e ac ion poin along he
beam di ec ion, and up o abou 30 mm in he ans e se di ec-
ion, he eby limi ing he decay ime accep ance. The selec-
ion s a egy is he same as used in he analysis o Re . [9].
Recons uc ed acks a e used o ind he decay e ex, and
je s a e buil ou o econs uc ed pa icles compa ible wi h
o igina ing om ha e ex. Cons ain s on he signal yield
a e de e mined om a i o he dije in a ian mass dis i-
bu ion. The main sou ce o backg ound is displaced e ices
om hea y- la ou decays o in e ac ions o pa icles wi h
de ec o ma e ial. To ake in o accoun he s ong dependence
o he backg ound le el on he sepa a ion om he beam axis,
di e en selec ion c i e ia a e used in di e en bins o Rxy,
and he inal i is pe o med in bins o his a iable.
The selec ion consis s o online ( igge ) and o line pa s.
The igge [30] is di ided in o a ha dwa e (L0) and a so -
wa e (HLT) s age. The L0 equi es a muon wi h high pTo
a had on, pho on o elec on wi h high ans e se ene gy in
he calo ime e s. In o de o educe he p ocessing ime o he
subsequen igge s ages, e en s wi h a la ge hi mul iplici y
in he SPD a e disca ded. The so wa e s age is di ided in o
wo pa s, which o his analysis di e be ween he 2011
and 2012 da a. In he 2011 sample, he i s so wa e s age
(HLT1) equi es a single high-pT ack wi h a la ge impac
pa ame e . The HLT1 selec ion o he 2012 sample was com-
plemen ed wi h a wo- ack e ex signa u e wi h loose ack
quali y c i e ia, in o de o imp o e he e iciency a la ge
displacemen s. A he second s age o he so wa e igge
(HLT2), e en s a e equi ed o pass ei he a dedica ed inclu-
si e displaced- e ex selec ion o a s anda d opological B
decay selec ion, which equi es a wo-, h ee- o ou - ack
e ex wi h a signi ican displacemen om all PVs [30]. The
inclusi e displaced- e ex selec ion uses an algo i hm simila
o ha used o he LHCb p ima y e ex econs uc ion [31].
A combina ion o equi emen s on he minimum numbe o
acks in he e ex (a leas ou ), he dis ance Rxy o he
e ex o he beam axis (a leas 0.4 mm), he in a ian mass
o he pa icles associa ed wi h he e ex (a leas 2 GeV/c2)
and he scala sum pTo he acks ha o m he e ex (a
leas 3 GeV/c), is used o de ine a se o igge selec ions
wi h su icien ly low a e.
Be o e he o line selec ion can be applied, he displaced
e ex co esponding o he decay o he π candida e mus
be econs uc ed. Fo hose e en s in which he HLT2 inclu-
si e displaced- e ex selec ion was success ul, he same e -
ex candida e ound in he igge is used; his app oach
di e s om ha used in he p e ious LHCb analysis [9]
and simpli ies he e alua ion o sys ema ic unce ain ies. Fo
e en s selec ed only by he opological B igge , a mod-
i ied e sion o he algo i hm is un on he ou pu o he
o line econs uc ion wi h he ollowing c i e ia: e ices
wi h 0.4<Rxy <1 mm mus ha e a leas eigh acks and
he in a ian mass o he sys em mus exceed 10 GeV/c2,
e ices wi h 1 <Rxy <5 mm mus ha e a leas six acks,
and hose wi h Rxy >5 mm mus ha e a leas i e acks.
To exclude backg ound due o in e ac ions wi h he de ec-
o ma e ial, e ices inside a e o egion a ound he VELO
de ec o elemen s a e disca ded. E en s wi h many pa al-
lel displaced acks, which can a ise om machine back-
g ound, a e iden i ied by he azimu hal dis ibu ion o hi s in
he VELO and a e also disca ded.
Nex , je s a e econs uc ed ollowing a pa icle low
app oach. The same se o inpu s as in Re . [32]isused,
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Eu . Phys. J. C (2017) 77 :812 Page 3 o 14 812
namely acks o cha ged pa icles and calo ime e ene gy
deposi s, a e sub ac ion o he ene gy associa ed wi h
cha ged pa icles. To emo e backg ound, acks ha a e
compa ible wi h coming om a PV, acks wi h a smalle
impac pa ame e o any p ima y e ex han o he dis-
placed e ex, and acks ha ha e an impac pa ame e o
he displaced e ex la ge han 2 mm a e all disca ded. The
an i-kTje clus e ing algo i hm is used [33], wi h a dis ance
pa ame e o R=0.7. The je momen um and je mass a e
calcula ed om he ou - ec o s o all cons i uen s o he
je . In simula ed e en s he je ene gy esponse is ound o
be close o uni y excep o he lowes je momen a, nea
he minimally equi ed ans e se momen um o 5 GeV/c.
The e o e, no je ene gy co ec ion was applied o his
sea ch.
To enhance he je pu i y he ac ion o he je ene gy
ca ied by cha ged pa icles should be a leas 0.1, he e
should be a leas one ack wi h ans e se momen um abo e
0.9 GeV/c, no pai o cons i uen s should ca y 90% o he je
ene gy, and no single cha ged o neu al cons i uen should
con ibu e mo e han 70 o 50% o he o al ene gy, espec-
i ely. To ensu e ha hey can eliably be associa ed o a
e ex, he je s a e also equi ed o ha e a leas wo con-
s i uen s wi h ack segmen s in he VELO. To accoun o
di e ences in igge and backg ound condi ions, o he
2012 da a his equi emen was igh ened o a leas ou
segmen s o Rxy <1 mm, and a leas h ee segmen s o
1<Rxy <2 mm. Fo each je an o igin poin is econ-
s uc ed om he je cons i uen s wi h VELO in o ma ion.
The je ajec o y is de ined based on his o igin poin and
he momen um o he je . Any je whose ajec o y does no
poin back o he candida e e ex wi hin 2 mm, o poin s
mo e closely o a p ima y e ex, is emo ed. Only candi-
da es wi h a leas wo je s passing hese c i e ia a e e ained.
Two inal c i e ia a e applied o he dije candida es. The
i s is ha he momen um ec o o he dije candida e
should be aligned wi h he displacemen ec o om a PV o
he econs uc ed e ex posi ion. This is implemen ed as a
equi emen on he dije in a ian mass di ided by he co -
ec ed mass, m/mco >0.7. The co ec ed mass is com-
pu ed as mco =m2+(psin θ)2+psin θ[34], whe e
mand pa e he econs uc ed mass and momen um o he
dije , and θis he minimum angle be ween he momen um
ec o and he displacemen ec o s o he e ex om any
PV in he e en . A equi emen on m/mco is p e e ed o e
one on he angle θi sel , since i s e iciency depends less
s ongly on he boos and he mass o he candida e [35]. The
second c i e ion is ha he kinema ic sepa a ion o he je s
should sa is y R=(η)2+(φ)2<2.2, whe e η
and φ a e he pseudo apidi y and azimu hal angle di e -
ences be ween he wo je s, espec i ely. This educes he
ail in he dije in a ian mass dis ibu ion by supp essing he
emaining back- o-back dije backg ound.
Table 1 Numbe o selec ed candida es pe gene a ed H0→π π
e en (e iciency) in pe cen o di e en π →qq,q=b,c,smodels
o 2011 and 2012 da a aking condi ions, as de i ed om simula ion.
The ela i e s a is ical unce ain y on he e iciency due o he limi ed
size o he simula ed sample is less han a ew pe cen
π mass (GeV/c2) 2011 2012
10 ps 100 ps 10 ps 100 ps
π →b¯
b25 0.45 0.097 0.46 0.111
π →b¯
b35 0.80 0.176 0.83 0.224
π →b¯
b43 0.73 0.190 0.77 0.222
π →b¯
b50 0.49 0.141 0.54 0.171
π →c¯c35 1.35 1.35
π →s¯s35 1.30 1.19
The o e all e iciency o econs uc and selec displaced
π decays in he simula ed samples is summa ized in Table
1 o he 2011 and 2012 da a aking condi ions. A la ge pa
o he ine iciency is due o he de ec o accep ance, which
is abou 13% (8%) and 6.5% (5.5%) o π pa icles wi h a
li e ime o 10 ps (100 ps) and masses o 25 and 50 GeV/c2,
espec i ely. O he impo an con ibu ions a e due o he
selec ion on he displacemen om he beamline, equi e-
men s on he minimum numbe o acks o ming he e ex,
he ma e ial in e ac ion e o, he educ ion in VELO acking
e iciency a la ge displacemen s, and he je selec ion [36].
The e iciency o long-li ed pa icles decaying o s- and c-
qua k pai s is highe han o decays o b-qua k pai s due o
he la ge numbe o acks o igina ing di ec ly om he π
decay e ex.
4 Sys ema ic unce ain ies
Sys ema ic unce ain ies on he e iciency a e ob ained om
s udies o da a-simula ion di e ences in con ol samples.
They a e epo ed in Tables 2and 3, o he 2011 and 2012
condi ions, espec i ely, and discussed in mo e de ail below.
Unce ain ies on he signal e iciency due o pa on-densi y
dis ibu ions, he simula ion o agmen a ion and had oniza-
ion, and he Higgs boson p oduc ion c oss-sec ion and kine-
ma ics a e no aken in o accoun .
The e ex econs uc ion e iciency can be spli in o wo
pa s, namely he ack econs uc ion e iciency and he e -
ex inding e iciency. The ack econs uc ion e iciency is
desc ibed by he simula ion o wi hin a ew pe cen , including
o highly displaced and low-momen um acks [37–39]. The
e ec o a sys ema ic change in his e iciency is s udied by
andomly emo ing 2% o he signal acks and eapplying
all selec ion c i e ia.
The e ex inding algo i hm is no ully e icien e en i
all acks a e econs uc ed. In pa icula , he e iciency o
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Table 2 O e iew o he
con ibu ions o he ela i e
sys ema ic unce ain y on he
signal e iciency and luminosi y
(in pe cen ) o di e en signal
samples in 2011 condi ions. The
unce ain y on he o al
e iciency is ob ained by
summing he indi idual
con ibu ions in quad a u e
π mass ( GeV/c2)2535435035,c¯c35, s¯s
π li e ime (ps) 10 100 10 100 10 100 10 100 10 10
T acking e iciency 4.24.13.33.23.02.83.02.71.81.7
Ve ex inding 3.84.23.33.92.83.73.72.62.92.8
Je econs uc ion 3.13.11.61.60.70.70.50.50.91.0
Je iden i ica ion 3.03.03.03.03.03.03.03.03.03.0
Je di ec ion 7.07.06.06.07.47.48.58.55
.95.7
L0 4.04.03.03.03.03.02.02.01.82.1
NSPD 1.71.72.02.01.61.62.32.31.71.6
HLT1 2.02.02.02.02.02.02.02.02.02.0
HLT2 3.03.03.03.03.03.03.03.03.03.0
To al e iciency 11.511.69.810.010.310.511.210.98.78.6
Luminosi y 1.71.71.71.71.71.71.71.71.71.7
Table 3 O e iew o he
con ibu ions o he ela i e
sys ema ic unce ain y on he
signal e iciency and luminosi y
(in pe cen ) o di e en signal
samples in 2012 condi ions. The
unce ain y on he o al
e iciency is ob ained by
summing he indi idual
con ibu ions in quad a u e
π mass ( GeV/c2)2535435035,c¯c35, s¯s
π li e ime (ps) 10 100 10 100 10 100 10 100 10 10
T acking e iciency 3.12.82.42.42.22.12.01.71.21.1
Ve ex inding 4.24.53.84.43.44.13.13.93.43.5
Je econs uc ion 2.72.71.11.10.70.70.30.30.91.0
Je iden i ica ion 3.03.03.03.03.03.03.03.03.03.0
Je di ec ion 5.85.85.35.36.16.17.97.95
.35.8
L0 4.04.02.52.52.02.02.02.02.02.0
NSPD 2.22.22.52.52.52.52.52.52.42.1
HLT1 2.02.02.02.02.02.02.02.02.02.0
HLT2 3.03.03.03.03.03.03.03.03.03.0
To al e iciency 10.510.69.29.49.19.510.410.68.68.9
Luminosi y 1.21.21.21.21.21.21.21.21.21.2
ind a low-mul iplici y seconda y e ex is educed in he
p oximi y o a high-mul iplici y PV. The e ec is s udied in
da a and simula ion using exclusi ely econs uc ed B0→
J/Ψ K∗0decays, which can be selec ed wi h high pu i y
wi hou igh equi emen s on he e ex. The e iciency o
he displaced e ex econs uc ion algo i hm o ind he B0
candida e is measu ed as a unc ion o he displacemen Rxy
in da a and simula ion [36]. The di e ence, weigh ed by he
Rxy dis ibu ion o he signal candida es, is used o de i e a
sys ema ic unce ain y.
Sys ema ic unce ain ies ela ed o he je econs uc ion
can be in oduced in wo ways: h ough di e ences be ween
da a and simula ion in he je econs uc ion e iciency and
h ough di e ences be ween da a and simula ion in he es-
olu ion on he je ene gy and di ec ion, which en e he dije
candida e kinema ic and m/mco selec ion and he dije
in a ian mass shape. The je econs uc ion e iciency has
been s udied p e iously in measu emen s o he Z+je
and Z+b-je c oss-sec ions and was ound o be consis en
be ween da a and simula ion [32,40]. The Z→μ+μ−+je
sample is used o s udy je - ela ed sys ema ic e ec s o his
analysis as well. To mimic he selec ion o he pa icle- low
inpu s, he PV associa ed o he Zis used as a p oxy o he
displaced e ex.
The di e ence be ween da a and simula ion wi h he
la ges impac on he je econs uc ion e iciency is he
ene gy esponse o low-pTje s, close o he h eshold o
5GeV/c. The sensi i i y o a di e en ene gy esponse in
da a and simula ion is e alua ed by inc easing he minimum
je pT o candida es passing he ull o line selec ion by 10%,
which is he unce ain y on he je ene gy scale. The change
in he o e all selec ion e iciency is assigned as a sys ema ic
unce ain y. By eplacing he je iden i ica ion c i e ia wi h a
equi emen on he pTbalance be ween he leading je and
he Zboson, he Z→μ+μ−sample can also be used o
s udy he di e ence in je iden i ica ion e iciency be ween
da a and simula ion. No di e ence la ge han 3% ela i e is
seen, which is assigned as a sys ema ic unce ain y.
To alida e he simula ion o he je -di ec ion esolu ion
he je -di ec ion is es ima ed sepa a ely wi h he cha ged and
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Eu . Phys. J. C (2017) 77 :812 Page 5 o 14 812
Fig. 1 Dije in a ian mass
dis ibu ion in he di e en Rxy
bins, o he 2011 da a sample.
Fo illus a ion, he bes i wi h
a signal π model wi h mass
35 GeV/c2and li e ime 10 ps is
o e laid. The solid blue line
indica es he o al backg ound
model, he sho -dashed g een
line indica es he signal model
o signal s eng h μ=1, and
he long-dashed ed line
indica es he bes - i signal
s eng h
R R
R R
R R
neu al componen s o he je in Z+je e en s. The dis-
ibu ion o he cha ged-neu al di e ence in he es ima ed
di ec ion is ound o be consis en be ween da a and simula-
ion o bo h he ηand he φp ojec ion, and ac oss he ull
ange o pT. To quan i y he e ec on he π signal e iciency,
an addi ional smea ing o he je -di ec ion is applied o je s
o selec ed candida es in he simula ion. The je angles wi h
espec o he beam di ec ion a e smea ed independen ly in
he ho izon al and e ical planes by abou one hi d o he
esolu ion, which is he la ges alue compa ible wi h he
compa ison o da a and simula ion in Z+je e en s.
The sys ema ic unce ain y ela ed o he L0 igge selec-
ion consis s o wo pa s, due o di e ences in he L0
calo ime e igge esponse be ween da a and simula ion,
and due o he di e ence be ween da a and simula ion in he
dis ibu ion o he SPD hi mul iplici y NSPD. The i s is e al-
ua ed by s udying he L0 calo ime e igge esponse on je s
econs uc ed in Z+je e en s, whe e he igge decision is
made based on he Z→μ+μ−decay p oduc s, and is inde-
penden o he je . The obse ed da a-simula ion di e ences
a e p opaga ed o he π econs uc ion e iciency and co e-
spond o sys ema ic unce ain ies o 2–4%, depending on he
π mass. Je s in Z+je e en s a e mos ly ligh -qua k je s,
while ou benchma k signal decays o bqua ks. I is ound
in simula ed e en s ha he e iciency o he L0 calo ime e
igge is p ac ically independen o je la ou . A small ac-
ion o b-qua k je s is igge ed exclusi ely by he L0 muon
igge , which is well modelled in he simula ion.
The second pa o he L0 sys ema ic unce ain y a ises
because he SPD mul iplici y is no well desc ibed in he
simula ion. This e ec is s udied wi h a Z→μ+μ−sample
igge ed by he dimuon L0 selec ion, which applies only a
loose selec ion on his quan i y. An e iciency co ec ion is
de i ed, which is abou 90% o 2011 da a, and abou 85%
o 2012 da a, wi h an unce ain y o 2–3%. The di e ence
in he co ec ion be ween he di e en π models is smalle
123
812 Page 6 o 14 Eu . Phys. J. C (2017) 77 :812
han he sys ema ic a ia ion. This co ec ion is applied o
he o e all de ec ion e iciency de i ed om he simula ion
and he unce ain y is aken as a sys ema ic unce ain y.
The di e ences be ween da a and simula ion in he HLT1
selec ion a e domina ed by he ack econs uc ion e i-
ciency, which was discussed abo e, and addi ional ack qual-
i y c i e ia. One such di e ence is due o a equi emen on
he numbe o VELO hi s o displaced acks. I is cha -
ac e ized using B0→J/Ψ K∗0decays selec ed wi h ig-
ge s ha do no apply such a equi emen . Fo his sample
he selec ion e iciency was ound o be 2% highe in da a
han in simula ed e en s, which is assigned as a sys ema ic
unce ain y. Fo π decays he inal-s a e ack mul iplici y
is la ge , which dilu es e ec s due o a mismodelling o he
single- ack e iciency.
The main sou ce o sys ema ic unce ain y in he HLT2
selec ion is he e ex econs uc ion e iciency, which was
discussed abo e. The e iciency o he opological B igge ,
which is ele an o a subse o he candida es, is accu a ely
desc ibed in simula ion. I is measu ed as a unc ion o Rxy
in da a and simula ion using B0→J/Ψ K∗0candida es ha
a e selec ed by a di e en , dimuon-based, igge c i e ion. A
maximum di e ence o 2–3% is obse ed, which is assigned
as a sys ema ic unce ain y.
5 Resul s
Cons ain s on he p esence o a signal a e de i ed om a
i o he dije in a ian mass dis ibu ions, shown in Figs. 1
and 2. To ake ad an age o he di e ence in he Rxy dis i-
bu ion o backg ound and signal, he da a a e di ided in o
six Rxy bins. The da a a e u he spli acco ding o da a ak-
ing yea o accoun o di e ences in unning condi ions and
Higgs boson p oduc ion c oss-sec ion. The signal e iciency
o each Rxy bin is ob ained om he simula ed samples
wi h π li e imes o 10 and 100 ps, wi h he decay ime dis-
Fig. 2 Dije in a ian mass
dis ibu ion in he di e en Rxy
bins, o he 2012 da a sample.
Fo illus a ion, he bes i wi h
a signal π model wi h mass
35 GeV/c2and li e ime 10 ps is
o e laid. The solid blue line
indica es he o al backg ound
model, he sho -dashed g een
line indica es he signal model
o signal s eng h μ=1, and
he long-dashed ed line
indica es he bes - i signal
s eng h
R R
R R
R R
123
Eu . Phys. J. C (2017) 77 :812 Page 7 o 14 812
Fig. 3 Expec ed (open ci cles
and do ed line) and obse ed
( illed ci cles and solid line)
uppe limi e sus li e ime o
di e en π masses and decay
modes. The g een (da k) and
yellow (ligh ) bands indica e he
quan iles o he expec ed uppe
limi co esponding o ±1σand
±2σ o a Gaussian dis ibu ion.
The decay π →b¯
bis assumed,
unless speci ied o he wise
ibu ions eweigh ed o mimic o he li e ime hypo heses as
needed.
Resul s a e p esen ed as uppe limi s on he signal s eng h
μ≡(σ/σ SM
gg→H0)·B(H0→π π ), whe e σis he excluded
signal c oss-sec ion, σSM
gg→H0is he SM Higgs boson p o-
duc ion c oss-sec ion ia he gluon usion p ocess and
B(H0→π π )is he b anching ac ion o he Higgs boson
decay o π pa icles. The b anching ac ion Bqq o he
π pa icle o he q¯q inal s a e (wi h q¯q=b¯
b,c¯co s¯s
depending on he inal s a e unde s udy) is assumed o be
100%. I he decay wid h o he π pa icle is domina ed
by o he decays han ha unde s udy, he limi s scale as
1/(Bqq (2−Bqq )). The Higgs boson p oduc ion c oss-sec ion
is assumed o be 15.11 pb a 7 TeV and 19.24 pb a 8 TeV
[41].
The CLsme hod [42] is used o de e mine uppe limi s.
The p o ile likelihood a io qμ
PLL =L(μ, ˆ
θ(μ))/L(ˆμ, ˆ
θ) is
chosen as a es s a is ic, whe e L(μ, θ) deno es he likeli-
hood as a unc ion o μand a se o nuisance pa ame e s
θ, which a e also ex ac ed om he da a; L(μ, ˆ
θ(μ)) is
he maximum likelihood o a hypo hesized alue o μand
L(ˆμ, ˆ
θ) is he global maximum likelihood. To es ima e he
sensi i i y o he analysis and he signi icance o a po en ial
signal, he expec ed uppe limi quan iles in he case o ze o
signal a e also e alua ed.
Fo each alue o μand θ he likelihood is e alua ed as
L(μ, θ) =iP(xi;μ, θ), whe e Pis he p obabili y den-
si y o e en iand he p oduc uns o e all selec ed e en s.
The obse ables xi o each candida e include he dije mass,
Rxy bin and da a aking yea . Fo each Rxy bin and da a ak-
ing yea , he in a ian mass dis ibu ion is modelled by he
sum o backg ound and signal componen s. The dis ibu ion
o he signal is modelled as a Gaussian dis ibu ion whose
pa ame e s a e ob ained om ully simula ed signal e en s.
Fo he backg ound dis ibu ion an empi ical model, ou lined
below, is adop ed.
Backg ound candida es can be ca ego ized in o wo con-
ibu ions. The i s ca ego y is mos ly due o he combina ion
123
812 Page 8 o 14 Eu . Phys. J. C (2017) 77 :812
Table 4 Obse ed 95% CL
signal s eng h (μ) uppe limi s
o di e en π models
π mass π li e ime (ps)
2 5 10 20 50 100 200 500
25 GeV/c21.64 0.83 1.12 1.22 2.84 4.37 9.28 22.82
35 GeV/c20.63 0.35 0.32 0.41 0.76 1.37 2.56 5.86
43 GeV/c20.52 0.21 0.16 0.21 0.35 0.63 1.12 2.77
50 GeV/c20.50 0.17 0.14 0.15 0.25 0.41 0.76 1.72
35 GeV/c2,π →c¯c0.33 0.17 0.16 0.20 0.39 0.64 1.19 2.90
35 GeV/c2,π →s¯s0.40 0.20 0.19 0.24 0.42 0.77 1.41 3.51
o a hea y- la ou decay e ex o an in e ac ion wi h de ec-
o ma e ial wi h pa icles om a p ima y in e ac ion. This
con ibu ion has a s eeply dec easing in a ian mass spec-
um. Following he app oach in Re . [9], he dis ibu ion
is modelled by he con olu ion o a alling exponen ial dis-
ibu ion wi h a bi u ca ed Gaussian. All pa ame e s o his
backg ound model a e ee o a y in he i .
The second ca ego y is due o S anda d Model dije e en s.
These e en s ha e candida es wi h je s ha a e app oxima ely
back- o-back in he ans e se plane. I is supp essed by
he selec ion on he dije opening angle R. I s emaining
con ibu ion has a less s eeply alling mass spec um. I is
desc ibed in he i wi h a simila unc ional shape as o
he i s ca ego y, bu wi h he pa ame e s and he ela i e
yields in he di e en bins ixed om a i o he in a ian
mass dis ibu ion o candida es ha ail he R equi emen .
In he inal i only he o al no maliza ion o his compo-
nen is a ied. The second componen is new compa ed o
he model used o he p e ious analysis [9]. I leads o a
be e desc ip ion o he high-mass ail, a he expense o
one ex a i pa ame e o each da a aking yea . I was
ound ha he esul o he i is no sensi i e o he exac
R equi emen used o selec he e en s o his compo-
nen .
All pa ame e s o he i o he in a ian mass dis ibu ion
a e allowed o loa independen ly in each bin, excep o
he ollowing nuisance pa ame e s: he dije in a ian mass
scale, he o e all signal e iciency, and he no maliza ion o
he second backg ound con ibu ion. All ele an sys ema ic
unce ain ies a e inco po a ed in he i model: he o e all
unce ain y on he e iciency, as desc ibed in Sec . 4, he
unce ain y on he dije in a ian mass scale, and he unce -
ain ies on he shape pa ame e s and ela i e no malisa ion
a ising om he ini e size o he simula ed signal samples.
Gaussian cons ain s on hese pa ame e s a e added o he
likelihood.
Al e na i es ha e been conside ed o he backg ound
mass model, in pa icula wi h an addi ional less s eeply
alling exponen ial o desc ibe he ail. Wi h hese models
he es ima ed backg ound yield a highe mass is simila o
Fig. 4 Obse ed uppe limi e sus li e ime o di e en π masses
and decay modes. The decay π →b¯
bis assumed, unless speci ied
o he wise
la ge han wi h he nominal backg ound model, leading o
igh e limi s on he signal. As he nominal model gi es he
mos conse a i e limi , no addi ional sys ema ic unce ain y
is assigned o backg ound modeling.
The e is no signi ican excess o signal in he da a. Uppe
limi s a 95% con idence le el (CL) as a unc ion o li e ime
o hidden- alley models wi h di e en π mass and decay
mode a e shown in Fig. 3and summa ized in Table 4and
Fig. 4. The bes sensi i i y is ob ained o a mass o abou
50 GeV/c2and a li e ime o abou 10 ps. The main imp o e-
men s wi h espec o he p e ious esul [9] a e due o he
enla ged da a sample, he imp o ed igge selec ions, and
he addi ion o he Rxy bin abo e 5 mm, which con ibu es
o he inc eased sensi i i y a la ge li e imes.
6 Conclusion
Resul s ha e been p esen ed om a sea ch o long-li ed pa -
icles wi h a mass in he ange 25–50 GeV/c2and a li e ime
be ween 2 and 500 ps. The pa icles a e assumed o be pai -
123
Eu . Phys. J. C (2017) 77 :812 Page 9 o 14 812
p oduced in he decay o a 125 GeV/c2S anda d-Model-like
Higgs boson and o decay in o wo je s. Besides decays o b¯
b,
which a e he bes mo i a ed in he con ex o hidden- alley
models [1,2], also decays o c¯cand s¯squa k pai s a e con-
side ed. No e idence o so a unknown long-li ed pa icles
is obse ed and limi s a e se as a unc ion o mass and li e-
ime. These measu emen s complemen o he cons ain s on
his p oduc ion model a he LHC [13,15] by placing s onge
cons ain s a small masses and li e imes.
Acknowledgemen s We exp ess ou g a i ude o ou colleagues in he
CERN accele a o depa men s o he excellen pe o mance o he
LHC. We hank he echnical and adminis a i e s a a he LHCb ins i-
u es. We acknowledge suppo om CERN and om he na ional agen-
cies: CAPES, CNPq, FAPERJ and FINEP (B azil); MOST and NSFC
(China); CNRS/IN2P3 (F ance); BMBF, DFG and MPG (Ge many);
INFN (I aly); NWO (The Ne he lands); MNiSW and NCN (Poland);
MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain);
SNSF and SER (Swi ze land); NASU (Uk aine); STFC (Uni ed King-
dom); NSF (USA). We acknowledge he compu ing esou ces ha a e
p o ided by CERN, IN2P3 (F ance), KIT and DESY (Ge many), INFN
(I aly), SURF (The Ne he lands), PIC (Spain), G idPP (Uni ed King-
dom), RRCKI and Yandex LLC (Russia), CSCS (Swi ze land), IFIN-
HH (Romania), CBPF (B azil), PL-GRID (Poland) and OSC (USA).
We a e indeb ed o he communi ies behind he mul iple open sou ce
so wa e packages on which we depend. Indi idual g oups o membe s
ha e ecei ed suppo om A H Founda ion (Ge many), EPLANET,
Ma ie Skłodowska-Cu ie Ac ions and ERC (Eu opean Union), Conseil
Géné al de Hau e-Sa oie, Labex ENIGMASS and OCEVU, Région
Au e gne (F ance), RFBR and Yandex LLC (Russia), GVA, Xun a-
Gal and GENCAT (Spain), He chel Smi h Fund, The Royal Socie y,
Royal Commission o he Exhibi ion o 1851 and he Le e hulme T us
(Uni ed Kingdom).
Open Access This a icle is dis ibu ed unde he e ms o he C ea i e
Commons A ibu ion 4.0 In e na ional License (h p://c ea i ecomm
ons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion,
and ep oduc ion in any medium, p o ided you gi e app op ia e c edi
o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e
Commons license, and indica e i changes we e made.
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