Measurement of CP observables in B± → DK± and B± → Dπ± with two- and four-body D decays

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

CP observables

in

B

±

→

D K

±

and

B

±

→

D

π

±

with two- and

four-body

D decays

.

LHCb

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received6April2016

Receivedinrevisedform8June2016 Accepted9June2016

Availableonline16June2016 Editor:W.-D.Schlatter

Measurements of CP observables in B±→D K± and B±→D

π

± decays are presented where the D mesonisreconstructedinthefinalstatesK±

π

∓,

π

±K∓,K+K−,

π

+

π

−,K±

π

∓

π

+

π

−,

π

±K∓

π

+

π

−and

π

+

π

−

π

+

π

−.ThisanalysisusesasampleofchargedB mesonsfrompp collisionscollectedbytheLHCb experimentin2011and2012,correspondingtoanintegratedluminosityof3.0 fb−1.VariousCP-violating effectsarereportedandtogetherthesemeasurementsprovideimportantinputforthedeterminationof theunitaritytriangleangle

γ

.Theanalysisofthefour-pionD decaymodeisthefirstofitskind.

©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Asetofoverconstrainingmeasurementsoftheunitaritytriangle fromtheCKM matrixiscentral to thevalidationofthe Standard Model(SM)descriptionofCP violation[1].Ofthese,theleast-well measuredistheangle

γ

≡

arg

(

−

V_udV_ub∗

/

V_cdV_cb∗

)

withaprecision, froma combination ofmeasurements, of about 7◦; this may be comparedwiththe 3◦ and

<

1◦ precision on theother angles

α

and

β

[2,3].Amongstthethreeangles,

γ

isuniqueinthatitdoes notdependonacouplingtothetopquarkandthusmaybe stud-iedattreelevel,largely avoidingpossibleinfluence fromnon-SM

CP violation.

Themostpowerfulmethodfordetermining

γ

intree-level de-cays isthrough measurement of relative partialwidths in B−

→

D K− decays, where D represents a D0 or D0 meson.1 The am-plitude for the B−

→

D0_K− _{contribution is proportional to V}

cb

while the amplitude for B−

→

D0K− is proportional to Vub.By

reconstructing hadronic D decays accessible to both D0 and D0

mesons,phaseinformationmaybeextractedfromtheinterference ofthetwoamplitudes.ThesizeoftheresultingdirectCP violation

isgovernedbythemagnitudeoftheratiorB oftheb

→

u

¯

cs

am-plitudetotheb

→

cus amplitude.

¯

The relativelylargevalue ofrB

(about0.1)inB−

→

D K−decaysmeansthattherelativephaseof thetwointerferingamplitudescanbeobtained.Thisrelativephase hasaCP-violating(weak)contributionandCP-conserving(strong) contribution

δ

B; a measurement of the total phase for both B+

and B− disentangles

γ

and

δ

B.Similar interferenceeffects occur

1 _{Theinclusionofcharge-conjugateprocessesisimpliedexceptinanydiscussion} ofasymmetry.

inB±

→

D

π

±decays,albeitwithreducedsensitivitytothephases because,duetoadditionalCabibbosuppressionfactors,theratioof amplitudesisabout20timessmaller.

The study of B−

→

D K− decays formeasurements of

γ

was first suggested for CP eigenstates of the D decay, for example the CP-even D

→

K+K− and D

→

π

+

π

− decays, labelled here GLWmodes[4,5].Theargumenthasbeenextendedtosuppressed

D

→

π

−K+decayswheretheinterplaybetweenthefavouredand suppressed decay paths in both the B− and the neutral D

de-cays results in a large charge asymmetry. This is the so-called ADSmode[6],whichintroduces adependencyontheratioofthe suppressed andfavoured D decayamplitudesrD andtheir phase

difference

δ

D.The B−

→ [

h+h−

]

Dh− ADS/GLW decays

(

h

=

K

,

π

)

havebeenstudiedattheB factories[7,8]andatLHCb[9].This let-tercontainstheupdatedandimprovedresultusingboththe2011 and2012datasamples.The2012databenefitsfromahigher B±

mesonproductioncross-sectionandamoreefficienttrigger,sothis updateisapproximatelyafactorfourincreaseinstatistics.

TheADS/GLWformalismcanbeextendedtofour-particleD

de-cays. However, there are multiple intermediate resonances with differingamplituderatiosandstrongphaseswiththeconsequence that the interference in the B− decay, and hence the sensitivity to

γ

,isdiluted[10].ForD

→

K−

π

+

π

+

π

−andD

→

π

−K+

π

+

π

−

decays this dilution is parameterised in terms of a coherence factor

κ

K 3_{π , an effective strong phase difference averaged over}

all contributing resonances

δ

K 3_D π, and an overall suppressed-to-favoured amplitude ratio rK 3_D π. Best sensitivity to

γ

is achieved using independent measurements of the

κ

K 3_{π and}

_δ

K 3π

D

param-eters, which have been determined using a sample of quantum-correlated D0D0 pairs [11,12], and by the study of D-mixing in

http://dx.doi.org/10.1016/j.physletb.2016.06.022

0370-2693/©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

thisfinal state [13]. Asimilar dilutionparameter, labelledthe CP

fractionF₊4π canbedefinedforD

→

π

+

π

−

π

+

π

−decays[14].For thisfinal state itis foundthat F₊4π

=

0

.

737

±

0

.

028 [15],so that thedecaybehaveslikeaCP-evenGLWmode,albeitwiththe inter-ferenceeffectsreducedbyafactor

(

2F₊4π

−

1

)

≈

0

.

5.

Thisletterincludesan analysisof B−

→ [

h+h−

π

+

π

−

]

Dh−

de-cays and supersedes the previous analysis of B−

→

[

π

−K+

π

+

π

−

]

Dh−[16] andcomplementsthestudyoftheB−

→

[

h+h−

π

0

_]

Dh− modes [17]. The analysis of the four-pion D

de-caymode isthefirstofits kind.In total,21measurementsofCP

observablesare reported.Twooftheseare ratiosof thefavoured

B−

→

D0K−andB−

→

D0

π

−partialwidths,

R_Kf_/π

=

(

B

−

_{→ [}

_f

_]

DK−

)

+ (

B+

→ [ ¯

f

]

DK+

)

(

B−

→ [

f

]

D

π

−

)

+ (

B+

→ [ ¯

f

]

D

π

+

)

,

(1)

where f is K−

π

+

(

π

−

π

+

)

and

¯

f is its charge-conjugate state. Three are double ratios that are sensitive to the partial widths of the (quasi-)GLW modes, f

=

π

+

π

−

(

π

+

π

−

)

and K+K−, nor-malisedtothoseofthefavouredmodesofthesamemultiplicity,

RK K

=

R K K K/π RK_Kπ_/π

,

R π π

₌

R π π K/π RK_Kπ_/π

,

R π π π π

₌

R π π π π K/π RK_Kπ π π_/π

.

(2)

Fiveobservablesarechargeasymmetries,

A_hf

=

(

B

−

_{→ [}

_f

_]

Dh−

)

− (

B+

→ [ ¯

f

]

Dh+

)

(

B−

→ [

f

]

Dh−

)

+ (

B+

→ [ ¯

f

]

Dh+

)

,

(3)

for h

=

K and f

=

K−

π

+

(

π

−

π

+

),

π

+

π

−

(

π

+

π

−

)

and K+K−. There are a further three asymmetries for h

=

π

and f

=

π

+

π

−

(

π

+

π

−

)

andK+K−.Fourobservablesarepartialwidthsof thesuppressedADSmodesrelativetotheircorrespondingfavoured decays, R_ADS¯f _(h)

=

(

B −

_{→ [ ¯}

_f

_]

Dh−

)

+ (

B+

→ [

f

]

Dh+

)

(

B−

→ [

f

]

Dh−

)

+ (

B+

→ [ ¯

f

]

Dh+

)

,

(4)

withwhichcomefourADS-modechargeasymmetries,

A_ADS¯f _(h)

=

(

B

−

_{→ [ ¯}

_f

_]

Dh−

)

− (

B+

→ [

f

]

Dh+

)

(

B−

→ [ ¯

f

]

Dh−

)

+ (

B+

→ [

f

]

Dh+

)

.

(5)

An alternative formulationof the ADS observables measures the suppressedADSmodesrelativetotheirfavoured counterparts, in-dependentlyfor B+ andB− mesons,

R₊₍¯f _h)

=

(

B +

_{→ [}

_f

_]

Dh+

)

(

B+

→ [ ¯

f

]

Dh+

)

,

R₋₍¯f _h)

=

(

B −

_{→ [ ¯}

_f

_]

Dh−

)

(

B−

→ [

f

]

Dh−

)

.

(6)

All the charge asymmetry measurements are affected by a pos-sible asymmetry in the B± production cross-section multiplied by any overall asymmetry from the LHCb detector, together de-noted as

σ

. This effective production asymmetry, defined as

AB±

=

σ

_(B−_)−σ_(B+₎

σ(B−)+σ(B+),ismeasuredinthisanalysisfromthecharge

asymmetry ofthemostabundant B−

→ [

K−

π

+

]

D

π

− and B−

→

[

K−

π

−

π

+

π

−

]

D

π

− modes.Thismeasurementisappliedasa

cor-rection to all other CP asymmetry results. In these modes, the possibleCP asymmetry, asderived fromexisting knowledgeof

γ

andrB inthisdecay[18],issmallerthantheuncertaintyon

exist-ing measurementsof the B± productionasymmetry [19].The CP

asymmetryisthusassumedtobezerowithasmallsystematic un-certainty.Remainingdetection asymmetries,notably between K−

andK+,arecorrectedforusingcalibrationsamples.

2. Detector and simulation

The LHCb detector [20] is a single-arm forward spectrometer covering the pseudorapidity range 2

<

η

<

5, designed for the studyofparticles containing b orc quarks.The detectorincludes a high-precision tracking systemconsisting ofa silicon-strip ver-tex detector surrounding the pp interaction region, a large-area silicon-strip detectorlocatedupstream ofadipole magnetwitha bending power ofabout 4 Tm, andthree stations of silicon-strip detectorsandstrawdrifttubesplaceddownstreamofthemagnet. Thetrackingsystemprovidesameasurementofmomentum, p,of chargedparticleswitharelativeuncertaintythatvariesfrom0.5% at low momentum to 1.0% at200 GeV/c. The minimum distance of atrackto aprimary vertex(PV), theimpact parameter (IP),is measured witha resolutionof

(

15

+

29

/

pT

)

μ

m,where pT isthe component ofthe momentum transverse to thebeam, inGeV

/

c. Different types ofcharged hadronsare distinguished using infor-mationfromtworing-imagingCherenkovdetectors.Photons, elec-tronsandhadronsareidentifiedbyacalorimetersystemconsisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadroniccalorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by asoftware stage,in whichall chargedparticles with

pT

>

500

(

300

)

MeV arereconstructedfor2011 (2012)data. At the hardware trigger stage, events are required to have a muon with high pT or a hadron, photon or electron with high transverse energy in the calorimeters. For hadrons, the trans-verse energy threshold is 3.5 GeV. The software trigger requires a two-,three- orfour-track secondaryvertexwithsignificant dis-placement fromthe primary pp interactionvertices. Atleast one chargedparticlemusthavetransversemomentum pT

>

1

.

7 GeV

/

c andbeinconsistentwithoriginatingfroma PV.Amultivariate al-gorithm [21] is used for the identification of secondary vertices consistentwiththedecayofab hadron.

In the simulation, pp collisions are generated using Pythia8 [22] with a specific LHCb configuration [23]. Decays of hadronic particles aredescribedby EvtGen[24],inwhichfinal-state radia-tionisgeneratedusingPhotos[25].The interactionofthe gener-atedparticleswiththedetector,anditsresponse,areimplemented usingtheGeant4 toolkit[26]asdescribedinRef.[27].

3. Event selection

Afterreconstructionofthe D mesoncandidatefromeithertwo or four charged particles, the same basic event selection is ap-plied toall B−

→

Dh− channelsofinterest.The reconstructed D

meson candidate mass is required to be within

±

25 MeV

/

c2 _of its known value [28]. This mass range corresponds to approxi-mately three times the mass resolution of the signal peaks. The kaonorpionoriginatingfromtheB±decay,subsequentlyreferred to as the bachelor particle, is required to have pT in the range 0

.

5–10

.

0 GeV

/

c and p in the range5–100 GeV

/

c. These require-ments ensure that the track iswithin the kinematic coverage of the RICHdetectors, whichare usedto provideparticle identifica-tion(PID)information.DetailsofthePIDcalibrationprocedureare givenin Sect.4. Inaddition,a kinematicfitisperformedtoeach decaychain,withvertexconstraintsappliedtoboththeB±andD

vertices,andthe D candidateconstrainedtoitsknownmass[29]. Events are required to have been triggered by either the decay productsofthesignalcandidateorparticlesproducedelsewherein the pp collision.TheB± mesoncandidateswithaninvariantmass intheinterval5079–5899 MeV

/

c2areretained.EachB±candidate isassociatedtothePVtowhichithasthesmallestIP.

For both the two- and four-body D-mode selections, a pair of boosted decision tree (BDT) discriminators, implementing the gradient boost algorithm [30], are employed to achieve further background suppression. The BDTs are trained using simulated

B−

→ [

K−

π

+

(

π

+

π

−

)

]

DK− decays together with a background

sample of K

π

± combinations with invariant mass in the range 5900–7200 MeV

/

c2.ForthefirstBDT,thosebackgroundswitha D

candidatemassmorethan

±

30 MeV

/

c2 _{awayfromtheknown D}0 massareusedinthetraining.InthesecondBDT,backgroundswith a D candidatemass within

±

25 MeV

/

c2 ofthe known D0 mass areused.Aloosecut ontheclassifierresponseofthefirstBDTis appliedpriortotrainingthesecondone.Thisfocussesthesecond BDTtraining onbackgroundsenriched withfullyreconstructed D

mesons.

TheinputtotheBDTisasetofquantitiesthatcharacterisethe signaldecay.Thesequantitiescan bedivided intotwocategories: (1)propertiesofanyparticleand(2)propertiesofcomposite par-ticlesonly(the D and B±candidates).Specifically:

1. p,pT andthesquareoftheIPsignificance;

2. decaytime,flightdistance,decayvertexquality,radialdistance betweenthedecayvertexandthePV, andtheanglebetween the particle’s momentum vector andthe lineconnecting the productionanddecayvertex.

Signal purity is improved by usinga variable that estimates the imbalanceofpT aroundtheB±candidate,definedas

I pT

=

pT

(

B±

)

− 

pT

pT

(

B±

)

+ 

pT

,

(7)

where the sum is taken over tracks lying within a cone around the B± candidate, excluding thetracks relatedto the signal. The coneisdefinedby acirclewitharadiusof1.5unitsintheplane ofpseudorapidityandazimuthalangle(expressed inradians).The BDT thus gives preference to B± candidates that are either iso-latedfromtherestoftheevent,orconsistentwitharecoilagainst anotherb hadron.

NoPIDinformationisusedintheBDTtrainingsotheefficiency for B−

→

D K− and B−

→

D

π

− decaysis similar, with insignifi-cantvariationsarisingfromthesmalldifferencesinthekinematics. Thecutson thetwo BDT selectionsare optimisedby minimising theexpecteduncertaintyon A_ADSπK(π π_(K)),asmeasured inthe invari-antmassfitdescribed below. Thepurityofthe sample isfurther improvedwithRICHinformationbyrequiringallkaonsandpions inthe D decaytobecorrectlyidentifiedwithaPIDselectionthat hasanefficiencyofabout85%perparticle.

Peakingbackgroundsfromcharmlessdecaysaresuppressedby requiringthat the flight distance significance ofthe D candidate

fromthe B± decayvertexislarger thantwo standarddeviations. Theresidualcharmlesscontributionisinterpolatedfromfitstothe

B± massspectrum(without thekinematicfitofthedecaychain) in both the lower and upper D-mass sidebands. The charmless yields are determined independently for B+ and B− candidates andare later usedin the massfit asfixed terms,with their un-certainties included in the systematic uncertainties of the final results. The largest residual charmless contributions are in the

B−

→ [

π

+

π

−

(

π

+

π

−

)

]

DK−modeswhichshowcharge-integrated

yieldsof88

±

11 and115

±

11 forthetwo- andfour-pionmodes. Thisis7%and8%ofthemeasuredsignalyields.

EvenwithPIDrequirements,thesuppressedADSsamples con-tain significantcross-feedfromfavoured signal decays wherethe

K− and a

π

+ from the D decay are misidentified as a

π

−

and K+. This contamination is reduced by removing any candi-date whose reconstructed D mass, under the exchange of mass

hypotheses between the kaon and an opposite-sign pion, lies within

±

15 MeV

/

c2 of theknown D0 mass.Thisvetoisalso ap-pliedtothefavouredmode,withthesameefficiency.Theresidual cross-feed rates are estimated in data from the favoured sam-ple, assuming the veto and PID efficiencies factorise; they are

(

4

.

3

±

0

.

2

)

×

10−5 for B−

→ [

K−

π

+

]

Dh− and

(

2

.

7

±

0

.

1

)

×

10−4

forB−

→ [

K−

π

+

π

+

π

−

]

Dh−.

Aftertheaboveselections,multiplecandidatesexistin0.1%and 1%ofeventsintheB−

→ [

h+h−

]

Dh−andB−

→ [

h+h−

π

+

π

−

]

Dh−

samples,respectively.Onlyonecandidatepereventisretainedfor themain fit.When morethanone candidateis selected,theone withthebestB±vertexqualityisretained.

4. Signal yields and systematic uncertainties

ThevaluesoftheCP observablesare determinedusingbinned maximum-likelihoodfitstotheinvariantmassdistributionsof se-lected B± candidates. Independent fits are used for the B−

→

[

h+h−

]

Dh− and B−

→ [

h+h−

π

+

π

−

]

Dh− samples. Information

from the RICH detectors is used to separate B−

→

D K−

from B−

→

D

π

− decays with a PID requirement on the bach-elor particle. Distinguishing between B+ and B− candidates, bachelor particle hypotheses, and four (three) D daughter final states, yields 16 (12) disjoint samples in the B−

→ [

h+h−

]

Dh−

(B−

→ [

h+h−

π

+

π

−

]

Dh−)fit,whicharefittedsimultaneously.The

total probability density function (PDF) is built from two signal PDFs,for B−

→

D K− andB−

→

D

π

− decays,andthreetypesof backgroundPDF.AllPDFsareidenticalforB+andB−decays.

1. B−

→

D

π

−

IntheD

π

−samplesanasymmetricdouble-Gaussian-like func-tionisusedforthe B±

→

D

π

±signal,

f

(

m

)

=

fcoreexp



−(

m

−

μ)

2 2

σ

2 c

+ (

m

−

μ)

2

α

L,R



+ (

1

−

fcore

)

exp



−(

m

−

μ)

2 2

σ

2 w



,

(8)

which has a peak position

μ

and core width

σ

c, where

α

L

(

m

<

μ

)

and

α

R

(

m

>

μ

)

parameterisethe tails.The

μ

and

α

parametersaresharedacrossallsamplesbutthecorewidth parametervariesindependentlyforeach D finalstate, except in the suppressed

π

K

(

π π

)

PDFs which are required to be identical to their favoured K

π

(

π π

)

counterpart. The addi-tional Gaussian function with a small fractional contribution ofabout1%isfoundnecessarytomodelsatisfactorilythetails ofthepeak.

The B−

→

D

π

− decaysmisidentifiedas B−

→

D K− are dis-placedtohighermassintheD K−subsamples.These misiden-tified candidates are modelled by the sum of two Gaussian functions with common mean but modified to include tail componentsasinEq.(8).The mean,widths andonetail pa-rameterarelefttovaryfreely.

2. B−

→

D K−

Inthe D K− samples,Eq.(8)isagainusedforthesignalPDF. The peakposition

μ

andthe two tailparameters

α

L and

α

R

are fixed to those ofthe B−

→

D

π

− signal function, asare thewidecomponentparameters fcoreand

σ

w.Thecorewidth

parameter in each D mode is related to the corresponding

B−

→

D

π

− widthby afreelyvarying ratiocommontoall D

finalstates.MisidentifiedB±

→

D K±candidatesappearinthe

D

π

−subsamplesandaredescribedbyafixedshapeobtained fromsimulation,whichislatervariedtodeterminea system-aticuncertaintyassociatedwiththischoice.

3. Combinatorial

background

Duetothelowbackgroundlevel,alinearfunctionissufficient todescribetheentireinvariantmassspectrum.Twocommon slopeparametersareused,oneforD

π

−andanotherforD K−

subsamplesbutyieldsvaryindependently. 4. Peaking

backgrounds

Charmless B± decayandthefavouredmode cross-feed back-groundsboth peak atthe B± mass andare indistinguishable from the signal. Their residual yields are estimated in data, entering the fit as fixed proportions of the favoured B−

→

D

π

− yield. A Gaussian function is used for the PDF, witha

(

25

±

2

)

MeV

/

c2 _{widthparameter thatis takenfrom} simula-tion;thisisabout50%widerthanthesignalPDF.

5. Partially

reconstructed

b -hadron

decays

Partially reconstructed backgrounds generally have lower in-variantmassthanthesignalpeak.Thedominantcontributions arefrom B−

→

Dh−

π

0_{, B}−

_→

_D∗0

_π

− _{and B}0

_→

_D∗+

_π

− de-cays where either a photon or a pion is missed in the re-construction.The distributionofeach ofthesesources inthe invariant mass spectrum depends on the spin and mass of the missing particle. If the missing particle has spin-parity 0−

(

1−

)

,thedistributionisparameterised byaparabolawith positive (negative) curvature convolved witha Gaussian res-olutionfunction. The kinematics of the decay that produced themissingparticle definethe endpointsofthe rangeofthe parabola. Decays in which both a particle is missed and a bachelor pion is misidentified as a kaon are parameterised witha semi-empiricalPDF,formed fromthesumofGaussian anderror functions. The parameters of each partially recon-structed PDF are fixed to the values found in fits to simu-lated events, and are varied as a source of systematic un-certainty.The yields ofeach contribution varyindependently in each subsample, where all partially reconstructed decay modesshareacommoneffectivechargeasymmetryacrossall

D modes.Thoughits effectismitigatedby the limitedrange ofthemassfit,largeCP violationinthelow-massbackground ispossibleintheGLWandADSsamples,soasystematic un-certaintyisassigned.

IntheB−

→ [

K+K−

]

Dh−samples,

Λ

0b

→ [

p+K−

π

+

]

Λ+ch − de-cays contribute to backgroundwhen the pion is missed and theprotonismisidentifiedasthesecondkaon.ThewidePDF of this componentis fixed from simulation but the yield in the B−

→ [

K+K−

]

D

π

− subsample varies freely. The

Λ

0_b

→

[

p+K−

π

+

]

Λ+cK

−_{yieldisconstrainedusingarecent} measure-mentof

B(Λ

_b0

→ Λ

+cK−

)/B(Λ

0b

→ Λ

+c

π

−

)

[31].Furthermore,

B0_s

→

D0K−

π

+decays,wherethepionismissed,forma back-ground for the suppressed B−

→

D K− modes. The yield of thiscomponentvariesinthe fitbutthe PDFis takenfroma simulationmodelofthethree-body B0

s decay[32],smearedto

matchtheresolutionmeasuredindata.

Inthe D K−subsamples,the B±

→

D

π

−cross-feedcanbe de-termined by the fit to data. The B−

→

D K− cross-feedinto the

D

π

− subsamples is not well separated frombackground, so the expectedyieldisdeterminedbyaPIDcalibrationprocedureusing approximately 20million D∗+

→ [

K−

π

+

]

D

π

+ decays.The clean

reconstruction ofthis charm decayis performedusingkinematic variablesonlyandthus providesahighpuritysample of K∓ and

π

± tracks, unbiased in the PID variables. The PID efficiency de-pends on track momentum and pseudorapidity, as well as the numberoftracks intheevent. The effectivePIDefficiencyofthe signalisdeterminedbyweightingthecalibrationsamplesuchthat the distributions of these variables match those of the selected candidates in the B−

→

D

π

− mass distribution. It is found that

Table 1

Signalyieldsasmeasuredinthe B−→ [h+h−]Dh− and

B−→ [h+h−π+π−]Dh−invariantmassfits,togetherwith theirstatisticaluncertainties.

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)) of B−

→

D K− decays passthe bachelor kaon PID

requirement;theremaining32.0%cross-feedintothe B−

→

D

π

−

sample.Withthisselection,approximately98%oftheB−

→

D

π

−

decays are correctlyidentified. Due to the size ofthe calibration sample,thestatisticaluncertaintyisnegligible;thesystematic un-certainty of the method is determined by the size of the signal track samples used, and thus increases for the lower statistics modes. Thesystematicuncertaintyon

PID(K) ranges from0.3%in B−

→ [

K−

π

+

]

DK−to1.5%in B−

→ [

π

+

π

−

π

+

π

−

]

DK−.

InordertomeasureCP asymmetries,thedetectionasymmetries for K± and

π

± must be taken into account. A detection asym-metry of

(

−

0

.

96

±

0

.

10

)

% is assignedfor each kaon in the final state, arising from thefact that the nuclear interaction length of

K− mesonsis shorterthanthat of K+ mesons.Thisiscomputed by comparing the charge asymmetries in D−

→

K+

π

−

π

− and

D−

→

KS0

π

− calibrationsamplesandweightingtothekinematics

ofthesignalkaons.Theequivalentasymmetryforpionsissmaller

(

−

0

.

17

±

0

.

10

)

% andistakenfromRef.[33].The CP asymmetries

in the favoured B−

→ [

K−

π

+

(

π

+

π

−

)

]

D

π

− decays are fixed to

zero,withasystematicuncertaintyof0.16%calculatedfrom exist-ingknowledgeof

γ

andrB inthisdecay[18],withnoassumption

madeaboutthestrongphase.Thisenablestheeffectiveproduction asymmetry, AB±, to be measured and simultaneously subtracted

from the charge asymmetry measurements in other modes. The signal yield foreachmode isa sumofthenumberofsignal and cross-feedcandidates;theirvaluesaregiveninTable 1.The corre-sponding invariant mass spectra,separatedby charge, are shown inFigs. 1–7.

To obtain the observables R_Kf_{/π ,} the ratio of yields must be corrected by the relative efficiency withwhich B−

→

D K− and

B−

→

D

π

− decaysare reconstructed andselected. From simula-tion, this ratio is found to be 1

.

017

±

0

.

017 and 1

.

018

±

0

.

026 forthe two- and four-body D decayselections. Theuncertainties are calculatedfrom the finite size of the simulatedsamples and accountforimperfectmodellingoftherelativepionandkaon ab-sorptioninthedetectormaterial.

The 21 observables of interest are free parameters of the fit. Thesystematicuncertaintiesassociatedwithfixedexternal param-eters are assessed by repeating the fit many times, varying the value of each external parameter accordingto a Gaussian distri-bution within itsuncertainty. The resultingspread(RMS)ineach observable’s value istaken asthe systematicuncertainty onthat observable dueto the external source. The systematic uncertain-ties, groupedintofourcategories, arelisted inTables 2 and 3for

Fig. 1. InvariantmassdistributionsofselectedB±→ [K±π∓]Dh± candidates,separatedbycharge,with B−(B+)candidatesontheleft(right).Thetopplotscontainthe

B±→D K±candidatesample,asdefinedbyaPIDrequirementonthebachelorparticle.Theremainingcandidatesareplacedinthebottomrow,reconstructedwithapion hypothesisforthebachelor.Thered(thick,open)andgreen(hatched-area)curvesrepresenttheB±→D K±and B±→Dπ±signals.Theshadedpartindicatespartially reconstructeddecays,thedottedline,wherevisible,showsthecombinatorialcomponent,andthetotalPDFisdrawnasathinblueline.(Forinterpretationofthereferences tocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig. 2. InvariantmassdistributionsofselectedB±→ [π±K∓]Dh±decays,separatedbycharge.Thedashedpinklineleftofthesignalpeakshowspartiallyreconstructed

B0

s→ [K+π−]DK−π+ decays,wherethebachelorpionismissed.Thefavouredmodecross-feedisalsoincludedinthefit,butistoosmalltobeseen.Seethecaptionof

Fig. 1forotherdefinitions.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

Table 2

SystematicuncertaintiesfortheB−→ [h+h−]Dh−CP observablesquotedasapercentageofthestatisticaluncertaintyontheobservable.PIDreferstothePIDcalibration procedure.Bkgreferstothechoiceofbackgroundshapesandyieldsinthefit.Simreferstotheuseoffinitesamplesofsimulatedeventstodetermineefficiencyratios.Asym referstothefixedpionandkaondetectionasymmetries,andtheassumptionofnoCP violationinB−→D0_π−_decays.

[%] AKπ K RKKπ/π AK KK AπK K RK K Aπ πK Aπ ππ Rπ π RπADSK(π ) RπADSK(K) Aπ K ADS(π ) AπADSK(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 Total 83 330 40 34 96 33 36 64 81 85 30 19 Table 3

SystematicuncertaintiesfortheB−→ [h+h−π+π−]Dh− CP observablesquotedasapercentageofthestatisticaluncertaintyontheobservable.SeetheTable 2captionfor definitions.

[%] RKπ π π

K/π Rπ π π π RπADSKπ π(K) RπADSKπ π(π ) AKKπ π π AπADSKπ π(K) AADSπKπ π(π ) Aπ π π πK Aπ π π ππ

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

Fig. 3. InvariantmassdistributionsofselectedB±→ [π+π−]Dh±candidates,separatedbycharge.Thedashedblacklinerepresentstheresidualcontributionfromcharmless decays.ThiscomponentispresentintheD finalstatesconsidered,butismostvisibleinthiscase.SeethecaptionofFig. 1forotherdefinitions.(Forinterpretationofthe coloursinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

Fig. 4. Invariant mass distributions ofselected B±→ [K+K−]Dh± candidates, separated by charge. The dashed cyan line represents partially reconstructed Λ0b→ [p+K−π+]Λ+ch

− _{decays,wherethepionismissedandthe protonismisidentifiedasakaon.SeethecaptionofFig. 1 forotherdefinitions. (Forinterpretationofthe}

referencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

thetwo-bodyandfour-bodyD modefits.Correlationsbetweenthe categoriesarenegligibleandthetotalsystematicuncertaintiesare givenbythesumsinquadrature.

5. Results

The results of the fits to data, withstatistical and systematic uncertainties,are: AK_Kπ

= −

0

.

0194

±

0

.

0072

±

0

.

0060 RK_Kπ_/π

=

0

.

0779

±

0

.

0006

±

0

.

0019 AK K_K

=

0

.

087

±

0

.

020

±

0

.

008 A_πK K

= −

0

.

0145

±

0

.

0050

±

0

.

0017 RK K

=

0

.

968

±

0

.

022

±

0

.

021 Aπ π_K

=

0

.

128

±

0

.

037

±

0

.

012 Aπ π_π

=

0

.

0043

±

0

.

0086

±

0

.

0031 Rπ π

=

1

.

002

±

0

.

040

±

0

.

026 Rπ_ADSK_(π)

=

0

.

00360

±

0

.

00012

±

0

.

00009 Rπ_ADSK_(K)

=

0

.

0188

±

0

.

0011

±

0

.

0010 Aπ_ADSK_(π)

=

0

.

100

±

0

.

031

±

0

.

009 Aπ_ADSK_(K)

= −

0

.

403

±

0

.

056

±

0

.

011

,

RK_Kπ π π_/π

=

0

.

0793

±

0

.

0010

±

0

.

0018 Rπ π π π

=

0

.

975

±

0

.

037

±

0

.

019 Rπ_ADSKπ π_(K)

=

0

.

0140

±

0

.

0015

±

0

.

0006

Fig. 5. InvariantmassdistributionsofselectedB±→ [K±π∓π+π−]Dh±candidates,separatedbycharge.SeethecaptionofFig. 1forthedefinitions.(Forinterpretationof thecoloursinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

Fig. 6. Invariantmassdistributionsofselected B±→ [π±K∓π+π−]Dh± candidates, separatedbycharge.Thedashed pinklineleftofthe signalpeakshowspartially reconstructedB0

s→ [K+π−π+π−]DK−π+decays,wherethebachelorpionismissed.SeethecaptionofFig. 1forotherdefinitions.(Forinterpretationofthereferencesto colourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

Rπ_ADSKπ π_(π)

=

0

.

00377

±

0

.

00018

±

0

.

00006 AK_Kπ π π

=

0

.

000

±

0

.

012

±

0

.

002 Aπ_ADSKπ π_(K)

= −

0

.

313

±

0

.

102

±

0

.

038 Aπ_ADSKπ π_(π)

=

0

.

023

±

0

.

048

±

0

.

005 Aπ π π π_K

=

0

.

100

±

0

.

034

±

0

.

018 Aπ π π π_π

= −

0

.

0041

±

0

.

0079

±

0

.

0024

.

These results supersede those in Refs. [9] and [17] except for theresultsrelating tothe four-pion D decay,which arereported forthe first time. The correlation matricesare given in the Ap-pendix. The statistical correlations for the observables RADS and AADS are small. The alternative ADS observables are calculated: Rπ₊₍K_K)

= (

2

.

58

±

0

.

23

)

%; Rπ₋₍K_K)

= (

1

.

15

±

0

.

14

)

%; Rπ₊₍K_π)

= (

3

.

22

±

0

.

18

)

×

10−3_{; Rπ}K

−(π)

= (

3

.

98

±

0

.

19

)

×

10−3; Rπ+(KKπ π)

= (

1

.

82

±

0

.

25

)

%; Rπ₋₍K_Kπ π₎

= (

0

.

98

±

0

.

20

)

%; Rπ₊₍K_π)π π

= (

3

.

68

±

0

.

26

)

×

10−3; and Rπ₋₍K_π)π π

= (

3

.

87

±

0

.

26

)

×

10−3, wherethe quoted uncertain-tiescombinestatisticalandsystematiceffects.

TheasymmetriesinthetwoCP-evenD decays,D

→

K+K−and

D

→

π

+

π

−, are averaged by notingthat their systematic uncer-taintiesarenearlyfullycorrelated,

ACP(K)

=

0

.

097

±

0

.

018

±

0

.

009

,

ACP(π)

= −

0

.

0098

±

0

.

0043

±

0

.

0021

.

Similarly the average ratio of partial widths from these D

modesis

R K K,π π

=

0

.

978

±

0

.

019

±

0

.

018

(

±

0

.

010

)

;

inthiscasethesystematicuncertainties,whicharedominatedby differentbackgroundestimations, areonly weaklycorrelated.The third uncertaintyarises only whenthe simplifying assumption is made that rB

=

0 in B−

→

D

π

− decays. In this case, R K K,π π

Fig. 7. InvariantmassdistributionsofselectedB±→ [π+π−π+π−]Dh±candidates,separatedbycharge.Thedashedblacklinerepresentstheresidualcontributionfrom charmlessdecays.SeethecaptionofFig. 1forotherdefinitions.(Forinterpretationofthecoloursinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

becomes equaltothe classicGLW observable RCP(K) [5].This

ad-ditionaluncertaintyis applicabletothe K K and

π π

modes indi-viduallybutthe equivalent uncertaintyforthefour-pion modeis lower,

±

0

.

005,duetothereducedcoherenceinthat D decay.

The significance of these measurements may be quantified from the likelihood ratio with respect to a CP-symmetric null hypothesis,



−

2 log

(L

0

/L)

. The significance of CP violation in the ADSmode B−

→ [

π

−K+

]

DK− is 8

.

0

σ

(standarddeviations)

and represents the first observation of CP violation in a single

B−

→

Dh−decaymode.Thecombinationofthetwo GLWmodes

B−

→ [

K+K−

]

DK− and B−

→ [

π

+

π

−

]

DK− also demonstrates a

CP-violationeffectwith5

.

0

σ

significance.Takentogether,theADS andGLW modes ofthe B−

→

D

π

− decays show evidence of CP

violation with 3

.

9

σ

significance after accounting for systematic uncertainties. The B−

→ [

π

+

π

−

π

+

π

−

]

DK− data shows a 2

.

7

σ

CP-violationeffect.

6. Acceptance effects

Thenon-uniformacceptanceacrossthephasespaceofthe four-body modes affects the applicability of the external coherence factor andstrong phase difference measurements [11] in the in-terpretation of these results. With an acceptance model for the four-body D decays from simulation, the effective values of the

D

→

K+

π

−

π

+

π

− coherence parameters are calculated using a rangeof plausible amplitude models. The acceptanceis found to be almost uniformand theeffective valuesof the coherence pa-rametersare closetothoseforperfectacceptance.The additional systematicuncertaintieson

κ

K 3_{π and}

_δ

K 3π

D ,wheninterpretingthe

four-bodyresultsreportedhere, are

±

0

.

01 and

±

2

.

3◦.Ina simi-larstudy,theadditionalsystematicuncertaintyassociatedwiththe modulationoftheCP fraction F₊4π bytheLHCbacceptanceis esti-matedtobe

±

0

.

02.

It has been shown that D-mixing effects must be takeninto account when using these CP observables in the determination of

γ

[34].ThecorrectionismostimportantintheADSobservables ofB−

→

D

π

− decaysandiscorrectedforusingknowledgeofthe decay-timeacceptance.Fromsimulationsamples,adecay-time ac-ceptancefunctionisdefinedforboththetwo-bodyandfour-body

D-modeselections.The D-mixingcoefficient

α

,definedin[34],is found to be

−

0

.

59 and

−

0

.

57 for the two- and four-body cases,

with negligible uncertainties compared to those of the x and y D-mixingparameters.

7. Discussion and conclusions

World-bestmeasurementsofCP observablesinB−

→

Dh− de-cays are obtained with the D meson reconstructed in K−

π

+,

K+K−,

π

+

π

−,

π

−K+, K−

π

+

π

+

π

− and

π

−K+

π

+

π

− final states;thissupersedesearlierwork[9,16].Measurements exploit-ingthefour-pion D decayarereportedforthefirsttime withthe

B−

→ [

π

+

π

−

π

+

π

−

]

DK− decayshowingan indication ofCP

vi-olationat the2

.

7

σ

level.The charge asymmetry inthismode is positive,similartotheclassicGLWmodes,B−

→ [

K+K−

]

DK−and

B−

→ [

π

+

π

−

]

DK−, in linewithexpectation fora multi-body D

modewithaCP fractiongreaterthan0.5[15].

AcomparisonwithSM expectationismadeby calculatingthe

CP observables fromcurrent best-fitvaluesof

γ

= (

73

.

2+6₋₇._.3₀

)

◦ as well as

δ

B

= (

125

.

4+₋77..08

)

◦ andrB

= (

9

.

70₋+00..6263

)

% for B±

→

D K± decays [2]. For B±

→

D

π

± decays, where no independent in-formation on rB and

δ

B is available, uniform PDFs are used,

180◦

< δ

B

<

360◦ and 0

.

004

<

rB

<

0

.

008. The D-decay

param-eters are taken from the literature: r2_D

= (

0

.

349

±

0

.

004

)

% and

δ

D

= (

191

.

8+₋149..57

)

◦[35];F 4π +

=

0

.

737

±

0

.

028[15];rK 3D π

= (

5

.

52

±

0

.

007

)

%,

δ

K 3_D π

= (

170+₋37₃₉

)

◦and

κ

K 3π D

=

0

.

32+ 0.12 −0.08 [11].Thecurrent worldaveragesoftheD-mixingparametersarex

= (

0

.

37

±

0

.

16

)

% andy

= (

0

.

66+₋₀0_..₁₀07

)

%[35],andthe

α

coefficientsreportedinSec.6 are usedfor thesmall D-mixingcorrection. Fortheseinputs, the central 68% confidence-level expectation interval is displayed in Fig. 8,togetherwiththeresultspresentedherein.Itisseenthatthe

B−

→

D K− measurements are compatible with expectation and that the improvement inthe knowledge ofthe AADS observables isparticularlysignificant.Themeasurementspresentedinthis pa-per improve many of the CP observables used in global fits for the unitaritytriangleangle

γ

aswell asthe hadronicparameters

rB and

δ

B forthesedecays.Animprovementintheglobalbest-fit

precisionon

γ

ofaround15%isanticipatedfromthiswork.

Acknowledgements

We express our gratitude to our colleagues in the CERN ac-celerator departments for the excellent performance of the LHC.

Fig. 8. ComparisonofselectedresultswithanSMexpectation(shaded)basedonexistingknowledgeoftheunderlyingparametersandD-decaymeasurements,asdescribed inthetext.ThefirstfiverowsshowB−→D K−observables,two-bodyD decayontheleftandfour-bodyontheright.ThelastthreerowsshowB−→Dπ−observables. We thank the technical andadministrative staff at the LHCb

in-stitutes. We acknowledge support from CERN and from the na-tional agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN(Italy); FOMandNWO (TheNetherlands);MNiSWandNCN (Poland);MEN/IFA (Romania);MinESandFANO(Russia);MINECO (Spain);SNSFandSER(Switzerland);NASU(Ukraine);STFC(United Kingdom);NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Ger-many), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (UnitedKingdom), RRCKIandYandexLLC(Russia), CSCS (Switzer-land),IFIN-HH(Romania),CBPF(Brazil),PL-GRID(Poland)andOSC (USA). We are indebted to the communities behind the multi-pleopensource softwarepackageson whichwedepend.

Individ-ualgroupsor membershavereceived supportfromAvH Founda-tion(Germany),EPLANET,MarieSkłodowska-CurieActionsandERC (European Union), Conseil Général de Haute-Savoie, Labex ENIG-MASSandOCEVU,RégionAuvergne(France),RFBRandYandexLLC (Russia),GVA,XuntaGalandGENCAT(Spain),HerchelSmithFund, The Royal Society, Royal Commission for the Exhibition of 1851 andtheLeverhulmeTrust(UnitedKingdom).

Appendix A. Correlation matrices

Thestatisticaluncertaintycorrelation matricesaregivenin Ta-ble A.4 and A.5forthe2-bodyand4-bodyfitstodata.The correla-tions betweensystematicuncertainties areprovidedinTables A.6 andA.7.

Table A.4

Statisticalcorrelationmatrixfromforthe2-bodyfit.

AKKπ R Kπ K/π AK KK AK Kπ RK K Aπ πK Aπ ππ Rπ π RπADSK(π ) Rπ K ADS(K) Aπ K ADS(π ) Aπ K ADS(K) AKπ K 1 0.00 0.02 0.09 0.00 0.01 0.05 0.00 0.00 0.00 0.01 0.01 RKKπ/π 1 0.00 0.00 −0.32 0.00 0.00 −0.18 0.01 −0.11 0.00 0.00 AK K K 1 −0.01 −0.01 0.00 0.02 0.00 0.00 0.00 0.00 0.00 AK K π 1 0.00 0.02 0.06 0.00 0.00 0.00 0.02 0.01 RK K _{1 0.00 0.00 0.06 −0.01 0.04 0.00 0.00} Aπ πK 1 −0.04 −0.04 0.00 0.00 0.00 0.00 Aπ π π 1 0.00 0.00 0.00 0.01 0.01 Rπ π _{1 0.00 0.02 0.00 0.00} RπADSK(π ) 1 −0.02 −0.04 0.00 RπK ADS(K) 1 0.02 0.10 AπK ADS(π ) 1 −0.05 AπK ADS(K) 1 Table A.5

Statisticalcorrelationmatrixfromforthe4-bodyfit.

RKKπ π π/π A Kπ π π K Rπ π π πC P Aπ π π ππ Aπ π π πK Rπ Kπ π A D S(K) Rπ Kπ π A D S(π ) Aπ Kπ π A D S(K) Aπ Kπ π A D S(π ) RKπ π π K/π 1 0.00 −0.31 0.00 0.00 −0.10 0.01 0.00 0.00 AKKπ π π 1 0.00 0.10 0.02 0.00 0.00 0.01 0.02 Rπ π π π C P 1 −0.00 −0.02 0.04 0.00 0.00 0.00 Aπ π π π π 1 −0.02 0.00 0.00 0.01 0.02 Aπ π π πK 1 0.00 0.00 0.00 0.00 RπA D SKπ π(K) 1 −0.05 0.08 0.01 RπKπ π A D S(π ) 1 0.00 −0.02 AπKπ π A D S(K) 1 −0.06 AπA D SKπ π(π ) 1 Table A.6

Correlationmatrixforthesystematicuncertaintiesinthe2-bodyanalysis.

AKKπ R

Kπ

K/π AK KK AπK K RK K Aπ πK Aπ ππ Rπ π RADS(π ) RADS(K) AADS(π ) AADS(K)

AKπ K 1 −0.03 0.20 0.21 0.00 0.01 0.36 −0.00 0.07 −0.09 −0.52 0.09 RKπ K/π 1 0.09 −0.10 −0.10 −0.06 −0.03 0.24 −0.01 −0.22 −0.03 −0.13 AK K K 1 −0.46 −0.29 0.03 0.24 0.01 −0.06 −0.10 0.05 −0.04 AK K π 1 0.18 0.32 0.50 −0.11 −0.15 0.31 0.42 0.33 RK K _{1 0.12 −0.05 0.19 0.12 0.32 0.07 0.23} Aπ πK 1 0.05 −0.30 −0.33 0.39 0.38 0.30 Aπ π π 1 −0.03 0.07 −0.06 0.25 0.11 Rπ π _{1 0.18 −0.16 −0.11 −0.06} RADS(π ) 1 −0.57 −0.56 −0.44 RADS(K) 1 0.56 0.76 AADS(π ) 1 0.40 AADS(K) 1 Table A.7

Correlationmatrixforthesystematicuncertaintiesinthe4-bodyanalysis.

RKKπ π π/π Rπ π π πC P Rπ Kπ π A D S(K) Rπ Kπ π A D S(π ) ABu AKKπ π π Aπ Kπ π A D S(K) Aπ Kπ π A D S(π ) Aπ π π πD K Aπ π π πDπ RKπ π π K/π 1 0.11 −0.04 0.13 −0.01 0.00 −0.13 0.17 −0.14 0.08 Rπ π π πC P 1 0.04 −0.06 0.01 0.02 −0.04 −0.04 0.07 −0.07 RπKπ π A D S(K) 1 0.14 −0.00 0.02 0.87 0.10 0.03 0.01 RπKπ π A D S(π ) 1 −0.04 −0.02 0.05 0.46 −0.35 0.24 ABu 1 −0.36 −0.05 −0.42 −0.03 −0.64 AKπ π π K 1 0.02 0.05 0.09 0.32 AπKπ π A D S(K) 1 −0.09 −0.04 0.02 AπKπ π A D S(π ) 1 −0.34 0.43 Aπ π π πD K 1 0.31 Aπ π π π Dπ 1

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Z. Ajaltouni

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G. Alkhazov

31

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P. Alvarez Cartelle

54

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A.A. Alves Jr

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S. Amato

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S. Amerio

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Y. Amhis

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L. An

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L. Anderlini

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G. Andreassi

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M. Andreotti

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R.B. Appleby

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11

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F. Archilli

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P. d’Argent

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A. Artamonov

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M. Artuso

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E. Aslanides

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G. Auriemma

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