University of Groningen
Search for CP violation in Lambda(0)(b)-> pK(- )and Lambda(0)(b) -> p pi(-) decays
Onderwater, C. J. G.; LHCb Collaboration
Published in:
Physics Letters B
DOI:
10.1016/j.physletb.2018.10.039
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Onderwater, C. J. G., & LHCb Collaboration (2018). Search for CP violation in Lambda(0)(b)-> pK(- )and
Lambda(0)(b) -> p pi(-) decays. Physics Letters B, 787, 124-133.
https://doi.org/10.1016/j.physletb.2018.10.039
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Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Search
for
CP violation
in
Λ
0
b
→
p K
−
and
Λ
0
b
→
p
π
−
decays
.
LHCb
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received18July2018
Receivedinrevisedform21September 2018
Accepted19October2018 Availableonline24October2018 Editor:L.Rolandi
A search for CP violation in Λ0
b→p K− and Λ0b→p
π
− decays is presented using a sample of pp collisions collectedwiththe LHCbdetector andcorresponding toan integratedluminosity of3.0 fb−1. TheCP-violatingasymmetriesaremeasuredtobeAp KCP−= −0.020±0.013±0.019 andACPpπ−= −0.035± 0.017±0.020,andtheirdifference Ap KCP−−ACPpπ−=0.014±0.022±0.010,wherethefirstuncertainties arestatisticalandthesecondsystematic.Thesearethemostprecisemeasurementsofsuchasymmetries todate.©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
The non-invariance of weak interactions under the combined applicationof charge conjugation (C )and parity( P ) transforma-tionsisaccommodatedwithintheStandardModelbytheCabibbo– Kobayashi–Maskawamechanism [1,2].TheviolationoftheCP
sym-metry was discovered in neutral-kaon decays [3], and later ob-served with B0 [4–12], B+ [13] and B0
s mesons [12,14].First
ev-idence for CP violation in the b-baryon sector was found more recently [15]. The decays
Λ
0b→
p K− andΛ
0b→
pπ
− are medi-atedbythesamequark-leveltransitionscontributingtocharmless two-body B0 and B0s decays to charged pions and kaons, where nonzero values of the CP asymmetries are well established [14]. Theinclusionofcharge-conjugateprocessesisimpliedthroughout. Predictions for the CP asymmetries in the decays of theΛ
0bbaryon to two-body charmless final states p K− or p
π
− range fromafew percentin thegeneralised factorisationapproach [16, 17] up to approximately 30% within the perturbative quantum-chromodynamicsformalism [18].Theonlymeasurementsofthese quantitiesavailabletodatewereperformedbytheCDF Collabora-tion [12].Theasymmetrieswerefoundtobecompatiblewithzero withinanuncertaintyof8 to9%.ThisLetter reportson a search forCP violation in
Λ
0b→
p K−and
Λ
0b→
pπ
− decays,using pp-collisiondatacollected withthe LHCbdetectoratcentre-of-massenergies of7and8 TeV and cor-respondingto3.0 fb−1ofintegratedluminosity.TheCP asymmetryisdefinedas ACPf
≡
(Λ
0 b→
f)
− (Λ
0 b→
f)
(Λ
0b→
f)
+ (Λ
0b→
f)
,
(1)where
is the partial width of the given decay, with f
≡
p K−(
pπ
−)
and f≡
p K+(
pπ
+)
. In addition, the difference ofthe two CP asymmetries,
ACP
≡
Ap K −CP
−
Apπ−
CP ,is alsoreported.
Asthemainsystematicuncertaintiescancelinthedifference,this quantity willbecome useful withthe increasing size of the data sample.
TheLetterisorganisedasfollows.Afterabriefintroductionon thedetector,triggerandsimulationinSec.2,theformalismneeded to relate the physical CP asymmetries to the experimental mea-surementsispresentedinSec.3.Then,theeventselectionandthe invariant-massfitaredescribed inSecs. 4and5,respectively.The determinationofinstrumentalasymmetriesandsystematic uncer-taintiesisdiscussedinSec.6.Finally,resultsaregivenand conclu-sionsaredrawninSec.7.
2. Detector,triggerandsimulation
The LHCb detector [19,20] isa single-armforward spectrome-tercoveringthepseudorapidity range 2
<
η
<
5,designedforthe studyofparticles containing b orc quarks.The detectorincludes ahigh-precisiontrackingsystemconsistingofasilicon-stripvertex detector surrounding the pp interaction region [21], a large-area silicon-strip detectorlocatedupstream ofadipole magnetwitha bending power ofabout 4Tm, andthree stations of silicon-strip detectors and straw drift tubes [22] placed downstream of the magnet. Thetracking systemprovides ameasurement ofthe mo-mentum, p, of chargedparticles witha relative uncertaintythat variesfrom0.5%atlowmomentumto1.0%at200 GeV/c.The min-imum distance of a track to a primary vertex (PV), the impact parameter(IP),ismeasuredwitharesolutionof(
15+
29/
pT)
μm, where pT is thecomponent ofthe momentum transverse to the beam, in GeV/c. Different types of charged hadrons are distin-guished usinginformation fromtwo ring-imaging Cherenkov de-tectors [23]. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshowerhttps://doi.org/10.1016/j.physletb.2018.10.039
0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
detectors,anelectromagneticcalorimeterandahadronic calorime-ter. Muons are identified by a system composed of alternating layersofiron andmultiwireproportional chambers [24]. The on-lineeventselectionisperformedbya trigger [25],whichconsists of a hardware stage, based on information fromthe calorimeter andmuon systems,followedby asoftwarestage,whichapplies a fulleventreconstruction.
Simulated events are used to study the modelling of var-ious mass line shapes. In the simulation, proton–proton colli-sions are generated using Pythia [26] with a specific LHCb con-figuration [27]. Decays of hadronic particles are described by EvtGen [28], in which final-state radiation is generated using Photos[29]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [30] asdescribedinRef. [31].
3. Formalism
TheCP asymmetries of
Λ
0b→
p K− andΛ
0b→
pπ
− decaysare approximatedasthesumsofvariousexperimentalquantitiesAp KCP−
=
Ap Kraw−−
ADp−
AK − D−
A p K− PID−
A Λ0b P−
A p K− trigger,
(2) ACPpπ−=
Arawpπ−−
ApD−
Aπ − D−
A pπ− PID−
A Λ0b P−
A pπ− trigger,
(3) where Arawf is the measured raw asymmetry between the yields ofthe decaysΛ
0b→
f andΛ
0b→
f ,with f=
p K−(
pπ
−)
and fitscharge conjugate; Ah
Distheasymmetry betweenthedetection efficienciesforparticleh anditschargeconjugate,withh
=
p,
K−or
π
−; the symbol APIDf stands for the asymmetry between the particle-identification(PID)efficienciesforthefinalstates f and f ;AΛ 0
b
P is the asymmetry betweenthe production cross-sectionsof
Λ
0b andΛ
0b baryons; and Atriggerf is the asymmetry between the trigger efficiencies for the particles in the final states f and f .Thislinearapproximation isvalidto agoodenoughaccuracydue tothesmallnessofthetermsinvolved.
Therawasymmetryisdefinedas
Arawf
≡
N
(Λ
0b→
f)
−
N(Λ
0b→
f)
N
(Λ
0b→
f)
+
N(Λ
0b→
f)
,
(4)where N denotes the observed signal yield for the given decay, obtainedinthisanalysisbymeansofextendedbinned maximum-likelihoodfitstothe p K−andp
π
−invariant-massspectra.Theproton, kaonandpion detectionasymmetries aredefined as ADp
≡
ε
p rec−
ε
recpε
recp+
ε
recp,
ADK−≡
ε
K− rec−
ε
K + recε
K− rec+
ε
recK+,
AπD−≡
ε
π− rec−
ε
π + recε
recπ−+
ε
recπ+,
(5)where
ε
rec is the total efficiency to reconstruct the given parti-cle, excluding PID. Such asymmetries are mostly due to the dif-ferentinteractioncross-sectionsofparticlesandantiparticleswith the detectormaterial. The kaon andpion detection asymmetries aremeasured usingcharm-mesoncontrol samplesemploying the procedures described in Refs. [32,33]. The kaon detection asym-metry is obtained by subtracting the raw asymmetries of theD+
→
K0S
π
+ and D+→
K−π
+π
+ decay modes and correcting fortheK0( AK0D ) [32] andpiondetectionasymmetries.Thelatteris measuredfromtheratioofpartiallytofullyreconstructed D∗+
→
D0(
→
K−π
+π
+π
−)
π
+ decays.The protondetection asymmetry isobtainedfromsimulatedevents.ThePIDasymmetriesaremeasuredfromlargecalibration sam-plesandaredefinedas
APIDf
≡
ε
f PID−
ε
f PIDε
PIDf+
ε
PIDf,
(6)where
ε
PIDf(f)isthePIDefficiencyforafinalstate f(
f)
givenaset ofPIDrequirements.The
Λ
0b productionasymmetryisdefinedasAΛ 0 b P
=
σ
(Λ
0b)
−
σ
(Λ
0b)
σ
(Λ
0b)
+
σ
(Λ
0b)
,
(7)where
σ
denotes the inclusive production cross-section in the LHCb acceptance. The production asymmetry is taken as an ex-ternalinput,followingRef. [34].Finally, asymmetries may arise if the hardware and software trigger usedto collect datado not havethe sameefficiencies on oppositely charged particles. These effects are estimatedthrough variousdata-driventechniques,asdescribedinSec.6.
4. Eventselection
Theeventselectionstartswiththereconstructionofb hadrons
formed by two oppositely charged tracks with pT
>
1 GeV/c, in-consistent with originating from anyPV and required to form a commonvertex. Eachb-hadron candidateneeds to have a trans-verse momentum greater than 1.
2 GeV/c and an invariant mass, computedassigningthepionmasstobothdaughtertracks,inthe rangebetween4.8and5.8 GeV/c2.Finally,eachb-hadroncandidate isrequiredtobeconsistentwithoriginatingfromaPV.Particle-identificationselectioncriteriaareappliedtodividethe datasample intomutuallyexclusivesubsamples correspondingto thefinal-statehypotheses p K−, p K+, p
π
−, pπ
+, K+π
−, K−π
+,K+K− and
π
+π
−. The latter four combinations are selected to study the background due to two-body B decays, where one or bothfinal-stateparticlesaremisidentified.The event selection is further refined using a boosted deci-sion tree (BDT) classifier [35,36] to reject combinatorial back-ground.Thisalgorithmcombinestheinformationfromseveral in-putquantitiestoobtainadiscriminantvariableusedtoclassifythe
b-hadroncandidatesassignalorbackground.Thefollowing prop-erties ofthe final-state particles are used asinput variables: the transverse momentum ofthe b-hadron decayproducts, the loga-rithmsoftheir
χ
2IP values,where
χ
IP2 isdefinedasthedifference in the vertex-fitχ
2 ofa givenPV reconstructed with and with-outthecandidateunderconsideration,thequalityofthecommon vertexfit of thetwo tracks and thedistance ofclosest approach betweenthetwotracks.TheBDTalsoexploitsthefollowing prop-erties ofthe b-hadron candidate: the transverse momentum, theχ
2IPquantity,andthelogarithmoftheflight distancewithrespect to the associated PV, defined asthat with the smallest
χ
2IP with respecttotheb-hadroncandidate.TheBDTistrainedusing simu-latedsignaldecaysandcombinatorialbackgroundeventsfromdata inthehigh-masssideband.
TheselectioncriteriaontheBDTclassifierandthePIDvariables areoptimisedseparatelyforthe
Λ
0b→
p K−andΛ
0b→
pπ
−decays. Twodifferentselections,denotedhereafterasSp K− and Spπ−,areaimed at obtaining the best statisticalsensitivity on each ofthe two CP asymmetries.CommonPID requirementsareused forthe final states containing only kaons andpions. Multiplecandidates are present inless than 0.05%of the eventsin the final sample. Only one candidate is acceptedfor each eventon the basis ofa reproduciblepseudorandomsequence.
Fig. 1. Invariant-massdistributions:(topleft)mp K−,(topright)mp K+,(bottomleft)mpπ−and(bottomright)mpπ+forcandidatespassingthe(top)Sp K−and(bottom)Spπ− selections.Theresultsofthefitsaresuperimposed.
5. Invariant-massfit
Foreachfinal-statehypothesis,namelyp K−,p K+, p
π
−,pπ
+,K+
π
−, K−π
+, K+K−andπ
+π
−,theinvariant-massdistribution of selected candidates is modelled by an appropriate probability densityfunction.Thesemodelsareusedtoperformasimultaneous fittothe eightinvariant-mass spectraanddetermineatoncethe yieldsofalltwo-bodyb-hadron decayscontributingtothespectra. Threecategoriesareconsideredforthebackground:combinatorial, dueto random association of tracks; partially reconstructed, due tomultibody b-hadrondecayswithoneormoreparticles not re-constructed;andcross-feed,arisingfromothertwo-bodyb-hadrondecayswhereoneorbothfinal-stateparticlesaremisidentified. The model used to describe each signal is obtained by con-volving the sum oftwo Gaussian functionswith common mean, accountingformass-resolutioneffects,withapower-lawfunction that accountsfor final-state photon radiationeffects. The power-lawdistributionistakenfromanalyticalquantum-electrodynamics calculations [37] and the correctness of the model is checked againstsimulatedeventsgeneratedwithPhotos[29].The param-etergoverning the taildueto final-state photon radiationeffects is different for each decay mode. This model describes well the invariant-massdistributionspredictedbythesimulation.
The combinatorial background is modelled using exponential functions.Thepartiallyreconstructedbackgroundisparameterised usingARGUSfunctions [38] convolvedwiththesumoftwo Gaus-sianfunctionswithzeromeanvalues,whoserelativefractionand widths are incommon withthe signal model. Finally,the cross-feedbackgroundismodelled usingsimulatedtwo-bodyb-hadron
decaysandakernelestimationmethod [39].Thecross-feed
back-ground yields are set to the corresponding two-body b-hadron
decay yields, determined by the simultaneous fit, multiplied by appropriate PID efficiency ratios. The efficiencies for a given PID requirementareobtainedfromlargecalibrationsamplesofD∗+
→
D0(
→
K−π
+)
π
+,Λ
→
pπ
− andΛ
+c→
p K−π
+ decays,withthe aidofsimulatedeventsinthecaseofprotonstoaccountfor phase-space regions not covered by the calibrationsamples (about20% oftheprotonsfromsignaldecays).Theefficienciesaredetermined inbinsofparticlemomentum,pseudorapidityandtrack multiplic-ity, as the performances of the RICH detectors depend on such variables. Theyarethen averagedoverthe momentumand pseu-dorapidity distributions of the final-state particles and over the distributionoftrackmultiplicityinselectedevents.AftertheapplicationoftheoptimalBDTandPIDrequirements, an extended binned maximum-likelihood fit with a bin width of 5 MeV/c2 is performed simultaneously to the eight two-body invariant-mass spectra for each of the two selections, Sp K− and Spπ−.Themp K− andmpπ− invariant-massdistributionsareshown
in Fig.1,withtheresultsofthe fitssuperimposed.The valuesof the raw asymmetries andof the signal yields obtainedfrom the fits tothe candidatespassing therespective Sp K− or Spπ−
selec-tionare Arawp K−
= (
1.
0±
1.
3)
%, Apπ− raw
= (
0.
5±
1.
7)
%,N p K− sig+
N p K+ sig=
8847±
125 andNsigpπ−+
Nsigpπ+=
6026±
105.The fit is validated by generating a large number of pseudo-experimental datasamplesaccordingtothe totalprobability den-sity function of the model and performing an extended binned maximum-likelihood fitto each sample. Theresulting pull distri-butions for Ap Kraw− and Apπ
−
raw are found to be Gaussian withzero meansandunitarywidths.
Fig. 2. Distributionsof(top)momentum,(middle)transversemomentumand(bottom)pseudorapidityfor(left)protonsfromΛ0
bdecaysand(right)Λ0bbaryons.The
distri-butionsarebackground-subtractedandnormalisedtounitarea.BeloweachplottheratiobetweenthetwodistributionscorrespondingtoΛ0b→p K−andΛ
0
b→pπ−decays
isalsoshown.
6. Instrumentalasymmetriesandsystematicuncertainties
Thedeterminationoftheinstrumentalasymmetriesintroduced inEqs. (2) and (3) iscrucialtoobtaintheCP asymmetries,as de-scribedinSec.3.
The kaon detection asymmetry is determined as a function of the kaon momentum, following the approach developed in Ref. [32] and subtracting ADK0
= (
0.
054±
0.
014)
% [32] and the piondetectionasymmetry. The momentum-dependentvalues are then weighted with the background-subtracted [40] momentum distribution of kaons fromΛ
0b→
p K− decays to obtain AK−D
=
(
−
0.
76±
0.
23)
%, where the dominant uncertainty is due to the finitesize ofthe samplesused. The piondetectionasymmetry is obtainedinananalogousway,adoptingtheapproachofRef. [33], and is determined to be AπD−= (
0.
13±
0.
11)
%. A different ap-proachis followed forthe proton detectionasymmetry, since no measurementofthisquantityisavailabletodate.Simulatedevents are used to obtain the reconstruction efficiency defined as the numberofreconstructedover generateddecays,inbinsofproton momentum.Then, according to Eq. (5), an asymmetry is defined andweights are computed from the background-subtracted [40] proton-momentumdistributionsofΛ
0b→
p K−andΛ
0b→
pπ
− de-cays.Theprotondetectionasymmetriesforbothdecaysarefound tobeequal,consistentwiththefactthatthekinematicsofthe pro-tonsforthe two decays do not exhibit significant differences, as showninFig.2.Thecommonvalueis ADp= (
1.
30±
0.
03±
0.
16±
0.
65)
%,where thefirstuncertaintyisduetothefiniteamountofsimulatedeventsandthesecondisassociatedtotheknowledgeof thematerialbudgetoftheLHCb detector.Thethirduncertaintyis duetotheassumptionsmadeontheprotonandantiproton cross-sectionsusedinthecomputation.
The PID asymmetries are calculated using calibration samples withtheaidofsimulationtoaccountforthelimitedphase-space coverage of the protons from
Λ
→
pπ
− andΛ
+c→
p K−π
+ de-cays. The dominantuncertainty comes fromdifferent PID perfor-mances in data andsimulation in the phase-space region where simulatedeventsare used.Thisdiscrepancyhasbeenstudied us-ing B0→
K+π
− decays, for which the phase-space coverage of calibration data is larger. The values of thePID asymmetries are foundtobe Ap KPID−= (−
0.
30±
0.
74)
% and APIDpπ−= (−
0.
18±
0.
73)
%. TheintegratedΛ
0b productionasymmetriesarecalculated con-volving the background-subtracted [40] two-dimensional trans-verse-momentum and rapidity distributions ofΛ
0b→
p K− andΛ
b0→
pπ
−candidateswiththeproductionasymmetriesmeasured asafunctionofthesamevariablesreportedinRef. [34].SinceΛ
0bbaryons selectedin the p K− or p
π
− final stateshave very sim-ilar kinematics,asshowninFig. 2,thevalue AΛ0
b
P
= (
2.
7±
1.
4)
%, averagedfor7and8 TeV data,isobtainedfortheproduction asym-metryofbothdecays.Asymmetries related to different trigger efficiencies for the charge-conjugated final states may arise. The efficiency for a charged hadron to be responsible forthe affirmative decision of the hardware trigger is determined as a function of transverse
Table 1
SystematicuncertaintiesonACPp K−andA pπ−
CP .
Systematic uncertainty Ap KCP−[%] A pπ−
CP [%]
Kaon or pion detection asymmetry 0.23 0.11 Proton detection asymmetry 0.67 0.67 PID asymmetry 0.74 0.73 Λ0 bproduction asymmetry 1.40 1.40 Trigger asymmetry 0.53 0.55 Signal model 0.02 0.02 Background model 0.23 0.47 PID efficiencies 0.57 0.74 Total 1.91 2.00
momentum, separately forpositively andnegatively charged par-ticles,usinga sample of
Λ
0b→ Λ
+c(
→
p K−π
+)
π
− decays.These efficiencies are used to determine the charge asymmetry intro-duced by the hardware trigger for the signal candidates that fire it. The charge asymmetry introduced by the hardware trig-ger for candidates that are retained independently of whether or not they are responsible for an affirmative hardware-trigger decision is determined studying a sample of B0→
K+π
− de-cays [25]. The asymmetry of the software trigger isalso studied using B0→
K+π
− decays, determining the charge asymmetry of the fraction of B0→
K+π
− decays forwhich both final-state hadronsfire thesoftware triggerwithrespectto thosefor which onlyonehadronfires.Thetotaltriggerasymmetriesaremeasured tobe Atriggerp K−= (
0.
18±
0.
53)
% and Aptriggerπ−= (−
0.
08±
0.
55)
%.The uncertainties are mainly due to the limited size of the samples usedintheirdetermination.Severalsources ofsystematicuncertainties associatedwiththe fit modelare investigated.The alternative models used to deter-mine systematicuncertainties associated withthe choices ofthe invariant-massshapesconsistinturnof: addinga Gaussian func-tion to theinvariant-mass resolution model used forsignals and cross-feedbackgroundstoaccountforlongtailsduetocandidates with a poor determination of the final-state particles momenta; changingthevalueoftheparametergoverningthefinal-state pho-tonradiation effectsaccordingtoits uncertainty;substitutingthe exponentialfunctionusedtomodelthecombinatorialbackground with a linear function and removing the partially reconstructed backgroundcomponentbyrejectingcandidateswithmp K−
(
mpπ−)
lowerthan5
.
5 GeV/c2.Whentestingalternativemodels,250 pseu-doexperiments are generatedaccording to the baseline fit model andusingasinput the centralvalues ofthe baseline results.Fits are performedto each of the generated samplesusing the base-line model and then the alternative models. The mean and the rootmeansquareofthedistributionofthedifferencebetweenthe rawasymmetriesdeterminedby thetwosets offitsareaddedin quadratureandtheresultingvalueistakenasasystematic uncer-tainty.Adifferentapproachisadoptedtoassesssystematic uncertain-tiesrelatedtothe knowledgeofthe PIDefficiencies. Samplesare generated using the baseline fit model and results.The baseline fitmodelisthenfitted250timestothegeneratedsamples, vary-ingthePIDefficienciesaccordingtotheiruncertainties,whichare mainly driven by the choice of the binning scheme used to di-videthephase-space.Theseuncertaintiesareassessedbychanging the baseline binning schemewith alternative schemes and com-putingagaintheefficiencies. Thelargest rootmean squareofthe rawasymmetrydistributionsistakenasasystematicuncertainty.
The systematic uncertainties due to the fitmodel choice, PID efficienciesdeterminationandinstrumentalasymmetries measure-ment,along withthe totaluncertainty obtainedas thequadratic sumoftheindividualcontributions,arereportedinTable1.
7. Resultsandconclusions
Using in Eqs. (2) and (3) the values of the raw asymmetries reported in Sec.5 andthose of the instrumental andproduction asymmetriesreportedinSec.6,thefollowingCP asymmetriesare obtained
ACPp K−
= −
0.
020±
0.
013±
0.
019,
ACPpπ−
= −
0.
035±
0.
017±
0.
020,
wherethefirstuncertaintiesarestatisticalandthesecond system-atic.The correlation between Ap KCP− and ApCPπ− isfoundto be0.5. NoevidenceforCP violationisobserved.
A quantity thatis independentfromthe protondetectionand
Λ
0b productionasymmetriesisobtainedbytakingthedifferenceACP
≡
Ap K − CP−
A pπ− CP=
A p K− raw−
AK − D−
A p K− PID−
A p K− trigger−
Aprawπ−+
Aπ − D+
A pπ− PID+
A pπ− trigger.
(8) The statistical and systematic correlations between the raw asymmetries,thePIDasymmetriesandthedetectionasymmetries aretakenintoaccountwhenpropagatingtheuncertaintytoACP,
obtaining
ACP
=
0.
014±
0.
022±
0.
010,
wherethefirstuncertaintyisstatisticalandthesecondsystematic. These results represent the world’s best measurements to date, with much improvedprecision withrespect to previous CDF de-terminations [12].
Acknowledgements
We express our gratitude to our colleagues in the CERN ac-celerator departments for the excellent performance of the LHC. WethankthetechnicalandadministrativestaffattheLHCb insti-tutes. WeacknowledgesupportfromCERNandfromthenational agencies:CAPES,CNPq,FAPERJandFINEP(Brazil);MOSTandNSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MINECO (Spain); SNSF andSER (Switzerland); NASU(Ukraine); STFC (United King-dom); NSF(USA). We acknowledge thecomputingresources that are provided by CERN, IN2P3 (France), KIT andDESY (Germany), INFN(Italy),SURF(Netherlands),PIC(Spain),GridPP(United King-dom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities behind the multiple open-source softwarepackageson whichwedepend.Individual groups or members have received support from AvH Foundation (Ger-many); EPLANET,MarieSkłodowska-Curie ActionsandERC (Euro-peanUnion);ANR,LabexP2IOandOCEVU,andRégion Auvergne-Rhône-Alpes (France); Key Research Programof FrontierSciences ofCAS,CASPIFI,andtheThousandTalentsProgram(China);RFBR, RSFandYandexLLC(Russia);GVA,XuntaGalandGENCAT(Spain); the Royal Society and the Leverhulme Trust (United Kingdom); Laboratory DirectedResearch andDevelopment program ofLANL (USA).
References
[1]N.Cabibbo,Unitarysymmetryandleptonicdecays,Phys.Rev.Lett.10(1963) 531.
[2]M.Kobayashi,T.Maskawa,CPviolationintherenormalizabletheoryofweak interaction,Prog.Theor.Phys.49(1973)652.
[3]J.H.Christenson,J.W.Cronin,V.L.Fitch,R.Turlay,Evidenceforthe2πdecayof theK0
2 meson,Phys.Rev.Lett.13(1964)138.
[4]BaBarCollaboration, B.Aubert,etal., ObservationofCPviolationinthe B0
mesonsystem,Phys.Rev.Lett.87(2001)091801,arXiv:hep-ex/0107013.
[5]BelleCollaboration,K.Abe,etal.,ObservationoflargeCPviolationinthe neu-tralB mesonsystem,Phys.Rev.Lett.87(2001)091802,arXiv:hep-ex/0107061.
[6]BaBar Collaboration, B.Aubert, et al., Observationof direct CPviolation in B0→K+π−decays,Phys.Rev.Lett.93(2004)131801,arXiv:hep-ex/0407057.
[7]BelleCollaboration,K.Abe,etal.,ObservationoflargeC P violationand evi-dencefordirectC P violationinB0→π+π−decays,Phys.Rev.Lett.93(2004)
021601,arXiv:hep-ex/0401029.
[8]BaBar Collaboration,B. Aubert, etal., Observation ofCPviolation inB0→
K+π− and B0→π+π−, Phys. Rev.Lett.99 (2007) 021603,arXiv:hep-ex/
0703016.
[9]BaBar Collaboration, J.P. Lees, et al., Measurementof C P asymmetries and branching fractions in charmless two-body B-mesondecays to pions and kaons,Phys.Rev.D87(2013)052009,arXiv:1206.3525.
[10]BelleCollaboration,J.Dalseno,etal.,MeasurementoftheC P violation param-etersinB0→π+π−decays,Phys.Rev.D88(2013)092003,arXiv:1302.0551.
[11]BelleCollaboration,Y.-T.Duh,etal.,Measurementsofbranchingfractionsand directC P asymmetriesforB→Kπ,B→π πandB→K K decays,Phys.Rev. D87(2013)031103,arXiv:1210.1348.
[12]CDFCollaboration, T.A.Aaltonen,et al.,Measurementsofdirect CP-violating asymmetries in charmless decays of bottom baryons, Phys. Rev.Lett. 113 (2014)242001,arXiv:1403.5586.
[13]LHCbCollaboration,R.Aaij,etal.,ObservationofCP violationinB±→D K± decays,Phys.Lett.B712(2012)203;
R.Aaij,etal.,Phys.Lett.B713(2012)351(Erratum)arXiv:1203.3662.
[14]LHCbCollaboration,R.Aaij,etal.,FirstobservationofCP violationinthedecays ofB0
s mesons,Phys.Rev.Lett.110(2013)221601,arXiv:1304.6173.
[15]LHCbCollaboration,R.Aaij,etal.,Measurementofmatter–antimatter differ-encesinbeautybaryondecays,Nat.Phys.13(2017)391,arXiv:1609.05216.
[16]Y.K.Hsiao,C.Q.Geng,DirectCPviolationinΛ0bdecays,Phys.Rev.D91(2015)
116007,arXiv:1412.1899.
[17]A.Ali,G. Kramer,C.-D.Lü, Experimentaltestsoffactorizationincharmless nonleptonictwo-bodyBdecays,Phys.Rev.D58(1998)094009,arXiv:hep-ph/ 9804363.
[18]C.-D.Lü,et al.,Anatomyofthe perturbativeQCD approachtothebaryonic decaysΛ0b→pπ,p K ,Phys.Rev.D80(2009)034011,arXiv:0906.1479.
[19]LHCbCollaboration,A.A.AlvesJr.,etal.,TheLHCb detectorattheLHC,J. In-strum.3(2008)S08005.
[20]LHCbCollaboration,R.Aaij,etal.,LHCbdetectorperformance,Int.J.Mod.Phys. A30(2015)1530022,arXiv:1412.6352.
[21]R.Aaij,et al., Performanceofthe LHCbvertexlocator, J.Instrum.9(2014) P09007,arXiv:1405.7808.
[22]R.Arink,et al.,Performanceofthe LHCboutertracker,J. Instrum.9(2014) P01002,arXiv:1311.3893.
[23]M.Adinolfi,etal.,PerformanceoftheLHCb RICHdetectorattheLHC,Eur.Phys. J.C73(2013)2431,arXiv:1211.6759.
[24]A.A.AlvesJr.,etal.,PerformanceoftheLHCbmuonsystem,J.Instrum.8(2013) P02022,arXiv:1211.1346.
[25]R.Aaij,etal.,TheLHCb triggeranditsperformancein2011,J.Instrum.8(2013) P04022,arXiv:1211.3055.
[26]T.Sjöstrand,S.Mrenna,P.Skands,AbriefintroductiontoPYTHIA8.1,Comput. Phys.Commun.178(2008)852,arXiv:0710.3820.
[27]I.Belyaev,etal.,HandlingofthegenerationofprimaryeventsinGauss,the LHCbsimulationframework,J.Phys.Conf.Ser.331(2011)032047.
[28]D.J.Lange,TheEvtGenparticledecaysimulationpackage,Nucl.Instrum. Meth-odsPhys.Res.,Sect.A462(2001)152.
[29]P.Golonka,Z.Was,PHOTOSMonteCarlo:aprecisiontoolforQEDcorrections inZ andW decays,Eur.Phys.J.C45(2006)97,arXiv:hep-ph/0506026.
[30]Geant4Collaboration,J.Allison,etal.,Geant4developmentsandapplications, IEEETrans.Nucl.Sci.53(2006)270;
Geant4Collaboration,S.Agostinelli,etal.,Geant4:asimulationtoolkit,Nucl. Instrum.MethodsPhys.Res.,Sect.A506(2003)250.
[31]M.Clemencic,etal.,TheLHCb simulationapplication,Gauss:design,evolution andexperience,J.Phys.Conf.Ser.331(2011)032023.
[32]LHCb Collaboration,R.Aaij,et al.,MeasurementofCP asymmetryin D0→
K−K+ and D0→π−π+ decays,J.HighEnergyPhys.07(2014)041,arXiv:
1405.2797.
[33]LHCb Collaboration, R.Aaij,et al., Measurementofthe D+s–D−s production
asymmetryin7 TeV pp collisions,Phys.Lett.B713(2012)186,arXiv:1205. 0897.
[34]LHCbCollaboration,R.Aaij,etal.,MeasurementofB0
,B0
s,B+andΛ0b
produc-tionasymmetriesin7 and8 TeV p p collisions,Phys.Lett.B774(2017)139, arXiv:1703.08464.
[35]B.P.Roe,etal.,Boosteddecisiontreesasanalternativetoartificialneural net-worksforparticleidentification,Nucl.Instrum.MethodsPhys.Res.,Sect.A543 (2005)577,arXiv:physics/0408124.
[36]L.Breiman,J.H.Friedman,R.A.Olshen,C.J.Stone,ClassificationandRegression Trees,WadsworthInternationalGroup,Belmont,California,USA,1984.
[37]E.Baracchini,G.Isidori,Electromagneticcorrectionstonon-leptonictwo-body BandDdecays,Phys.Lett.B633(2006)309,arXiv:hep-ph/0508071.
[38]ARGUS Collaboration,H.Albrecht,etal.,Measurementofthepolarizationin thedecayB→J/ψK∗,Phys.Lett.B340(1994)217.
[39]K.S.Cranmer,Kernel estimationinhigh-energyphysics, Comput.Phys. Com-mun.136(2001)198,arXiv:hep-ex/0011057.
[40]M.Pivk,F.R.Le Diberder,sPlot:astatisticaltooltounfolddatadistributions, Nucl. Instrum. Methods Phys. Res., Sect. A 555 (2005) 356, arXiv:physics/ 0402083.
LHCbCollaboration
