Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Measurement
of
CP asymmetry
in
D
0
→
K
−
K
+
decays
.
The
LHCb
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received1November2016
Receivedinrevisedform11January2017 Accepted27January2017
Availableonline3February2017 Editor: M.Doser
Ameasurementofthetime-integratedCP asymmetryintheCabibbo-suppresseddecayD0→K−K+ is performedusingpp collisiondata,correspondingtoanintegratedluminosityof3 fb−1,collectedwiththe LHCbdetectoratcentre-of-massenergiesof7and8 TeV.Theflavourofthecharmmesonatproductionis determinedfromthechargeofthepioninD∗+→D0
π
+andD∗−→D0π
−decays.Thetime-integratedCP asymmetryACP(K−K+)isobtainedassumingnegligibleCP violationincharmmixingandin Cabibbo-favoured D0→K−
π
+, D+→K−π
+π
+ and D+→K0π
+ decays used as calibrationchannels. It is foundtobeACP(K−K+)= (0.14±0.15 (stat)±0.10 (syst))%.
AcombinationofthisresultwithpreviousLHCbmeasurementsyields
ACP(K−K+)= (0.04±0.12 (stat)±0.10 (syst))%,
ACP(
π
−π
+)= (0.07±0.14 (stat)±0.11 (syst))%.Thesearethe mostprecisemeasurementsfromasingleexperiment.Theresult for ACP(K−K+)isthe mostprecisedeterminationofatime-integratedCP asymmetryinthecharmsectortodate,andneither measurementshowsevidenceofCP asymmetry.
©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
IntheStandardModel(SM), theviolationofthecharge-parity (CP) symmetry is governed by an irreducible complex phase in theCabibbo–Kobayashi–Maskawa(CKM)matrix.Charmedhadrons providethe onlywayto probeCP violation withup-typequarks. Recentstudies ofCP violation inweak decays of D mesonshave not shown evidence of CP symmetry breaking [1], while its vi-olationis well established in decays of mesons with down-type quarks(strangeandbeauty)[2–6].
TheCP-evendecays1 D0
→
K−K+ andD0→
π
−π
+ aresingly Cabibbo-suppressed,andforthesedecaysD0andD0mesonsshare thesamefinalstate.TheamountofCP violationinthesedecaysis expectedtobebelowthepercentlevel[7–14],butlarge theoreti-caluncertainties duetolong-distanceinteractionsprevent precise SM predictions. In the presence of physics beyond the SM, the expectedCP asymmetriescouldbeenhanced[15],althoughan ob-servationnearthecurrentexperimentallimitswouldbeconsistent withtheSMexpectation.The CP asymmetriesinthesedecaysare sensitive to both direct and indirect CP violation [1,16]. Thedi-1 ThroughoutthisLetter,chargeconjugationisimplicitunlessotherwisestated.
rect CP violationis associatedwiththebreaking ofCP symmetry
in the decay amplitude. Under SU
(
3)
flavour symmetry, the di-rectCP asymmetriesinthedecaysD0→
K−K+ andD0→
π
−π
+ areexpectedtohavethesamemagnitudesandoppositesign[17]. IndirectCP violation,occurringthrough D0–D0 mixingand inter-ference processesin themixingandthe decay,is expectedtobe smallandismeasuredtobebelow10−3 [1].The most recent measurements of the time-integrated indi-vidual CP asymmetries in D0
→
K−K+ and D0→
π
−π
+ decays havebeenperformedby theLHCb[18],CDF[19],BaBar[20] and Belle[21]collaborations.The measurement in Ref. [18] uses D0 mesons produced in semileptonicb-hadrondecays(B
→
D0μ
−ν
μ X ),wherethechargeof the muon is used to identify(tag) the flavour ofthe D0 me-son atproduction,whiletheother measurementsuse D0 mesons produced in the decay of the D∗
(
2010)
+ meson, hereafter re-ferred to as D∗+. Charmed hadrons maybe produced atthe ppcollisionpointeitherdirectly,orintheinstantaneousdecaysof ex-cited charm states.Thesetwo sources arereferred toas prompt. Charmedhadronsproduced inthedecaysofb-hadronsare called secondarycharmedhadrons.
ThisLetter presents ameasurement ofthe time-integrated CP
asymmetryinthe D0
→
K−K+ decayrateshttp://dx.doi.org/10.1016/j.physletb.2017.01.061
0370-2693/©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
ACP
(
D0→
K−K+)
≡
(
D0→
K−K+)
− (
D0→
K−K+)
(
D0→
K−K+)
+ (
D0→
K−K+)
,
(1) usingadatasample ofproton–proton(pp)collisionsat centre-of-massenergies of 7and 8 TeV,collected by the LHCbdetector in 2011 and 2012, corresponding to approximately 3 fb−1 of inte-gratedluminosity.TodistinguishthetwoCP-conjugatedecays,the flavour ofthe D0 atproductionmust be known.In thisanalysis, the flavour of the D0 is tagged by the charge of the soft pion,π
s+, in the strongdecay D∗+→
D0π
s+.A combination withtherecentmeasurementofthedifferencebetweenthetime-integrated
CP asymmetriesofD0
→
K−K+andD0→
π
−π
+decays,ACP
≡
ACP
(
K−K+)
−
ACP(
π
−π
+)
, in prompt charm decays [16] allowsthedeterminationof ACP
(
π
−π
+)
takingintoaccountthecorrela-tionbetween
ACP andACP
(
K−K+)
.Inaddition,a combinationofthemeasurements usingprompt charm decaysandthe measure-mentsusingsecondary charmdecaysfromsemileptonicb-hadron
decays[18]atLHCbyieldsthemostprecisemeasurementofthese quantitiesbyasingleexperiment.
Themethodtodetermine ACP
(
K−K+)
followsthestrategyde-scribed in Ref. [18]. In the analysis of D∗+
→
D0(
→
K−K+)
π
s+decays, two nuisance asymmetries must be considered, the pro-duction asymmetry of the D∗+ meson AP
(
D∗+)
, and thedetec-tion asymmetry AD
(
π
s+)
of thesoft pioncaused by noncharge-symmetricinteractionprobabilitieswiththedetectormaterialand instrumental asymmetry. The measured raw asymmetry in the numberofobservedsignaldecays,definedas
Araw
≡
N
(
D0→
K−K+)
−
N(
D0→
K−K+)
N
(
D0→
K−K+)
+
N(
D0→
K−K+)
,
(2)isrelatedtotheCP asymmetryvia
ACP
(
D0→
K−K+)
=
Araw(
D0→
K−K+)
−
AP(
D∗+)
−
AD(
π
s+),
(3)assuming that the asymmetries are small and that the recon-struction efficiencies can be factorised. The decay D∗+
→
D0(
→
K−
π
+)
π
s+ isusedasacalibrationchannelto determinethe pro-duction and detectionasymmetries. Since this decay is Cabibbo-favoured,anegligibleCP asymmetryisassumed.Incontrasttothe decayintotwokaons,the finalstate K−π
+ isnot CP symmetric.Therefore,additionaldetectionasymmetries arisingfromthefinal stateparticlesarepresent,giving
Araw
(
D0→
K−π
+)
=
AP(
D∗+)
+
AD(
π
s+)
+
AD(
K−π
+).
(4)In order to evaluate the detection asymmetry of the final state
K−
π
+,enhancedbythedifferentinteractioncross-sectionsof pos-itivelyandnegatively chargedkaonsin thedetectormaterial,the Cabibbo-favoureddecay D+→
K−π
+π
+ isemployed.Inanalogy tothe D0→
K−π
+ decay,theraw asymmetryin thischannelis givenbyAraw
(
D+→
K−π
+π
+)
=
AP(
D+)
+
AD(
K−π
l+)
+
AD(
π
h+).
(5)Thepionwiththelowertransverse momentum,
π
l+,ischosento cancel the effect of the detection asymmetry of the pion of the decay D0→
K−π
+.The remaining productionasymmetry oftheD+ meson AP
(
D+)
, and the detection asymmetry of the otherpion
π
h+areeliminatedbyincorporatingtheCabibbo-favoured de-cay D+→
K0π
+ in the measurement. There, the measured raw asymmetryconsistsoftheproductionasymmetry AP(
D+)
,thede-tectionasymmetryoftheneutralkaon AD
(
K0)
,andthedetectionasymmetryofthepion AD
(
π
+)
Araw
(
D+→
K0π
+)
=
AP(
D+)
+
AD(
K0)
+
AD(
π
+).
(6)The specific choice that the pion withthe higher(lower) trans-versemomentum inthedecayD+
→
K−π
+π
+ isusedtocancel theeffectofthedetectionasymmetryofthepioninD+→
K0π
+(D0
→
K−π
+)isbasedonthecomparisonofthekinematic spec-tra of therespective pions.The detectionasymmetry AD(
K0)
in-cludes CP violation, mixing and different cross-sections for the interaction ofneutral kaonswiththe detectormaterial. However, alloftheseeffectsareknown,andAD
(
K0)
iscalculatedtobesmallsinceonlyneutralkaonsthatdecaywithinthefirstpartofthe de-tector areselected[18].ThecombinationofEqs.(3)–(6)yieldsan expressionforACP
(
D0→
K−K+)
thatonlydependsonmeasurablerawasymmetriesandthecalculableK0 detectionasymmetry,
ACP
(
D0→
K−K+)
(7)=
Araw(
D0→
K−K+)
−
Araw(
D0→
K−π
+)
+
Araw(
D+→
K−π
+π
+)
−
Araw(
D+→
K0π
+)
+
AD(
K0).
2. Detectorandeventselection
The LHCbdetector[22,23] isa single-armforward spectrome-tercoveringthepseudorapidity range2
<
η
<
5,designedforthe 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 ofabout4 Tm, andthreestations of silicon-strip detectorsandstrawdrifttubesplaceddownstreamofthemagnet. Thetrackingsystemprovidesameasurementofthemomentumof chargedparticleswitharelativeuncertaintythatvariesfrom0.5% at low momentum to 1.0% at200 GeV/c. The minimum distance of atrackto aprimary vertex(PV), theimpact parameter (IP),is measured witharesolutionof(
15+
29/
pT)μm,where pT isthe componentofthemomentumtransversetothebeam,inGeV/c.Different typesofchargedhadronsare distinguished using in-formation from two ring-imaging Cherenkov detectors. Photons, electrons andhadronsareidentifiedbyacalorimetersystem con-sistingofscintillating-padandpreshowerdetectors,an electromag-neticcalorimeterandahadroniccalorimeter.Muonsareidentified by a system composed of alternating layers of iron and multi-wireproportionalchambers.Themagneticfieldinsidethedetector breaks thesymmetry betweentrajectories ofpositively and neg-ativelycharged particles asthepositive particles are deflectedin one direction, and the negative particles in the opposite direc-tion. Due to the imperfect symmetry of the detector, this can leadtodetectionasymmetries.Periodicallyreversingthemagnetic fieldpolaritythroughoutdata-takingalmostcancelstheeffect.The configuration with the magnetic field pointing upwards, MagUp (downwards,MagDown),bendspositively(negatively)charged par-ticlesinthehorizontalplanetowardsthecentreoftheLHCring.
The singly Cabibbo-suppressed decay mode D0
→
K−K+ and the Cabibbo-favoured modes D0→
K−π
+, D+→
K−π
+π
+ andD+
→
K0π
+ are selected, where the D0 candidates come from the D∗+→
D0π
+decay.The D∗+ andD+candidatesmustsatisfy anonlineeventselectionperformedbyatrigger,whichconsistsof ahardwareandsoftwarestage,andasubsequentofflineselection. The hardware stage of the trigger is based on information from the calorimeterandmuonsystems,followed by asoftwarestage, whichappliesa fulleventreconstruction.Inordertoavoid asym-metriesarising fromthehardware trigger,each ofthefourdecay channelsisrequiredtosatisfyatriggerthatisindependentofthe decay considered.Both thesoftware triggerandoffline event se-lectionusekinematicvariablesanddecaytimetoisolatethesignaldecaysfromthebackground.To ensurea cancellationofpossible trigger asymmetries in the software stage, for each of the cali-brationchannelsa specificationaboutwhich particletriggers the eventismade.
AllsecondaryparticlesfromD0 andD+decaysarerequiredto besignificantlydisplacedfromanyprimary pp interactionvertex, andhavemomentumandtransversemomentum pT largerthana minimumvalue. The final state hadrons are combinedinto a D0
(D+) candidate.The D∗+ vertexis formedby D0 and
π
s+candi-dates,andisconstrainedtocoincidewiththeassociated PV[24]. Similarly, a vertex fit of the D+ decay products is made, where theD+candidateisconstrainedtooriginatefromthe correspond-ingPV. In D+
→
K0π
+ decays,theneutralkaonisreconstructed viadecaysintotwochargedpions,whicharedominatedbydecays oftheshort-lived neutralkaon,KS0.The massofthe K0 mesonis constrainedto the nominalmass ofthe K0S state [25].Decays of
K0
S
→
π
+π
− arereconstructedusing only KS0 mesons thatdecay early enough forthe secondary pions to be reconstructed in the vertexdetector.Furtherrequirements are placed on: the track fit quality; the
D∗+ and D0 (D+) vertexfit quality; the D0 (D+) meson trans-versemomentumanditsdecaydistance;thesmallestvalueof
χ
2IP, ofboththeD0(D+)candidateanditsdecayproductswithrespect to all PVs in the event. The
χ
2IP is defined asthe difference be-tweenthevertex-fit
χ
2ofthePVreconstructedwithandwithout theconsideredparticle.For D0 candidates,aselection criterionis placedontheanglebetweentheD0momentuminthelaboratory frameandthemomentumofthekaonorthepioninthe D0 rest frame.ForD+candidates,additionalrequirementsonthe pseudo-rapidities,momenta andtransversemomenta ofthe particles are appliedin orderto matchthe kinematicdistributions ofthe twoD+decaymodes.
Cross-feed backgrounds from D meson decays with a kaon misidentified asa pion,and vice versa, are reduced using parti-cleidentification requirements. After these selection criteria, the dominantbackgroundin D∗+
→
D0π
+s decaysconsistsofgenuine
D0 candidates paired with unrelated pions originating from the primary interactionvertex. The main backgroundin the distribu-tions of D+
→
K−π
+π
+ and D+→
K0π
+ decays is combina-torial.For the D0 channels, fiducial requirementsare imposed to exclude kinematic regions having a large asymmetry in the soft pion reconstruction efficiency [16]. These regions occur because lowmomentumparticlesofonechargeatlargeorsmallanglesin thehorizontalplanemaybedeflectedeitheroutofthedetector ac-ceptanceorintothenon-instrumentedbeampiperegion,whereas particles withthe other charge are morelikely to remain within theacceptance.About70%oftheselectedcandidatesareretained afterthesefiducialrequirements.TheD0candidatessatisfyingtheselectioncriteriaareaccepted for further analysis if the mass difference
δ
m≡
m(
h+h−π
s+)
−
m
(
h+h−)
for h=
K,
π
is in the range 139.
77–151.
57 MeV/c2. To reduce the combinatorial background, the mass of the re-constructed D0 candidate is required to lie in the range 1850– 1884 MeV/c2 and1847–1887 MeV/c2 forD0→
K−K+ andD0→
K−
π
+decays,respectively.Thiswindowcorrespondstoabouttwo standarddeviationsofthemassresolution,asestimatedfromafit tothemassdistribution ofthecharm mesoncandidates.The D+candidatesareselectedbyrequiringthereconstructedmasstolie ina1820–1920 MeV/c2 masswindow.
ThedatasampleincludeseventswithmultipleD∗+candidates. Themajorityoftheseeventscontains thesame reconstructed D0
meson combined with different soft pion candidates. The frac-tion of events with multiple candidates in the considered range of
δ
m is about 6.5% for D0→
K−K+ events and about4.9% forD0
→
K−π
+ events. Thesefractions are approximatelythe same for each magnet polarity. One of the multiplecandidates is ran-domlyselectedandretained,theothersarediscarded.The fulldata setsrecorded in2011and2012at 7and8 TeV, respectively,areusedforthisanalysis.Theycorrespondtoan inte-gratedluminosityofabout1 fb−1and2 fb−1,respectively.In2011, approximately60%ofthedatawasrecordedwithmagnetpolarity MagDown, whereas in 2012 approximately the same amount of datawastakenwitheachmagnetpolarity.Thedataaresplit into four subsamples according to the magnet polarity and the data-takingyear.
3. Measurementoftheasymmetries
Therawasymmetriesandthesignalyieldsaredeterminedfrom binned likelihood fits to the
δ
m distributions in the D0 decay modes, andtotheinvariant massdistributions m(
D+)
in the D+channels.Thefitsaresimultaneousforbothflavoursandthe back-groundyieldsare allowedto differbetweenthem.The fitstothe fourdecaychannelsaremadeindependentlyinthe four subsam-ples.
Thesignalshapeofthe
δ
m distributionisdescribedbythesum ofthreeGaussian functions, twoofwhichhavea commonmean. ThemeansandwidthsoftheGaussiandistributionsareallowedto differbetweenD0 andD0 becauseofapossiblecharge-dependent biasinthemeasurementofthemomentum,whilealltheother pa-rametersareshared.Thebackgroundisdescribedbyan empirical functionconsistingoftheproduct ofanexponential functionand apower-lawfunctionmodellingthephase-spacethreshold[26]Pbkg
(δ
m|
A,
B, δ
m0)
∝ (δ
m− δ
m0)
Ae−B(δm−δm0),
(8) wherethethresholdδ
m0 isfixedtotheknownπ
+mass[25].The parameters A and B describe the shape and are commonto D0andD0 decays.
Thesignal shapeofthe D+ decaysisdescribed bythesumof twoGaussian distributionsandabifurcatedGaussian distribution. ThebifurcatedGaussiandistributiondescribestheasymmetrictails oftheinvariantmassdistributionarising fromradiative processes inthedecay.Thebackgroundismodelledbya singleexponential function,withthesameslopefortheD+andD−states.
Theproductionanddetectionasymmetriesdependonthe kine-matics ofthe particlesinvolved.Ifthekinematicdistributionsare very different, this maylead to an imperfect cancellation ofthe nuisanceasymmetries in ACP
(
K−K+)
.Toremove anyresidualef-fect, the kinematic distributions of the four decay channels are equalised by means of a weighting procedure [19]. Fiducial re-gions where this weighting procedure is not possible due to a lack of events in one of the channels are already excluded by the requirements on kinematic variables of the D+ decays. Fits to the
δ
m andm(
D+)
distributions ofthe unweighted data sam-ples are used to obtain the kinematic distribution of the signal component by disentangling the signal and background compo-nents withthe sPlot technique [27]. Then, the normalised signal distributions of the four channels are compared. To obtain the greatest possible statistical sensitivity, especially for the channel with the lowest yield D+→
K0π
+, the following order of the weighting steps is chosen: first, the D+→
K−π
+π
+ kinematic distributionsareweightedtoreproducetheD+→
K0π
+ kinemat-ics;second, D0→
K−π
+ distributionsare weightedto reproduce the D+→
K−π
+π
+ kinematics, and, last, the D0→
K−K+ dis-tributionsareweightedtoreproducetheD0→
K−π
+ kinematics. Ateach step,theweightsalreadycalculatedintheprevioussteps are applied. Some of the steps are repeated until a satisfactory agreement of the distributions is achieved. The underlying D∗+Table 1
Signalyieldsofthefourchannelsbeforeandafterthekinematicweighting.Inthe caseoftheweightedsamples,effectiveyieldsaregiven.
Channel Before weighting After weighting
D0→K−K+ 5.56 M 1.63 M
D0→K−π+ 32.4 M 2.61 M
D+→K−π+π+ 37.5 M 13.67 M
D+→K0π+ 1.06 M 1.06 M
but the selection requirements can introduce differencesfor the
K−K+andK−
π
+finalstates,whichareobservedinthe kinemat-icaldistributionsoftheD∗+ candidates.Thevariablesusedforthe weightingprocedureare: pT,η
andazimuthalangleϕ
oftheD∗+ candidates;pTandη
oftheD+mesons;pT,η
andϕ
ofthepionin theD+→
K0π
+channelandofthehigher-transverse-momentum pion in D+→
K−π
+π
+ decays; pT,η
andϕ
of the kaon and the pion in the D0→
K−π
+ and D+→
K−π
+π
+ modes. For the weighting of the D+→
K−π
+π
+ decay to agree with theD0
→
K−π
+ decay, the pionwiththe lower transverse momen-tum in the D+→
K−π
+π
+ channel is used. For all weighting steps, by default, each variable is divided in 20 uniform bins. If necessary,thetransversemomentaaretransformedtotheinterval [0,
1] toaccount forlongtailsinthedistributions. Theprocedure leadstoafeweventsinscarcelypopulatedbinshavingverylarge weights.Inordertomitigatesuchaneffect,anupperboundtothe weightsisapplied.Afterapplying the weights, the effective sample size is given by Neff
= (
iN=1wi)
2/(
iN=1w2i)
,where wi istheweightofcan-didatei andN isthetotalnumberofcandidates.Thenumbersof signaldecaysdeterminedfromfitstothesamplesbeforeandafter weightingaregiveninTable 1.
Thedetectionasymmetry AD
(
K0)
oftheneutralkaonisidenti-fiedasoneofthesources oftheresidualasymmetry.Themethod ofcalculationisdescribed infulldetailinRef. [18]andisapplied hereinthesameway.Basedonthereconstructedtrajectoriesand a model of the detectormaterial, the expected asymmetries are determined forall neutral kaon candidatesindividually andthen averaged. The calculated values are
(
−
0.
052±
0.
013)
% for 2011, and(
−
0.
054±
0.
014)
% for2012data.Theindividualvaluesforthedifferentcategoriesdonotdifferbetweensamplestakenwith dif-ferentmagnetpolarities.
The rawasymmetriesoftheweightedsamples,determinedby the fits to the
δ
m and m(
D+)
distributions shown in Fig. 1, are presentedinTable 2.Therawasymmetriesarecombinedwiththe calculated detection asymmetry of the neutral kaon. Testing the four independent measurements of ACP(
K−K+)
for mutualcon-sistency gives
χ
2/
ndf=
0.
80,corresponding to a p-valueof 0.50. The asymmetriesobtainedwiththetwomagnetpolaritieswithin each yeararearithmetically averagedin ordertoensure the can-cellationofdetectionasymmetrieswhichreversesignwithmagnet polarity. The finalresultisthen calculatedastheweighted mean of thetwo data-taking periods. Theweighted average ofthe val-uescorrespondingtoallsubsamplesiscalculatedasACP(
K−K+)
=
(
0.
14±
0.
15)
%,wheretheuncertaintyisstatistical.Theweighting procedureshiftstheobservedvalueof ACP(
K−K+)
by0.
04%. 4. SystematicuncertaintiesPossible systematicshifts ofthe measured CP asymmetry can be causedby biasesinthedeterminationofindividualraw asym-metries and non-cancellation of detection and production asym-metries. The determination of raw asymmetries is studied using severalsuitablealternativesignalandbackgroundmodelsinthefit ofthemassdistributions.Pseudoexperimentsaregeneratedbased on the alternative fit results. The baseline model is fitted to the pseudoexperimentdistributions.Thisisindependentlydoneforthe fourdatacategoriesandall channels.Themaximumobserved de-viationsbetweenthealternativeresultsandtheresultsofthefits to the generated pseudoexperiment distributions are combined, anda value of0
.
025% isassignedassystematicuncertainty. This strategy allows systematicshifts andstatisticalfluctuations tobe disentangled.Partially reconstructedandmisidentifiedthree-bodycharm de-cays might producea peakingbackground inthe
δ
m distributionof the Cabibbo-suppressed decay D0
→
K−K+. This background could therefore contribute to the signal yields obtained withthe fit.Iftheseincorrectlyreconstructeddecaysweretohavean asym-metry differentfromthat ofsignal decays,the determinedsignal asymmetry would be shifted. Simulated events are used toesti-Table 2
Measuredasymmetriesin% withtheirstatisticaluncertainties.
2011 MagUp MagDown Mean
Araw(D0→K+K−) −1.85±0.24 0.05±0.20 −0.90±0.16 Araw(D0→K−π+) −2.87±0.18 −1.43±0.15 −2.15±0.12 Araw(D+→K−π+π+) −1.946±0.095 −2.044±0.079 −1.995±0.062 Araw(D+→K0π+) −0.95±0.30 −0.93±0.25 −0.94±0.20 AD(K0) −0.052 −0.052 −0.052 ACP(K−K+) −0.03±0.43 0.32±0.37 0.14±0.28
2012 MagUp MagDown Mean
Araw(D0→K−K+) −1.92±0.15 −0.03±0.15 −0.98±0.10 Araw(D0→K−π+) −2.23±0.11 −1.65±0.11 −1.939±0.079 Araw(D+→K−π+π+) −1.291±0.045 −1.993±0.044 −1.642±0.031 Araw(D+→K0π+) −0.92±0.17 −0.83±0.17 −0.88±0.12 AD(K0) −0.054 −0.054 −0.054 ACP(K−K+) −0.11±0.26 0.40±0.26 0.14±0.18
2011+2012 MagUp MagDown Mean
Araw(D0→K−K+) −1.90±0.12 −0.01±0.12 −0.95±0.10 Araw(D0→K−π+) −2.411±0.095 −1.574±0.090 −2.005±0.079 Araw(D+→K−π+π+) −1.411±0.041 −2.005±0.038 −1.714±0.031 Araw(D+→K0π+) −0.93±0.15 −0.86±0.14 −0.89±0.12 AD(K0) −0.053 −0.053 −0.053 ACP(K−K+) −0.09±0.22 0.37±0.21 0.14±0.15
Fig. 1. Fitstotheδm andtothem(D+)distributionscorrespondingtothewholedatasampleandbothflavours.Datasamplesafterthekinematicweightingdescribedinthe textareused.
mate the relative fraction of peaking background,which is then combined with production anddetection asymmetries measured atLHCb[18,28] inorderto obtaina conservativeestimate ofthe asymmetry of thisbackground. A value of 0
.
015% is assigned as systematicuncertainty.In order to test the influence ofkinematic regions with high asymmetries of the final state particles in the channels D0
→
K−π
+, D+→
K−π
+π
+ and D+→
K0π
+, such regions are ex-cludedinanalogytothetreatmentofthesoftpion.Thedifference inthe valuesfor ACP(
K−K+)
,0.
040%, istakenas systematicun-certainty.
Possible incomplete cancellation of detection and produc-tion asymmetries is accountedfor in several differentways. The weighting procedure is designed to equalise kinematic distribu-tions,butaperfectagreementcannot bereachedbecauseof bin-ning effects, the sequential rather than simultaneous weighting and the reduction of large weights. This effect is estimated by repeatingtheweightingwithalternativeconfigurations,which in-cludeschangingthenumberofbins,analternativewayofdealing with highweights and weighting in a reduced set of kinematic variables.Foreachconfiguration,theCP asymmetryisdetermined andthe maximum deviation fromthe baseline result, 0
.
062%, is propagated as a systematic uncertainty. Additionally, the kine-matic dependence of the raw asymmetries observed in data are modelledwithkinematically dependentdetectionandproduction asymmetries assignedto each particle in the decay. These mod-elled detection and production asymmetries are then combined withtheweightedkinematicdistributionsindatatocalculatethe rawasymmetriespresentintheindividualchannels.Themodelled raw asymmetries are combined to give the final CP asymmetryaccordingto Eq.(7). Since no CP asymmetry in D0
→
K−K+ is includedin this calculation, an ideal kinematicweighting, corre-spondingtoaperfectcancellationofall detectionandproduction asymmetries,wouldresult inthis CP asymmetrybeing zero.The obtaineddeviationis0.054%andistreatedasanindependent sys-tematicuncertainty.Charmedmesonsproducedinthedecayofbeautyhadronsare suppressedbytherequirementofasmall
χ
2IPofthecharmmeson
candidates with respect to the PV. Nevertheless, a certain frac-tion of thesedecay chains passes the selection. Thisleads to an effective production asymmetry that depends on the production asymmetry of the charm mesons, the production asymmetry of the beauty hadronsand thefraction of secondary charm decays. The latter is determined for the D0 decays by a fit to the
χ
2IP distributions when the selection requirement on this quantity is removed. This yields an estimatedsecondary fraction of4
.
0% for thechannel D0→
K−K+ and4.
9% for thechannel D0→
K−π
+. For the D+ decay channels, a conservative estimate of the dif-ference in the fraction of secondary charm fsec based on these numbers and on a comparison with simulated events, is made:fsec(D+
→
K−K+π
+)
−
fsec(D+→
K0π
+)
=
4.
5%.A combination of thesenumbers withthe production asymmetries measured at LHCb[28–31]yieldsavalueof0.
039%,whichisassignedasa sys-tematicuncertainty.Thesystematicuncertaintyontheneutralkaondetection asym-metry is 0
.
014%. Further sources of systematic uncertainty are investigatedby performingconsistencychecks.The analysisis re-peated using more restrictive particle identification requirements andtheresultisfound tobecompatiblewiththebaselineresult. Additionally, the measurement of the CP asymmetry is repeated splittingthedata-taking periodintosmallerintervals, andinbins of the momentum of the kaon in the decays D0→
K−π
+ andD+
→
K−π
+π
+. No evidence of any dependence is found. All quoted systematic uncertainties are summarised in Table 3 and addedinquadraturetoobtaintheoverallsystematicuncertainty.5. SummaryandcombinationwithpreviousLHCb measurements
The time-integrated CP asymmetry in D0
→
K−K+ decays is measuredusingdatacollectedbytheLHCbexperimentand deter-minedtobeACP
(
K−K+)
= (
0.
14±
0.
15 (stat)±
0.
10 (syst))
%.
(9)ThisresultcanbecombinedwithpreviousLHCbmeasurementsof the same and related observables. In Ref. [18], ACP
(
K−K+)
wasTable 3
Systematicuncertaintiesfromthedifferentcategories.Thequadraticsumisusedto computethetotalsystematicuncertainty.
Category Systematic uncertainty [%]
Determination of raw asymmetries:
Fit model 0.025
Peaking background 0.015
Cancellation of nuisance asymmetries:
Additional fiducial cuts 0.040
Weighting configuration 0.062
Weighting simulation 0.054
Secondary charm meson 0.039
Neutral kaon asymmetry 0.014
Total 0.10
measuredtobe AslCP
(
K−K+)
= (−
0.
06±
0.
15 (stat)±
0.
10 (syst))
% for D0 mesons originating from semileptonic b-hadron decays. Sincethesame D+decaychannelswereemployedforthe cancel-lation ofdetection asymmetries, the resultis partially correlated withthevalue presented inthisLetter. The statisticalcorrelation coefficient is calculated as shown in Appendix A, and isρ
stat=
0.
36 and thesystematicuncertainties areconservatively assumed tobefullycorrelated.A weightedaverageresultsinthefollowing combinedvaluefortheCP asymmetryintheD0→
K−K+channelAcombCP
(
K−K+)
= (
0.
04±
0.
12 (stat)±
0.
10 (syst))
%.
(10)ThedifferenceinCP asymmetriesbetweenD0
→
K−K+andD0→
π
−π
+ decays,ACP,wasmeasuredatLHCbusingpromptcharm
decays [16]. A combination of the measurement of ACP
(
K−K+)
presentedinthisLetterwith
ACP yieldsavalueforACP
(
π
+π
−)
ACP
(
π
+π
−)
=
ACP(
K+K−)
−
ACP= (
0.
24±
0.
15 (stat)±
0.
11 (syst))
%.
(11)The statisticalcorrelation coefficient of thetwo measurements is
ρ
stat=
0.
24,andthesystematicuncertainties ofthetwo analyses areassumedtobefullyuncorrelated.Thecorrelationcoefficientbetweenthisvalueandthe measure-ment of Asl
CP
(
π
−π
+)
= (−
0.
19±
0.
20 (stat)±
0.
10 (syst))
% usingsemileptonically-tagged decays at LHCb [18] is
ρ
stat=
0.
28. The weightedaverageofthevaluesisAcombCP
(
π
−π
+)
= (
0.
07±
0.
14 (stat)±
0.
11 (syst))
%,
where,again,thesystematicuncertaintiesareassumedtobe fully correlated.When addingthe statisticalandsystematic uncertain-ties in quadrature, the values for the CP asymmetries in D0
→
K−K+andD0→
π
−π
+haveacorrelationcoefficientρ
full
=
0.
61. Fig. 2showstheLHCbmeasurementsofCP asymmetryusingboth pion- and muon-tagged D0→
K−K+ and D0→
π
−π
+ decays. Additionally, thelatestcombinedvaluesoftheHeavy Flavour Av-eraging Group [1] for these quantities are presented. The time-integrated CP asymmetries can be interpreted in terms of direct andindirectCP violationasshowninAppendix B.In conclusion, no evidence of CP violation is found in the Cabibbo-suppresseddecays D0
→
K−K+ andD0→
π
−π
+.These results are obtained assuming that there is no CP violation inD0–D0 mixingandnodirectCP violationintheCabibbo-favoured
D0
→
K−π
+, D+→
K−π
+π
+ and D+→
K0π
+ decay modes. The combined LHCb results are the most precise measurements oftheindividualtime-integratedCP asymmetriesACP(
K−K+)
andACP
(
π
−π
+)
fromasingleexperimenttodate.Acknowledgements
We express our gratitude to our colleagues in the CERN ac-celerator departments forthe excellent performance of the LHC.
Fig. 2. Measurements ofCP violation asymmetries in D0→K−K+ and D0→
π−π+ decays.Alongside the two LHCbmeasurements, presentedinthis Letter (greenellipse)andinRef.[18](blueellipse),andtheircombination(redellipse), thelatestvalueoftheHeavyFlavourAveragingGroup[1]isshown(blackellipse). ThelatteralreadyincludesthemeasurementofACPwithmuon(pion)-taggedD0 decays,using3(1)fb−1pp collisiondatacollectedwiththeLHCbdetector[18,32]. The68% confidencelevelcontoursaredisplayedwherethestatisticaland system-aticuncertaintiesareaddedinquadrature.(Forinterpretationofthereferencesto colourinthisfigure,thereaderisreferredtothewebversionofthisarticle.) 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);MNiSW andNCN (Poland);MEN/IFA (Romania); MinESand FASO(Russia); MINECO (Spain);SNSFandSER(Switzerland);NASU(Ukraine);STFC(United Kingdom); NSF (USA). We acknowledge the computingresources that are provided by CERN, IN2P3 (France), KIT and DESY (Ger-many), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom),RRCKI andYandexLLC (Russia),CSCS (Switzer-land),IFIN-HH(Romania),CBPF(Brazil),PL-GRID(Poland)andOSC (USA). We are indebted to the communities behind the multi-ple opensourcesoftwarepackagesonwhich wedepend. Individ-ual groupsormembershavereceived 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. Calculationofcorrelations
Since the measurement of ACP
(
K−K+)
using semileptonicb-hadron decaysemploys the same prompt D+ calibration chan-nels, it is correlated to the value obtained from prompt charm decays. Due to different selection requirements and a different weightingprocedureofthecandidates,theasymmetriesmeasured forthe D+ channels arenot fullycorrelated. Thecorrelation fac-tor
ρ
betweentwoweightedsubsamples X andY ofalargerdata sample Z isgivenbyρ
=
Zω
Xω
Y 2 Xω
2X Yω
2Y,
(12)where
ω
X andω
Y are theweights ofcandidatesinthe X and Ysubsamples.WhereasthefourD+
→
KS0π
+datasampleshave cor-relation factorsρ
K0Sπ between 0
.
64 and 0.
70,thecorrelation fac-torsofthe D+→
K−π
+π
+ samples,ρ
Kπ π ,areintherange0.
07Table 4
SummaryofthemeandecaytimesoftheD0→h−h+candidatesusedinthemeasurementsofACP andACP usingpromptand semileptonic D0 decays,andtheir combinedvalues.The firstuncertaintyoftheresults is statistical,andthesecondoneaccountsforthesystematics.
Tag Mode Measurement t(hh) /τ(D0) Ref.
Prompt K− K+ ACP 2.1524±0.0005±0.0162 [16] Prompt π−π+ ACP 2.0371±0.0005±0.0151 [16] Prompt K− K+ ACP(K−K+) 2.2390±0.0007±0.0187 – Prompt π−π+ ACP(K−K+)− ACP 2.1237±0.0008±0.0375 – Semileptonic K− K+ ACP 1.082±0.001±0.004 [18] Semileptonic π−π+ ACP 1.068±0.001±0.004 [18] Semileptonic K− K+ ACP(K−K+) 1.051±0.001±0.004 [18] Semileptonic π−π+ ACP(K−K+)− ACP 1.0370±0.0011±0.0089 – Pr.+sl. π−π+ ACP(K−K+)− ACP 1.7121±0.0007±0.0267 – Pr.+sl. K− K+ ACP(K−K+) 1.6111±0.0007±0.0109 – to0
.
08.Themainreasonforthesesmallcorrelationsistheprescal-ingofthe D+
→
Kπ
+π
+datainthesemileptonicanalysiswhich was removed in the prompt case. From thesenumbers, for each data category the correlationρ
ACP of the values for ACP(
K−K+)
arecalculatedasρ
ACP=
1σ
Aprompt CPσ
sl ACPρ
K0 Sπσ
prompt K0Sπσ
sl K0 Sπ+
ρ
Kπ πσ
Kpromptπ πσ
Kslπ π.
(13)Here,
σ
represents the statistical uncertainty of the measured asymmetry of the respective channel. This results in correlation factorsbetween0.
34 and0.
37 forthefourdatacategories. When combining these correlations in a similar way to Eq. (13), the statisticalcorrelationρ
stat betweenthe semileptonic andprompt measurementsof ACP(
K+K−)
isobtainedtobeρ
stat=
0.
36.Theother correlation factors presentedin Sec. 5 are obtained usingasimilarstrategy.
Appendix B.Meandecaytimes
Thetime-integratedCP asymmetry ACP
(
K−K+)
isnotonlysen-sitivetodirectCP violation,butalsohasacontributionfrom indi-rect CP violation. This contribution depends on the mean decay timeinunitsofthelifetimeoftheD0mesons,
t
(
hh)
/
τ
(
D0)
,asACP
≈
adirCP−
A t(
hh)
τ
(
D0)
,
(14)whereadirCP isthedirect CP violation term,
τ
(
D0)
the D0 lifetime andA ameasureofindirectCP violation.Moredetailsaboutthemethodandthesystematicuncertaintiesconsidered canbefound in[16,18].
When calculating ACP
(
π
−π
+)
from ACP(
K−K+)
andACP, a
difference of the mean decay time of the D0
→
K−K+ samples usedformeasuring ACP(
K−K+)
andACP leads toan additional
contributionwhichisproportionaltothisdifferenceandthesizeof indirectCP violation.Thiscanbeaccountedforbyaddingthis dif-ferencetothemeandecaytimeofthe D0
→
π
−π
+ sampleused intheACP measurement. In Table 4this modified meandecay
timeislabelledby ACP
(
K−K+)
−
ACP. Appendix C. SupplementarymaterialSupplementarymaterialrelatedtothisarticlecanbefound on-lineathttp://dx.doi.org/10.1016/j.physletb.2017.01.061.
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TheLHCbCollaboration
