Physics Le e s B 760 (2016) 117–131
Con en s lis s a ailable a ScienceDi ec
Physics Le e s B
www.else ie .com/loca e/physle b
Measu emen o CP obse ables in B±→DK±and B±→Dπ±
wi h wo- and ou -body Ddecays
.LHCb Collabo a ion
a i c l e i n o a b s a c
A icle his o y:
Recei ed 6 Ap il 2016
Recei ed in e ised o m 8 June 2016
Accep ed 9 June 2016
A ailable online 16 June 2016
Edi o : W.-D. Schla e
Measu emen s o CP obse ables in B±→DK±and B±→Dπ±decays a e p esen ed whe e he D
meson is econs uc ed in he final s a es K±π∓, π±K∓, K+K−, π+π−, K±π∓π+π−, π±K∓π+π−and
π+π−π+π−. This analysis uses a sample o cha ged Bmesons om pp collisions collec ed by he LHCb
expe imen in 2011 and 2012, co esponding o an in eg a ed luminosi y o 3.0 b
−1. Va ious CP- iola ing
e ec s a e epo ed and oge he hese measu emen s p o ide impo an inpu o he de e mina ion o
he uni a i y iangle angle γ. The analysis o he ou -pion Ddecay mode is he fi s o i s kind.
©2016 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3.
1. In oduc ion
A se o o e cons aining measu emen s o he uni a i y iangle
om he CKM ma ix is cen al o he alida ion o he S anda d
Model (SM) desc ip ion o CP iola ion [1]. O hese, he leas -well
measu ed is he angle γ≡a g(−VudV∗
ub/Vcd V∗
cb)wi h a p ecision,
om a combina ion o measu emen s, o abou 7◦; his may be
compa ed wi h he 3◦and <1◦p ecision on he o he angles α
and β[2,3]. Amongs he h ee angles, γis unique in ha i does
no depend on a coupling o he op qua k and hus may be s ud-
ied a ee le el, la gely a oiding possible influence om non-SM
CP iola ion.
The mos powe ul me hod o de e mining γin ee-le el de-
cays is h ough measu emen o ela i e pa ial wid hs in B−→
DK−decays, whe e D ep esen s a D0o D0meson.1The am-
pli ude o he B−→D0K−con ibu ion is p opo ional o Vcb
while he ampli ude o B−→D0K−is p opo ional o Vub. By
econs uc ing had onic Ddecays accessible o bo h D0and D0
mesons, phase in o ma ion may be ex ac ed om he in e e ence
o he wo ampli udes. The size o he esul ing di ec CP iola ion
is go e ned by he magni ude o he a io Bo he b →u¯
cs am-
pli ude o he b →c¯
us ampli ude. The ela i ely la ge alue o B
(abou 0.1) in B−→DK−decays means ha he ela i e phase o
he wo in e e ing ampli udes can be ob ained. This ela i e phase
has a CP- iola ing (weak) con ibu ion and CP-conse ing (s ong)
con ibu ion δB; a measu emen o he o al phase o bo h B+
and B−disen angles γand δB. Simila in e e ence e ec s occu
1The inclusion o cha ge-conjuga e p ocesses is implied excep in any discussion
o asymme y.
in B±→Dπ±decays, albei wi h educed sensi i i y o he phases
because, due o addi ional Cabibbo supp ession ac o s, he a io o
ampli udes is abou 20 imes smalle .
The s udy o B−→DK−decays o measu emen s o γwas
fi s sugges ed o CP eigens a es o he Ddecay, o example
he CP-e en D →K+K−and D →π+π−decays, labelled he e
GLW modes [4,5]. The a gumen has been ex ended o supp essed
D →π−K+decays whe e he in e play be ween he a ou ed and
supp essed decay pa hs in bo h he B−and he neu al Dde-
cays esul s in a la ge cha ge asymme y. This is he so-called
ADS mode [6], which in oduces a dependency on he a io o he
supp essed and a ou ed Ddecay ampli udes Dand hei phase
di e ence δD. The B−→[h+h−]Dh−ADS/GLW decays (h =K, π)
ha e been s udied a he B ac o ies [7,8] and a LHCb [9]. This le -
e con ains he upda ed and imp o ed esul using bo h he 2011
and 2012 da a samples. The 2012 da a benefi s om a highe B±
meson p oduc ion c oss-sec ion and a mo e efficien igge , so his
upda e is app oxima ely a ac o ou inc ease in s a is ics.
The ADS/GLW o malism can be ex ended o ou -pa icle Dde-
cays. Howe e , he e a e mul iple in e media e esonances wi h
di e ing ampli ude a ios and s ong phases wi h he consequence
ha he in e e ence in he B−decay, and hence he sensi i i y
o γ, is dilu ed [10]. Fo D →K−π+π+π−and D →π−K+π+π−
decays his dilu ion is pa ame e ised in e ms o a cohe ence
ac o κK3π, an e ec i e s ong phase di e ence a e aged o e
all con ibu ing esonances δK3π
D, and an o e all supp essed- o-
a ou ed ampli ude a io K3π
D. Bes sensi i i y o γis achie ed
using independen measu emen s o he κK3πand δK3π
Dpa am-
e e s, which ha e been de e mined using a sample o quan um-
co ela ed D0D0pai s [11,12], and by he s udy o D-mixing in
h p://dx.doi.o g/10.1016/j.physle b.2016.06.022
0370-2693/©2016 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by
SCOAP3.
118 LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131
his final s a e [13]. A simila dilu ion pa ame e , labelled he CP
ac ion F4π
+can be defined o D →π+π−π+π−decays [14]. Fo
his final s a e i is ound ha F4π
+=0.737 ±0.028 [15], so ha
he decay beha es like a CP-e en GLW mode, albei wi h he in e -
e ence e ec s educed by a ac o (2F4π
+−1) ≈0.5.
This le e includes an analysis o B−→[h+h−π+π−]Dh−de-
cays and supe sedes he p e ious analysis o B−→
[π−K+π+π−]Dh−[16] and complemen s he s udy o he B−→
[h+h−π0]Dh−modes [17]. The analysis o he ou -pion Dde-
cay mode is he fi s o i s kind. In o al, 21 measu emen s o CP
obse ables a e epo ed. Two o hese a e a ios o he a ou ed
B−→D0K−and B−→D0π−pa ial wid hs,
R
K/π=(B−→[ ]DK−)+(B+→[¯
]DK+)
(B−→[ ]Dπ−)+(B+→[¯
]Dπ+),(1)
whe e is K−π+(π−π+)and
¯
is i s cha ge-conjuga e s a e.
Th ee a e double a ios ha a e sensi i e o he pa ial wid hs
o he (quasi-)GLW modes, =π+π−(π+π−)and K+K−, no -
malised o hose o he a ou ed modes o he same mul iplici y,
RKK =
RKK
K/π
RKπ
K/π
,Rππ =
Rππ
K/π
RKπ
K/π
,Rππππ =
Rππππ
K/π
RKπππ
K/π
.(2)
Fi e obse ables a e cha ge asymme ies,
A
h=(B−→[ ]Dh−)−(B+→[¯
]Dh+)
(B−→[ ]Dh−)+(B+→[¯
]Dh+),(3)
o h =Kand =K−π+(π−π+), π+π−(π+π−)and K+K−.
The e a e a u he h ee asymme ies o h =πand =
π+π−(π+π−)and K+K−. Fou obse ables a e pa ial wid hs o
he supp essed ADS modes ela i e o hei co esponding a ou ed
decays,
R¯
ADS(h)=(B−→[¯
]Dh−)+(B+→[ ]Dh+)
(B−→[ ]Dh−)+(B+→[¯
]Dh+),(4)
wi h which come ou ADS-mode cha ge asymme ies,
A¯
ADS(h)=(B−→[¯
]Dh−)−(B+→[ ]Dh+)
(B−→[¯
]Dh−)+(B+→[ ]Dh+).(5)
An al e na i e o mula ion o he ADS obse ables measu es he
supp essed ADS modes ela i e o hei a ou ed coun e pa s, in-
dependen ly o B+and B−mesons,
R¯
+(h)=(B+→[ ]Dh+)
(B+→[¯
]Dh+),R¯
−(h)=(B−→[¯
]Dh−)
(B−→[ ]Dh−).(6)
All he cha ge asymme y measu emen s a e a ec ed by a pos-
sible asymme y in he B±p oduc ion c oss-sec ion mul iplied
by any o e all asymme y om he LHCb de ec o , oge he de-
no ed as σ. This e ec i e p oduc ion asymme y, defined as
AB±=σ(B−)−σ(B+)
σ(B−)+σ(B+), is measu ed in his analysis om he cha ge
asymme y o he mos abundan B−→[K−π+]Dπ−and B−→
[K−π−π+π−]Dπ−modes. This measu emen is applied as a co -
ec ion o all o he CP asymme y esul s. In hese modes, he
possible CP asymme y, as de i ed om exis ing knowledge o γ
and Bin his decay [18], is smalle han he unce ain y on exis -
ing measu emen s o he B±p oduc ion asymme y [19]. The CP
asymme y is hus assumed o be ze o wi h a small sys ema ic un-
ce ain y. Remaining de ec ion asymme ies, no ably be ween K−
and K+, a e co ec ed o using calib a ion samples.
2. De ec o and simula ion
The LHCb de ec o [20] 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 consis ing o a silicon-s ip e -
ex de ec o su ounding he pp in e ac ion egion, a la ge-a ea
silicon-s ip de ec o loca ed ups eam o a dipole magne wi h a
bending powe o abou 4Tm, 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 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/pT)μm, whe e pTis he
componen o he momen um ans e se o he beam, in GeV/c.
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 ified by a calo ime e sys em consis ing
o scin illa ing-pad 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 ified 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 igge consis s o a ha dwa e s age,
based on in o ma ion om he calo ime e and muon sys ems,
ollowed by a so wa e s age, in which all cha ged pa icles wi h
pT>500 (300)MeV a e econs uc ed o 2011 (2012) da a.
A he ha dwa e igge s age, e en s a e equi ed o ha e 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. Fo had ons, he ans-
e se ene gy h eshold is 3.5 GeV. The so wa e igge equi es
a wo-, h ee- o ou - ack seconda y e ex wi h significan dis-
placemen om he p ima y pp in e ac ion e ices. A leas one
cha ged pa icle mus ha e ans e se momen um pT>1.7GeV/c
and be inconsis en wi h o igina ing om a PV. A mul i a ia e al-
go i hm [21] is used o he iden ifica ion o seconda y e ices
consis en wi h he decay o a bhad on.
In he simula ion, pp collisions a e gene a ed using Py hia 8
[22] wi h a specific LHCb configu a ion [23]. Decays o had onic
pa icles a e desc ibed by E Gen [24], in which final-s a e adia-
ion is gene a ed using Pho os [25]. 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 [26] as desc ibed in Re . [27].
3. E en selec ion
A e econs uc ion o he Dmeson candida e om ei he wo
o ou cha ged pa icles, he same basic e en selec ion is ap-
plied o all B−→Dh−channels o in e es . The econs uc ed D
meson candida e mass is equi ed o be wi hin ±25 MeV/c2o
i s known alue [28]. This mass ange co esponds o app oxi-
ma ely h ee imes he mass esolu ion o he signal peaks. The
kaon o pion o igina ing om he B±decay, subsequen ly e e ed
o as he bachelo pa icle, is equi ed o ha e pTin he ange
0.5–10.0GeV/c and pin he ange 5–100 GeV/c. These equi e-
men s ensu e ha he ack is wi hin he kinema ic co e age o
he RICH de ec o s, which a e used o p o ide pa icle iden ifica-
ion (PID) in o ma ion. De ails o he PID calib a ion p ocedu e a e
gi en in Sec . 4. In addi ion, a kinema ic fi is pe o med o each
decay chain, wi h e ex cons ain s applied o bo h he B±and D
e ices, and he Dcandida e cons ained o i s known mass [29].
E en s a e equi ed o ha e been igge ed by ei he he decay
p oduc s o he signal candida e o pa icles p oduced elsewhe e in
he pp collision. The B±meson candida es wi h an in a ian mass
in he in e al 5079–5899 MeV/c2a e e ained. Each B±candida e
is associa ed o he PV o which i has he smalles IP.
LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131 119
Fo bo h he wo- and ou -body D-mode selec ions, a pai
o boos ed decision ee (BDT) disc imina o s, implemen ing he
g adien boos algo i hm [30], a e employed o achie e u he
backg ound supp ession. The BDTs a e ained using simula ed
B−→[K−π+(π+π−)]DK−decays oge he wi h a backg ound
sample o Kπ±combina ions wi h in a ian mass in he ange
5900–7200 MeV/c2. Fo he fi s BDT, hose backg ounds wi h a D
candida e mass mo e han ±30 MeV/c2away om he known D0
mass a e used in he aining. In he second BDT, backg ounds wi h
a Dcandida e mass wi hin ±25 MeV/c2o he known D0mass
a e used. A loose cu on he classifie esponse o he fi s BDT is
applied p io o aining he second one. This ocusses he second
BDT aining on backg ounds en iched wi h ully econs uc ed D
mesons.
The inpu o he BDT is a se o quan i ies ha cha ac e ise he
signal decay. These quan i ies can be di ided in o wo ca ego ies:
(1) p ope ies o any pa icle and (2) p ope ies o composi e pa -
icles only ( he Dand B±candida es). Specifically:
1. p, pTand he squa e o he IP significance;
2. decay ime, fligh dis ance, decay e ex quali y, adial dis ance
be ween he decay e ex and he PV, and he angle be ween
he pa icle’s momen um ec o and he line connec ing he
p oduc ion and decay e ex.
Signal pu i y is imp o ed by using a a iable ha es ima es he
imbalance o pTa ound he B±candida e, defined as
IpT=pT(B±)−pT
pT(B±)+pT
,(7)
whe e he sum is aken o e acks lying wi hin a cone a ound
he B±candida e, excluding he acks ela ed o he signal. The
cone is defined by a ci cle wi h a adius o 1.5 uni s in he plane
o pseudo apidi y and azimu hal angle (exp essed in adians). The
BDT hus gi es p e e ence o B±candida es ha a e ei he iso-
la ed om he es o he e en , o consis en wi h a ecoil agains
ano he bhad on.
No PID in o ma ion is used in he BDT aining so he efficiency
o B−→DK−and B−→Dπ−decays is simila , wi h insignifi-
can a ia ions a ising om he small di e ences in he kinema ics.
The cu s on he wo BDT selec ions a e op imised by minimising
he expec ed unce ain y on AπK(ππ)
ADS(K), as measu ed in he in a i-
an mass fi desc ibed below. The pu i y o he sample is u he
imp o ed wi h RICH in o ma ion by equi ing all kaons and pions
in he Ddecay o be co ec ly iden ified wi h a PID selec ion ha
has an efficiency o abou 85% pe pa icle.
Peaking backg ounds om cha mless decays a e supp essed by
equi ing ha he fligh dis ance significance o he Dcandida e
om he B±decay e ex is la ge han wo s anda d de ia ions.
The esidual cha mless con ibu ion is in e pola ed om fi s o he
B±mass spec um (wi hou he kinema ic fi o he decay chain)
in bo h he lowe and uppe D-mass sidebands. The cha mless
yields a e de e mined independen ly o B+and B−candida es
and a e la e used in he mass fi as fixed e ms, wi h hei un-
ce ain ies included in he sys ema ic unce ain ies o he final
esul s. The la ges esidual cha mless con ibu ions a e in he
B−→[π+π−(π+π−)]DK−modes which show cha ge-in eg a ed
yields o 88 ±11 and 115 ±11 o he wo- and ou -pion modes.
This is 7% and 8% o he measu ed signal yields.
E en wi h PID equi emen s, he supp essed ADS samples con-
ain significan c oss- eed om a ou ed signal decays whe e he
K−and a π+ om he Ddecay a e misiden ified as a π−
and K+. This con amina ion is educed by emo ing any candi-
da e whose econs uc ed Dmass, unde he exchange o mass
hypo heses be ween he kaon and an opposi e-sign pion, lies
wi hin ±15 MeV/c2o he known D0mass. This e o is also ap-
plied o he a ou ed mode, wi h he same efficiency. The esidual
c oss- eed a es a e es ima ed in da a om he a ou ed sam-
ple, assuming he e o and PID efficiencies ac o ise; hey a e
(4.3 ±0.2) ×10−5 o B−→[K−π+]Dh−and (2.7 ±0.1) ×10−4
o B−→[K−π+π+π−]Dh−.
A e he abo e selec ions, mul iple candida es exis in 0.1% and
1% o e en s in he B−→[h+h−]Dh−and B−→[h+h−π+π−]Dh−
samples, espec i ely. Only one candida e pe e en is e ained o
he main fi . When mo e han one candida e is selec ed, he one
wi h he bes B± e ex quali y is e ained.
4. Signal yields and sys ema ic unce ain ies
The alues o he CP obse ables a e de e mined using binned
maximum-likelihood fi s o he in a ian mass dis ibu ions o se-
lec ed B±candida es. Independen fi s a e used o he B−→
[h+h−]Dh−and B−→[h+h−π+π−]Dh−samples. In o ma ion
om he RICH de ec o s is used o sepa a e B−→DK−
om B−→Dπ−decays wi h a PID equi emen on he bach-
elo pa icle. Dis inguishing be ween B+and B−candida es,
bachelo pa icle hypo heses, and ou ( h ee) Ddaugh e final
s a es, yields 16 (12) disjoin samples in he B−→[h+h−]Dh−
(B−→[h+h−π+π−]Dh−) fi , which a e fi ed simul aneously. The
o al p obabili y densi y unc ion (PDF) is buil om wo signal
PDFs, o B−→DK−and B−→Dπ−decays, and h ee ypes o
backg ound PDF. All PDFs a e iden ical o B+and B−decays.
1. B−→Dπ−
In he Dπ−samples an asymme ic double-Gaussian-like unc-
ion is used o he B±→Dπ±signal,
(m)= co e exp −(m−μ)2
2σ2
c+(m−μ)2αL,R
+(1− co e)exp −(m−μ)2
2σ2
w,(8)
which has a peak posi ion μand co e wid h σc, whe e
αL(m<μ)and αR(m>μ)pa ame e ise he ails. The μand
αpa ame e s a e sha ed ac oss all samples bu he co e wid h
pa ame e a ies independen ly o each Dfinal s a e, excep
in he supp essed πK(ππ)PDFs which a e equi ed o be
iden ical o hei a ou ed Kπ(ππ)coun e pa . The addi-
ional Gaussian unc ion wi h a small ac ional con ibu ion
o abou 1% is ound necessa y o model sa is ac o ily he ails
o he peak.
The B−→Dπ−decays misiden ified as B−→DK−a e dis-
placed o highe mass in he DK−subsamples. These misiden-
ified candida es a e modelled by he sum o wo Gaussian
unc ions wi h common mean bu modified o include ail
componen s as in Eq. (8). The mean, wid hs and one ail pa-
ame e a e le o a y eely.
2. B−→DK−
In he DK−samples, Eq. (8) is again used o he signal PDF.
The peak posi ion μand he wo ail pa ame e s αLand αR
a e fixed o hose o he B−→Dπ−signal unc ion, as a e
he wide componen pa ame e s co e and σw. The co e wid h
pa ame e in each Dmode is ela ed o he co esponding
B−→Dπ−wid h by a eely a ying a io common o all D
final s a es. Misiden ified B±→DK±candida es appea in he
Dπ−subsamples and a e desc ibed by a fixed shape ob ained
om simula ion, which is la e a ied o de e mine a sys em-
a ic unce ain y associa ed wi h his choice.
120 LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131
3. Combina o ial backg ound
Due o he low backg ound le el, a linea unc ion is sufficien
o desc ibe he en i e in a ian mass spec um. Two common
slope pa ame e s a e used, one o Dπ−and ano he o DK−
subsamples bu yields a y independen ly.
4. Peaking backg ounds
Cha mless B±decay and he a ou ed mode c oss- eed back-
g ounds bo h peak a he B±mass and a e indis inguishable
om he signal. Thei esidual yields a e es ima ed in da a,
en e ing he fi as fixed p opo ions o he a ou ed B−→
Dπ−yield. A Gaussian unc ion is used o he PDF, wi h a
(25 ±2)MeV/c2wid h pa ame e ha is aken om simula-
ion; his is abou 50% wide han he signal PDF.
5. Pa ially econs uc ed b-had on decays
Pa ially econs uc ed backg ounds gene ally ha e lowe in-
a ian mass han he signal peak. The dominan con ibu ions
a e om B−→Dh−π0, B−→D∗0π−and B0→D∗+π−de-
cays whe e ei he a pho on o a pion is missed in he e-
cons uc ion. The dis ibu ion o each o hese sou ces in he
in a ian mass spec um depends on he spin and mass o
he missing pa icle. I he missing pa icle has spin-pa i y
0−(1−), he dis ibu ion is pa ame e ised by a pa abola wi h
posi i e (nega i e) cu a u e con ol ed wi h a Gaussian es-
olu ion unc ion. The kinema ics o he decay ha p oduced
he missing pa icle define he endpoin s o he ange o he
pa abola. Decays in which bo h a pa icle is missed and a
bachelo pion is misiden ified as a kaon a e pa ame e ised
wi h a semi-empi ical PDF, o med om he sum o Gaussian
and e o unc ions. The pa ame e s o each pa ially econ-
s uc ed PDF a e fixed o he alues ound in fi s o simu-
la ed e en s, and a e a ied as a sou ce o sys ema ic un-
ce ain y. The yields o each con ibu ion a y independen ly
in each subsample, whe e all pa ially econs uc ed decay
modes sha e a common e ec i e cha ge asymme y ac oss all
Dmodes. Though i s e ec is mi iga ed by he limi ed ange
o he mass fi , la ge CP iola ion in he low-mass backg ound
is possible in he GLW and ADS samples, so a sys ema ic un-
ce ain y is assigned.
In he B−→[K+K−]Dh−samples, Λ0
b→[p+K−π+]Λ+
ch−de-
cays con ibu e o backg ound when he pion is missed and
he p o on is misiden ified as he second kaon. The wide PDF
o his componen is fixed om simula ion bu he yield in
he B−→[K+K−]Dπ−subsample a ies eely. The Λ0
b→
[p+K−π+]Λ+
cK−yield is cons ained using a ecen measu e-
men o B(Λ0
b→Λ+
cK−)/B(Λ0
b→Λ+
cπ−)[31]. Fu he mo e,
B0
s→D0K−π+decays, whe e he pion is missed, o m a back-
g ound o he supp essed B−→DK−modes. The yield o
his componen a ies in he fi bu he PDF is aken om a
simula ion model o he h ee-body B0
sdecay [32], smea ed o
ma ch he esolu ion measu ed in da a.
In he DK−subsamples, he B±→Dπ−c oss- eed can be de-
e mined by he fi o da a. The B−→DK−c oss- eed in o he
Dπ−subsamples is no well sepa a ed om backg ound, so he
expec ed yield is de e mined by a PID calib a ion p ocedu e using
app oxima ely 20 million D∗+ →[K−π+]Dπ+decays. The clean
econs uc ion o his cha m decay is pe o med using kinema ic
a iables only and hus p o ides a high pu i y sample o K∓and
π± acks, unbiased in he PID a iables. The PID efficiency de-
pends on ack momen um and pseudo apidi y, as well as he
numbe o acks in he e en . The e ec i e PID efficiency o he
signal is de e mined by weigh ing he calib a ion sample such ha
he dis ibu ions o hese a iables ma ch hose o he selec ed
candida es in he B−→Dπ−mass dis ibu ion. I is ound ha
Table 1
Signal yields as measu ed in he B−→[h+h−]Dh−and
B−→[h+h−π+π−]Dh−in a ian mass fi s, oge he wi h
hei s a is ical unce ain ies.
Decay mode Yield
B±→K±π∓Dπ±378,050 ±650
B±→K±π∓DK±29,470 ±230
B±→K+K−Dπ±50,140 ±270
B±→K+K−DK±3816 ±92
B±→π+π−Dπ±14,680 ±130
B±→π+π−DK±1162 ±48
B±→π±K∓Dπ±1360 ±44
B±→π±K∓DK±553 ±34
B±→K±π∓π+π−Dπ±142,910 ±390
B±→K±π∓π+π−DK±11,330 ±140
B±→π+π−π+π−Dπ±19,360 ±150
B±→π+π−π+π−DK±1497 ±60
B±→π±K∓π+π−Dπ±539 ±26
B±→π±K∓π+π−DK±159 ±17
68.0% (PID(K)) o B−→DK−decays pass he bachelo kaon PID
equi emen ; he emaining 32.0% c oss- eed in o he B−→Dπ−
sample. Wi h his selec ion, app oxima ely 98% o he B−→Dπ−
decays a e co ec ly iden ified. Due o he size o he calib a ion
sample, he s a is ical unce ain y is negligible; he sys ema ic un-
ce ain y o he me hod is de e mined by he size o he signal
ack samples used, and hus inc eases o he lowe s a is ics
modes. The sys ema ic unce ain y on PID(K) anges om 0.3% in
B−→[K−π+]DK− o 1.5% in B−→[π+π−π+π−]DK−.
In o de o measu e CP asymme ies, he de ec ion asymme ies
o K±and π±mus be aken in o accoun . A de ec ion asym-
me y o (−0.96 ±0.10)%is assigned o each kaon in he final
s a e, a ising om he ac ha he nuclea in e ac ion leng h o
K−mesons is sho e han ha o K+mesons. This is compu ed
by compa ing he cha ge asymme ies in D−→K+π−π−and
D−→K0
Sπ−calib a ion samples and weigh ing o he kinema ics
o he signal kaons. The equi alen asymme y o pions is smalle
(−0.17 ±0.10)% and is aken om Re . [33]. The CP asymme ies
in he a ou ed B−→[K−π+(π+π−)]Dπ−decays a e fixed o
ze o, wi h a sys ema ic unce ain y o 0.16% calcula ed om exis -
ing knowledge o γand Bin his decay [18], wi h no assump ion
made abou he s ong phase. This enables he e ec i e p oduc ion
asymme y, AB±, o be measu ed and simul aneously sub ac ed
om he cha ge asymme y measu emen s in o he modes. The
signal yield o each mode is a sum o he numbe o signal and
c oss- eed candida es; hei alues a e gi en in Table 1. The co e-
sponding in a ian mass spec a, sepa a ed by cha ge, a e shown
in Figs. 1–7.
To ob ain he obse ables R
K/π, he a io o yields mus be
co ec ed by he ela i e efficiency wi h which B−→DK−and
B−→Dπ−decays a e econs uc ed and selec ed. F om simula-
ion, his a io is ound o be 1.017 ±0.017 and 1.018 ±0.026
o he wo- and ou -body Ddecay selec ions. The unce ain ies
a e calcula ed om he fini e size o he simula ed samples and
accoun o impe ec modelling o he ela i e pion and kaon ab-
so p ion in he de ec o ma e ial.
The 21 obse ables o in e es a e ee pa ame e s o he fi .
The sys ema ic unce ain ies associa ed wi h fixed ex e nal pa am-
e e s a e assessed by epea ing he fi many imes, a ying he
alue o each ex e nal pa ame e acco ding o a Gaussian dis i-
bu ion wi hin i s unce ain y. The esul ing sp ead (RMS) in each
obse able’s alue is aken as he sys ema ic unce ain y on ha
obse able due o he ex e nal sou ce. The sys ema ic unce ain-
ies, g ouped in o ou ca ego ies, a e lis ed in Tables 2 and 3 o
LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131 121
Fig. 1. In a ian mass dis ibu ions o selec ed B±→[K±π∓]Dh±candida es, sepa a ed by cha ge, wi h B−(B+)candida es on he le ( igh ). The op plo s con ain he
B±→DK±candida e sample, as defined by a PID equi emen on he bachelo pa icle. The emaining candida es a e placed in he bo om ow, econs uc ed wi h a pion
hypo hesis o he bachelo . The ed ( hick, open) and g een (ha ched-a ea) cu es ep esen he B±→DK±and B±→Dπ±signals. The shaded pa indica es pa ially
econs uc ed decays, he do ed line, whe e isible, shows he combina o ial componen , and he o al PDF is d awn as a hin blue line. (Fo in e p e a ion o he e e ences
o colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.)
Fig. 2. In a ian mass dis ibu ions o selec ed B±→[π±K∓]Dh±decays, sepa a ed by cha ge. The dashed pink line le o he signal peak shows pa ially econs uc ed
B0
s→[K+π−]DK−π+decays, whe e he bachelo pion is missed. The a ou ed mode c oss- eed is also included in he fi , bu is oo small o be seen. See he cap ion o
Fig. 1 o o he defini ions. (Fo in e p e a ion o he e e ences o colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.)
Table 2
Sys ema ic unce ain ies o he B−→[h+h−]Dh−CP obse ables quo ed as a pe cen age o he s a is ical unce ain y on he obse able. PID e e s o he PID calib a ion
p ocedu e. Bkg e e s o he choice o backg ound shapes and yields in he fi . Sim e e s o he use o fini e samples o simula ed e en s o de e mine efficiency a ios. Asym
e e s o he fixed pion and kaon de ec ion asymme ies, and he assump ion o no CP iola ion in B−→D0π−decays.
[%] AKπ
KRKπ
K/πAKK
KAKK
πRKK Aππ
KAππ
πRππ RπK
ADS(π)RπK
ADS(K)AπK
ADS(π)AπK
ADS(K)
PID 42 95 11 1 38 9 9 39 29 25 15 5
Bkg 65 190 34 3 84 30 28 48 69 74 24 15
Sim 21 250 14 0 24 8 7 13 29 30 8 5
Asym 23 27 11 34 6 7 20 5 12 13 7 8
To al 83 330 40 34 96 33 36 64 81 85 30 19
Table 3
Sys ema ic unce ain ies o he B−→[h+h−π+π−]Dh−CP obse ables quo ed as a pe cen age o he s a is ical unce ain y on he obse able. See he Table 2 cap ion o
defini ions.
[%] RKπππ
K/πRππππ RπKππ
ADS(K)RπKππ
ADS(π)AKπππ
KAπKππ
ADS(K)AπKππ
ADS(π)Aππππ
KAππππ
π
PID 37 43 1 2 1 1 0 0 1
Bkg 63 28 40 33 2 36 8 54 21
Sim 160 0 0 0 0 1 0 0 0
Asym 20 5 7 6 16 5 5 8 22
To al 180 51 41 34 16 36 10 54 30
122 LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131
Fig. 3. In a ian mass dis ibu ions o selec ed B±→[π+π−]Dh±candida es, sepa a ed by cha ge. The dashed black line ep esen s he esidual con ibu ion om cha mless
decays. This componen is p esen in he Dfinal s a es conside ed, bu is mos isible in his case. See he cap ion o Fig. 1 o o he defini ions. (Fo in e p e a ion o he
colou s in his figu e, he eade is e e ed o he web e sion o his a icle.)
Fig. 4. In a ian mass dis ibu ions o selec ed B±→[K+K−]Dh±candida es, sepa a ed by cha ge. The dashed cyan line ep esen s pa ially econs uc ed Λ0
b→
[p+K−π+]Λ+
ch−decays, whe e he pion is missed and he p o on is misiden ified as a kaon. See he cap ion o Fig. 1 o o he defini ions. (Fo in e p e a ion o he
e e ences o colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.)
he wo-body and ou -body Dmode fi s. Co ela ions be ween he
ca ego ies a e negligible and he o al sys ema ic unce ain ies a e
gi en by he sums in quad a u e.
5. Resul s
The esul s o he fi s o da a, wi h s a is ical and sys ema ic
unce ain ies, a e:
AKπ
K=−0.0194 ±0.0072 ±0.0060
RKπ
K/π=0.0779 ±0.0006 ±0.0019
AKK
K=0.087 ±0.020 ±0.008
AKK
π=−0.0145 ±0.0050 ±0.0017
RKK =0.968 ±0.022 ±0.021
Aππ
K=0.128 ±0.037 ±0.012
Aππ
π=0.0043 ±0.0086 ±0.0031
Rππ =1.002 ±0.040 ±0.026
RπK
ADS(π)=0.00360 ±0.00012 ±0.00009
RπK
ADS(K)=0.0188 ±0.0011 ±0.0010
AπK
ADS(π)=0.100 ±0.031 ±0.009
AπK
ADS(K)=−0.403 ±0.056 ±0.011,
RKπππ
K/π=0.0793 ±0.0010 ±0.0018
Rππππ =0.975 ±0.037 ±0.019
RπKππ
ADS(K)=0.0140 ±0.0015 ±0.0006
LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131 123
Fig. 5. In a ian mass dis ibu ions o selec ed B±→[K±π∓π+π−]Dh±candida es, sepa a ed by cha ge. See he cap ion o Fig. 1 o he defini ions. (Fo in e p e a ion o
he colou s in his figu e, he eade is e e ed o he web e sion o his a icle.)
Fig. 6. In a ian mass dis ibu ions o selec ed B±→[π±K∓π+π−]Dh±candida es, sepa a ed by cha ge. The dashed pink line le o he signal peak shows pa ially
econs uc ed B0
s→[K+π−π+π−]DK−π+decays, whe e he bachelo pion is missed. See he cap ion o Fig. 1 o o he defini ions. (Fo in e p e a ion o he e e ences o
colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.)
RπKππ
ADS(π)=0.00377 ±0.00018 ±0.00006
AKπππ
K=0.000 ±0.012 ±0.002
AπKππ
ADS(K)=−0.313 ±0.102 ±0.038
AπKππ
ADS(π)=0.023 ±0.048 ±0.005
Aππππ
K=0.100 ±0.034 ±0.018
Aππππ
π=−0.0041 ±0.0079 ±0.0024.
These esul s supe sede hose in Re s. [9] and [17] excep o
he esul s ela ing o he ou -pion Ddecay, which a e epo ed
o he fi s ime. The co ela ion ma ices a e gi en in he Ap-
pendix. The s a is ical co ela ions o he obse ables RADS and
AADS a e small. The al e na i e ADS obse ables a e calcula ed:
RπK
+(K)=(2.58 ±0.23)%; RπK
−(K)=(1.15 ±0.14)%; RπK
+(π)=(3.22 ±
0.18) ×10−3; RπK
−(π)=(3.98 ±0.19)×10−3;RπKππ
+(K)=(1.82 ±
0.25)%; RπKππ
−(K)=(0.98 ±0.20)%; RπKππ
+(π)=(3.68 ±0.26)×10−3;
and RπKππ
−(π)=(3.87 ±0.26)×10−3, whe e he quo ed unce ain-
ies combine s a is ical and sys ema ic e ec s.
The asymme ies in he wo CP-e en Ddecays, D →K+K−and
D →π+π−, a e a e aged by no ing ha hei sys ema ic unce -
ain ies a e nea ly ully co ela ed,
ACP(K)=0.097 ±0.018 ±0.009,
ACP(π)=−0.0098 ±0.0043 ±0.0021 .
Simila ly he a e age a io o pa ial wid hs om hese D
modes is
RKK,ππ=0.978 ±0.019 ±0.018(±0.010);
in his case he sys ema ic unce ain ies, which a e domina ed by
di e en backg ound es ima ions, a e only weakly co ela ed. The
hi d unce ain y a ises only when he simpli ying assump ion is
made ha B=0in B−→Dπ−decays. In his case, RKK,ππ
124 LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131
Fig. 7. In a ian mass dis ibu ions o selec ed B±→[π+π−π+π−]Dh±candida es, sepa a ed by cha ge. The dashed black line ep esen s he esidual con ibu ion om
cha mless decays. See he cap ion o Fig. 1 o o he defini ions. (Fo in e p e a ion o he colou s in his figu e, he eade is e e ed o he web e sion o his a icle.)
becomes equal o he classic GLW obse able RCP(K)[5]. This ad-
di ional unce ain y is applicable o he KK and ππ modes indi-
idually bu he equi alen unce ain y o he ou -pion mode is
lowe , ±0.005, due o he educed cohe ence in ha Ddecay.
The significance o hese measu emen s may be quan ified
om he likelihood a io wi h espec o a CP-symme ic null
hypo hesis, −2log(L0/L). The significance o CP iola ion in
he ADS mode B−→[π−K+]DK−is 8.0 σ(s anda d de ia ions)
and ep esen s he fi s obse a ion o CP iola ion in a single
B−→Dh−decay mode. The combina ion o he wo GLW modes
B−→[K+K−]DK−and B−→[π+π−]DK−also demons a es a
CP- iola ion e ec wi h 5.0 σsignificance. Taken oge he , he ADS
and GLW modes o he B−→Dπ−decays show e idence o CP
iola ion wi h 3.9 σsignificance a e accoun ing o sys ema ic
unce ain ies. The B−→[π+π−π+π−]DK−da a shows a 2.7 σ
CP- iola ion e ec .
6. Accep ance e ec s
The non-uni o m accep ance ac oss he phase space o he ou -
body modes a ec s he applicabili y o he ex e nal cohe ence
ac o and s ong phase di e ence measu emen s [11] in he in-
e p e a ion o hese esul s. Wi h an accep ance model o he
ou -body Ddecays om simula ion, he e ec i e alues o he
D →K+π−π+π−cohe ence pa ame e s a e calcula ed using a
ange o plausible ampli ude models. The accep ance is ound o
be almos uni o m and he e ec i e alues o he cohe ence pa-
ame e s a e close o hose o pe ec accep ance. The addi ional
sys ema ic unce ain ies on κK3πand δK3π
D, when in e p e ing he
ou -body esul s epo ed he e, a e ± 0.01 and ± 2.3◦. In a simi-
la s udy, he addi ional sys ema ic unce ain y associa ed wi h he
modula ion o he CP ac ion F4π
+by he LHCb accep ance is es i-
ma ed o be ± 0.02.
I has been shown ha D-mixing e ec s mus be aken in o
accoun when using hese CP obse ables in he de e mina ion
o γ[34]. The co ec ion is mos impo an in he ADS obse ables
o B−→Dπ−decays and is co ec ed o using knowledge o he
decay- ime accep ance. F om simula ion samples, a decay- ime ac-
cep ance unc ion is defined o bo h he wo-body and ou -body
D-mode selec ions. The D-mixing coefficien α, defined in [34], is
ound o be −0.59 and −0.57 o he wo- and ou -body cases,
wi h negligible unce ain ies compa ed o hose o he xand y
D-mixing pa ame e s.
7. Discussion and conclusions
Wo ld-bes measu emen s o CP obse ables in B−→Dh−de-
cays a e ob ained wi h he Dmeson econs uc ed in K−π+,
K+K−, π+π−, π−K+, K−π+π+π−and π−K+π+π−final
s a es; his supe sedes ea lie wo k [9,16]. Measu emen s exploi -
ing he ou -pion Ddecay a e epo ed o he fi s ime wi h he
B−→[π+π−π+π−]DK−decay showing an indica ion o CP i-
ola ion a he 2.7 σle el. The cha ge asymme y in his mode is
posi i e, simila o he classic GLW modes, B−→[K+K−]DK−and
B−→[π+π−]DK−, in line wi h expec a ion o a mul i-body D
mode wi h a CP ac ion g ea e han 0.5 [15].
A compa ison wi h SM expec a ion is made by calcula ing he
CP obse ables om cu en bes -fi alues o γ=(73.2+6.3
−7.0)◦as
well as δB=(125.4+7.0
−7.8)◦and B=(9.70+0.62
−0.63)% o B±→DK±
decays [2]. Fo B±→Dπ±decays, whe e no independen in-
o ma ion on Band δBis a ailable, uni o m PDFs a e used,
180◦<δ
B<360◦and 0.004 < B<0.008. The D-decay pa am-
e e s a e aken om he li e a u e: 2
D=(0.349 ±0.004)% and
δD=(191.8+9.5
−14.7)◦[35]; F4π
+=0.737 ±0.028 [15]; K3π
D=(5.52 ±
0.007)%, δK3π
D=(170+37
−39)◦and κK3π
D=0.32+0.12
−0.08 [11]. The cu en
wo ld a e ages o he D-mixing pa ame e s a e x =(0.37 ±0.16)%
and y =(0.66+0.07
−0.10)%[35], and he αcoefficien s epo ed in Sec. 6
a e used o he small D-mixing co ec ion. Fo hese inpu s, he
cen al 68% confidence-le el expec a ion in e al is displayed in
Fig. 8, oge he wi h he esul s p esen ed he ein. I is seen ha he
B−→DK−measu emen s a e compa ible wi h expec a ion and
ha he imp o emen in he knowledge o he AADS obse ables
is pa icula ly significan . The measu emen s p esen ed in his pa-
pe imp o e many o he CP obse ables used in global fi s o
he uni a i y iangle angle γas well as he had onic pa ame e s
Band δB o hese decays. An imp o emen in he global bes -fi
p ecision on γo a ound 15% is an icipa ed om his wo k.
Acknowledgemen s
We exp ess ou g a i ude o ou colleagues in he CERN ac-
cele a o depa men s o he excellen pe o mance o he LHC.
LHCb Collabo a ion / Physics Le e s B 760 (2016) 117–131 125
Fig. 8. Compa ison o selec ed esul s wi h an SM expec a ion (shaded) based on exis ing knowledge o he unde lying pa ame e s and D-decay measu emen s, as desc ibed
in he ex . The fi s fi e ows show B−→DK−obse ables, wo-body Ddecay on he le and ou -body on he igh . The las h ee ows show B−→Dπ−obse ables.
We hank he echnical and adminis a i e s a a he LHCb in-
s i u es. We acknowledge suppo om CERN and om he na-
ional agencies: CAPES, CNPq, FAPERJ and FINEP (B azil); NSFC
(China); CNRS/IN2P3 (F ance); BMBF, DFG and MPG (Ge many);
INFN (I aly); FOM and NWO (The Ne he lands); MNiSW and NCN
(Poland); MEN/IFA (Romania); MinES and FANO (Russia); MINECO
(Spain); SNSF and SER (Swi ze land); NASU (Uk aine); STFC (Uni ed
Kingdom); 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 Kingdom), 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 i-
ple open sou ce so wa e packages on which we depend. Indi id-
ual 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 ENIG-
MASS and OCEVU, Région Au e gne (F ance), RFBR and Yandex LLC
(Russia), GVA, Xun aGal 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).
Appendix A. Co ela ion ma ices
The s a is ical unce ain y co ela ion ma ices a e gi en in Ta-
ble A.4 and A.5 o he 2-body and 4-body fi s o da a. The co ela-
ions be ween sys ema ic unce ain ies a e p o ided in Tables A.6
and A.7.
