Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Measurement
of
y
CP
in
D
0
–D
0
oscillation
using
quantum
correlations
in
e
+
e
−
→
D
0
D
0
at
√
s
=
3
.
773 GeV
BESIII
Collaboration
M. Ablikim
a,
M.N. Achasov
h,
1,
X.C. Ai
a,
O. Albayrak
d,
M. Albrecht
c,
D.J. Ambrose
au,
A. Amoroso
ay,
ba,
F.F. An
a,
Q. An
av,
J.Z. Bai
a,
R. Baldini Ferroli
s,
Y. Ban
af,
D.W. Bennett
r,
J.V. Bennett
d,
M. Bertani
s,
D. Bettoni
u,
J.M. Bian
at,
F. Bianchi
ay,
ba,
E. Boger
x,
8,
O. Bondarenko
z,
I. Boyko
x,
R.A. Briere
d,
H. Cai
bc,
X. Cai
a,
O. Cakir
ao,
2,
A. Calcaterra
s,
G.F. Cao
a,
S.A. Cetin
ap,
J.F. Chang
a,
G. Chelkov
x,
3,
G. Chen
a,
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a,
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b,
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a,
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ad,
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aa,
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p,
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u,
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at,
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av,
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u,
M. Fritsch
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w,
C.D. Fu
a,
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I. Garzia
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D.X. Lin
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C.X. Liu
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F.H. Liu
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Fang Liu
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Feng Liu
e,
H.B. Liu
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H.H. Liu
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H.H. Liu
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H.M. Liu
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J. Liu
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J.P. Liu
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J.Y. Liu
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K. Liu
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K.Y. Liu
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L.D. Liu
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P.L. Liu
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Q. Liu
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S.B. Liu
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X. Liu
aa,
X.X. Liu
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Y.B. Liu
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Z.A. Liu
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Zhiqiang Liu
a,
Zhiqing Liu
w,
H. Loehner
z,
X.C. Lou
a,
5,
H.J. Lu
p,
J.G. Lu
a,
R.Q. Lu
q,
Y. Lu
a,
Y.P. Lu
a,
C.L. Luo
ac,
M.X. Luo
bd,
T. Luo
as,
X.L. Luo
a,
M. Lv
a,
X.R. Lyu
ar,
∗
,
F.C. Ma
ab,
H.L. Ma
a,
L.L. Ma
ah,
Q.M. Ma
a,
S. Ma
a,
T. Ma
a,
X.N. Ma
ae,
X.Y. Ma
a,
F.E. Maas
m,
M. Maggiora
ay,
ba,
Q.A. Malik
ax,
Y.J. Mao
af,
Z.P. Mao
a,
S. Marcello
ay,
ba,
J.G. Messchendorp
z,
J. Min
a,
T.J. Min
a,
R.E. Mitchell
r,
X.H. Mo
a,
Y.J. Mo
e,
C. Morales Morales
m,
K. Moriya
r,
N.Yu. Muchnoi
h,
1,
H. Muramatsu
at,
Y. Nefedov
x,
F. Nerling
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I.B. Nikolaev
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1,
Z. Ning
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S. Nisar
g,
S.L. Niu
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S.L. Olsen
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Q. Ouyang
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S. Pacetti
t,
P. Patteri
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M. Pelizaeus
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H.P. Peng
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K. Peters
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J.L. Ping
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R.G. Ping
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R. Poling
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Y.N. Pu
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M. Qi
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S. Qian
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C.F. Qiao
ar,
L.Q. Qin
ah,
N. Qin
bc,
X.S. Qin
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Y. Qin
af,
Z.H. Qin
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J.F. Qiu
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K.H. Rashid
ax,
C.F. Redmer
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H.L. Ren
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M. Ripka
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G. Rong
a,
X.D. Ruan
k,
V. Santoro
u,
A. Sarantsev
x,
6,
M. Savrié
v,
K. Schoenning
bb,
S. Schumann
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T. Weber
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aaInstituteofHighEnergyPhysics,Beijing100049,People’sRepublicofChina bBeihangUniversity,Beijing100191,People’sRepublicofChina
cBochumRuhr-University,D-44780Bochum,Germany dCarnegieMellonUniversity,Pittsburgh,PA 15213,USA
eCentralChinaNormalUniversity,Wuhan430079,People’sRepublicofChina
fChinaCenterofAdvancedScienceandTechnology,Beijing100190,People’sRepublicofChina
gCOMSATSInstituteofInformationTechnology,Lahore,DefenceRoad,OffRaiwindRoad,54000Lahore,Pakistan hG.I.BudkerInstituteofNuclearPhysicsSBRAS(BINP),Novosibirsk630090,Russia
iGSIHelmholtzcentreforHeavyIonResearchGmbH,D-64291Darmstadt,Germany jGuangxiNormalUniversity,Guilin541004,People’sRepublicofChina
kGuangXiUniversity,Nanning530004,People’sRepublicofChina lHangzhouNormalUniversity,Hangzhou310036,People’sRepublicofChina mHelmholtzInstituteMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany nHenanNormalUniversity,Xinxiang453007,People’sRepublicofChina
oHenanUniversityofScienceandTechnology,Luoyang471003,People’sRepublicofChina pHuangshanCollege,Huangshan245000,People’sRepublicofChina
qHunanUniversity,Changsha410082,People’sRepublicofChina rIndianaUniversity,Bloomington,IN 47405,USA
sINFNLaboratoriNazionalidiFrascati,I-00044,Frascati,Italy tINFNandUniversityofPerugia,I-06100,Perugia,Italy uINFNSezionediFerrara,I-44122,Ferrara,Italy vUniversityofFerrara,I-44122,Ferrara,Italy
wJohannesGutenbergUniversityofMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany xJointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia
yJustusLiebigUniversityGiessen,II.PhysikalischesInstitut,Heinrich-Buff-Ring16,D-35392Giessen,Germany z
KVI-CART,UniversityofGroningen,NL-9747AAGroningen,TheNetherlands
aaLanzhouUniversity,Lanzhou730000,People’sRepublicofChina abLiaoningUniversity,Shenyang110036,People’sRepublicofChina acNanjingNormalUniversity,Nanjing210023,People’sRepublicofChina adNanjingUniversity,Nanjing210093,People’sRepublicofChina aeNankaiUniversity,Tianjin300071,People’sRepublicofChina afPekingUniversity,Beijing100871,People’sRepublicofChina agSeoulNationalUniversity,Seoul,151-747RepublicofKorea ahShandongUniversity,Jinan250100,People’sRepublicofChina
aiShanghaiJiaoTongUniversity,Shanghai200240,People’sRepublicofChina ajShanxiUniversity,Taiyuan030006,People’sRepublicofChina
akSichuanUniversity,Chengdu610064,People’sRepublicofChina alSoochowUniversity,Suzhou215006,People’sRepublicofChina amSunYat-SenUniversity,Guangzhou510275,People’sRepublicofChina anTsinghuaUniversity,Beijing100084,People’sRepublicofChina aoIstanbulAydinUniversity,34295Sefakoy,Istanbul,Turkey apDogusUniversity,34722Istanbul,Turkey
aqUludagUniversity,16059Bursa,Turkey
arUniversityofChineseAcademyofSciences,Beijing100049,People’sRepublicofChina asUniversityofHawaii,Honolulu,HI 96822,USA
atUniversityofMinnesota,Minneapolis,MN 55455,USA auUniversityofRochester,Rochester,NY 14627,USA
awUniversityofSouthChina,Hengyang421001,People’sRepublicofChina axUniversityofthePunjab,Lahore-54590,Pakistan
ayUniversityofTurin,I-10125,Turin,Italy
azUniversityofEasternPiedmont,I-15121,Alessandria,Italy baINFN,I-10125,Turin,Italy
bbUppsalaUniversity,Box516,SE-75120Uppsala,Sweden bcWuhanUniversity,Wuhan430072,People’sRepublicofChina bdZhejiangUniversity,Hangzhou310027,People’sRepublicofChina beZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina
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Articlehistory:
Received7January2015
Receivedinrevisedform19March2015 Accepted6April2015
Availableonline9April2015 Editor:L.Rolandi Keywords: BESIII D0–D0oscillation yCP Quantumcorrelation
Wereportameasurementoftheparameter
y
CP inD
0–D0oscillationsperformedbytakingadvantageofquantumcoherencebetweenpairs ofD0D0mesonsproducedin
e
+e− annihilationsnearthreshold.Inthiswork,doubly-tagged
D
0D0events,whereone D decays toaCP eigenstate
andtheotherD decays in asemileptonicmode,are reconstructedusing adata sampleof2.92 fb−1 collectedwith theBESIII detectoratthecenter-of-massenergyof√s=3.773 GeV.We obtainyCP= (−2.0±1.3±0.7)%,wherethefirstuncertaintyisstatisticalandthesecondissystematic.Thisresultiscompatiblewiththecurrent worldaverage.
©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense
(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
1.1.Charmoscillation
Itiswell knownthatoscillations betweenmesonand antime-son, also called mixing, can occur when the flavor eigenstates differ from the physical mass eigenstates. These effects provide a mechanism whereby interference in the transition amplitudes
of mesons and antimesons may occur. They may also allow for
manifestation of CP violation (CPV) in the underlying dynamics
[1,2]. Oscillations in the K0–K0 [3], B0–B0 [4] and B0
s–B0s [5]
systemsare established; their oscillationratesare well-measured andconsistentwithpredictionsfromtheStandardModel (SM)[6]. Afteranaccumulationofstrongevidencefromavarietyof exper-iments[7–9], D0–D0 oscillationswere recentlyfirmly established by LHCb[10].The results were soon confirmed by CDF[11] and Belle[12].
Theoscillationsareconventionallycharacterizedbytwo dimen-sionless parameters x
=
m/
and y= /
2, where
m and
are the mass and width differences between the two mass
eigenstatesand
istheaveragedecaywidthofthoseeigenstates. The mass eigenstates can be written as
|
D1,2=
p|
D0±
q|
D0, where p and q are complex parameters andφ
=
arg(
q/
p)
is a CP-violating phase. Using the phase convention CP|
D0= +|
D0, theCP eigenstatesoftheD mesoncanbewrittenas
|
DCP+≡
|
D 0+ |
D0√
2,
|
DCP−≡
|
D0− |
D0√
2.
(1)*
Correspondingauthor.E-mailaddress:guanyh@ihep.ac.cn(Y.H. Guan).
1 AlsoattheNovosibirskStateUniversity,Novosibirsk,630090,Russia. 2 AlsoatAnkaraUniversity,06100Tandogan,Ankara,Turkey.
3 AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia andattheFunctionalElectronicsLaboratory,TomskStateUniversity,Tomsk,634050, Russia.
4 CurrentlyatIstanbulArelUniversity,34295Istanbul,Turkey. 5 AlsoatUniversityofTexasatDallas,Richardson,Texas75083,USA. 6 AlsoatthePNPI,Gatchina188300,Russia.
7 AlsoatBogaziciUniversity,34342Istanbul,Turkey.
8 AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia.
The difference in the effective lifetime between D decaysto CP eigenstatesandflavoreigenstatescanbeparameterizedby yCP.In
theabsenceofdirectCPV,butallowing forsmallindirectCPV,we have[13] yCP
=
1 2 y cosφ
q p+
pq−
x sinφ
q p−
pq.
(2)In the absence of CPV,one has
|
p/
q|
=
1 andφ
=
0, leading to yCP=
y.Although D0–D0 mixing from short-distance physics is sup-pressedby theCKMmatrix[14,15]andtheGIM mechanism[16], sizeablecharmmixingcanarisefromlong-distanceprocessesand newphysics[1,17].Currentexperimentalprecision[18]isnot suf-ficienttoconcludewhetherphysicsbeyondtheSMisinvolved,and furtherconstraintsareneeded.Sofar,themostprecise determina-tionofthesizeofthemixinghasbeenobtainedbymeasuringthe time-dependent decay rate in the D
→
K±π
∓ channel [10–12]. However, the resulting information on the mixing parameters x and y is highly correlated. It is important to access the mixing parametersx andy directlytoprovidecomplementaryconstraints. Inthisanalysis,weuseatime-integratedmethodtoextract yCP,asproposedinthereferences[19–22],whichusesthresholdD0D0 pairproductionine+e−
→
γ
∗→
D0D0.Inthisprocess,theD0D0 pairisinastateofdefinite C= −
1,such thatthetwo D mesons necessarilyhaveoppositeCP eigenvalues.The methodutilizesthe semileptonicdecaysof D meson andhence,avoids the complica-tionsfromhadroniceffectsinD decays,thusprovidesacleanand uniquewaytoprobetheD0–D0 oscillation.1.2. Formalism
In the semileptonic decays of neutral D mesons (denoted as D
→
l),9thepartialdecaywidthisonlysensitivetoflavorcontentanddoesnotdependontheCP eigenvalueoftheparentD meson. However,thetotaldecaywidthofthe DCP±doesdependonitsCP eigenvalue:
CP
±= (
1±
yCP)
.Thus, the semileptonicbranchingfraction ofthe CP eigenstates DCP± is
BD
CP±→l≈
BD
→l(
1∓
yCP),andyCP canbeobtainedas
Table 1
D finalstatesreconstructedinthisanalysis.
Type Mode CP+ K+K−,π+π−, K0 Sπ 0π0 CP− K0Sπ0, K 0 Sω, K 0 Sη Semileptonic K∓e±ν, K∓μ±ν yCP
≈
1 4BD
CP−→lBD
CP+→l−
BD
CP+→lBD
CP−→l.
(3)AtBESIII, quantum-correlated D0D0 pairsproduced at thresh-oldallowustomeasure
BD
CP±→l.Specifically,webeginwithafullyreconstructed D candidatedecaying intoa CP eigenstate, the so-calledSingle Tag(ST). We havethus taggedthe CP eigenvalueof thepartner D meson.ForasubsetoftheSTevents,theso-called Double Tag(DT)events, thistaggedpartner D mesonisalso ob-servedviaoneofthesemileptonicdecaychannels. CP violationin D decays isknown to be very small [18], andcan be safely ne-glected.Therefore,
BD
CP∓→l canbeobtainedasBD
CP∓→l=
NCP±;l NCP±·
ε
CP±ε
CP±;l,
(4)whereNCP±(NCP±;l)and
ε
CP±(ε
CP±;l)denotethesignalyieldsanddetection efficiencies of ST decays D
→
CP±
(DT decays D D→
CP
±;
l), respectively. For CP eigenstates, as listed in Table 1, we choose modeswith unambiguous CP contentand copiousyields. The CP violation in K0S decays is known to be very small, it is therefore neglected. The semileptonic modes used for the DT in thisanalysisare K∓e±ν
andK∓μ
±ν
.1.3. TheBESIIIdetectoranddatasample
The analysispresented in thispaper isbased on a data sam-plewithanintegratedluminosityof2.92 fb−1[23] collectedwith the BESIII detector [24] at the center-of-mass energy of
√
s=
3.
773 GeV.TheBESIIIdetectorisageneral-purposesolenoidal de-tector attheBEPCII [25]double storagerings. Thedetectorhasa geometrical acceptanceof 93% of the full solid angle. We briefly describe thecomponentsof BESIIIfromthe interactionpoint (IP) outwards.Asmall-cellmaindriftchamber(MDC),usinga helium-basedgastomeasuremomentaandspecificionizationsofcharged particles, is surrounded by a time-of-flight (TOF) system based onplasticscintillatorsthat determinestheflighttimesofcharged particles.ACsI(Tl)electromagneticcalorimeter(EMC)detects elec-tromagnetic showers. These componentsare all situatedinside a superconducting solenoidmagnet, that providesa 1.0 Tmagnetic field parallel to the beam direction. Finally, a multi-layer resis-tive plate counter system installed in the iron flux return yoke ofthemagnetisusedto trackmuons. Themomentumresolution for charged tracks in the MDC is 0.5% for a transverse momen-tumof1 GeV/
c.TheenergyresolutionforshowersintheEMCis 2.5%(5.0%)for1 GeVphotonsinthebarrel(endcap)region.More detailsonthefeaturesandcapabilitiesofBESIIIcanbefound else-where[24].High-statisticsMonteCarlo(MC) simulationsare usedto eval-uatethedetectionefficiencyandto understandbackgrounds.The geant4-based[26]MCsimulationprogramisdesignedtosimulate interactions ofparticles in thespectrometer and thedetector re-sponse.Fortheproduction of
ψ(
3770)
,the kkmc [27] package is used;thebeamenergyspreadandtheeffectsofinitial-state radi-ation(ISR) areincluded.TheMCsamplesconsist ofthe D D pairs withconsiderationofquantumcoherenceforallmodesrelevantto thisanalysis, non-D D decays ofψ(
3770)
, ISR productionof low-massψ
states,andQEDandqq continuum¯
processes.Theeffectiveluminosity ofthe MC samples is about10 times that ofthe an-alyzed data. Known decays recorded by the Particle Data Group (PDG) [6] are generated with evtgen [28,29] using PDG branch-ing fractions, and the remaining unknown decays are generated with lundcharm[30].Final-stateradiation(FSR)ofchargedtracks istakenintoaccountwiththe photos package[31].
2. Eventselectionanddataanalysis
Each chargedtrackisrequiredto satisfy
|
cosθ
|
<
0.
93,whereθ
isthepolaranglewithrespecttothebeamaxis.Chargedtracks other than K0S daughtersare requiredtobewithin 1 cmoftheIP
transversetothebeamlineandwithin10 cmoftheIP alongthe beamaxis.Particleidentificationforchargedhadronsh (h
=
π
,
K ) is accomplishedby combiningthe measured energyloss (dE/
dx) inthe MDCandtheflight timeobtainedfromtheTOF toforma likelihoodL(
h)
for eachhadron hypothesis. The K± (π
±) candi-datesarerequiredtosatisfyL(
K)
>
L(
π
)
(L(
π
)
>
L(
K)
).The K0S candidates are selected with a vertex-constrained fit frompairs ofoppositelychargedtracks,which arerequiredto be within 20 cm of the IP along the beam direction; no constraint in the transverse plane is required. The two charged tracks are not subjected to the particle identification discussed above, and are assumedto be pions. We impose 0
.
487 GeV/
c2<
Mπ+π−<
0
.
511 GeV/
c2, that is within about3 standard deviations of the observed K0S mass,andthetwotracksareconstrainedtooriginate
fromacommondecayvertexbyrequiringthe
χ
2 ofthevertexfit to belessthan100. Thedecayvertexisrequiredto beseparated from theIP with asignificance greater than two standard devia-tions.ReconstructedEMCshowersthatareseparatedfromthe extrap-olated positions ofanycharged tracksby morethan 10standard deviationsaretakenasphotoncandidates.Theenergydepositedin nearbyTOFcountersisincludedtoimprovethereconstruction effi-ciencyandenergyresolution.Photoncandidatesmusthavea min-imum energy of 25 MeV for barrelshowers (
|
cosθ
|
<
0.
80) and 50 MeV for end cap showers (0.
84<
|
cosθ
|
<
0.
92). The show-ers in the gap between the barrel and the end cap regions are poorly reconstructedandthusexcluded.The showertiming is re-quired to be no later than 700 ns after the reconstructed event start time to suppress electronic noise and energy deposits un-related to theevent. Theη
andπ
0 candidates are reconstructed frompairsofphotons.DuetothepoorerresolutionintheEMCend capregions,thosecandidateswithbothphotonscomingfromEMC end caps arerejected. The invariant mass Mγ γ is requiredto be 0.
115 GeV/
c2<
Mγ γ<
0.
150 GeV/
c2 forπ
0 and0.
505 GeV/
c2<
Mγ γ<
0.
570 GeV/
c2 forη
candidates. The photon pair is kine-matically constrainedtothe nominalmass oftheπ
0 orη
[6]to improvethemesonfour-vectorcalculation.The
ω
candidates are reconstructed through the decayω
→
π
+π
−π
0. For all modes withω
candidates, sideband events in the Mπ+π−π0 spectrumareusedtoestimatepeakingbackgrounds from non-ω
D→
K0Sπ
+π
−π
0 decays.We take the signal region as (0.7600,0.8050) GeV/
c2 andthe sideband regions as(0.6000, 0.7300) GeV/
c2 or(0.8300,0.8525) GeV/
c2.Theupperedgeofthe right sideband is restrictedbecause of the K∗ρ
background that alterstheshapeofMπ+π−π0.Thesidebandsarescaledtothe esti-matedpeakingbackgroundsinthesignalregion.Thescalingfactor is determinedfrom afit tothe Mπ+π−π0 distribution indata,as shown inFig. 1
, wheretheω
signal is determined with theMC shape convolutedwithaGaussian whoseparametersare leftfree in thefit to better matchdataresolution, andthebackground is modeledbyapolynomialfunction.Fig. 1. FittotheinvariantmassMπ+π−π0 foreventsreconstructedfromdata.The solidlineisthetotalfitandthedashedlineshowsthepolynomialbackground.The shadedareashowsthesignalregionandcross-hatchedareasshowthesidebands.
Table 2
Requirementson
E forSTD candidates.
Mode Requirement (GeV)
K+K− −0.020< E<0.020 π+π− −0.030< E<0.030 K0 Sπ0π0 −0.080< E<0.045 K0Sπ0 −0.070< E<0.040 K0 Sω −0.050< E<0.030 K0 Sη −0.040< E<0.040
2.1.SingletagsusingCP modes
Toidentify the reconstructed D candidates, we use two vari-ables,the beam-constrainedmass MBC andthe energydifference
E,whicharedefinedas
MBC
≡
E2beam
/
c4− |
pD
|
2/
c2,
(5)E
≡
ED−
Ebeam,
(6)where
pD and ED are the momentumandenergy ofthe D
can-didateinthee+e−center-of-masssystem,andEbeam isthebeam energy.The D signalpeaksatthenominalD mass inMBC andat zeroin
E. We accept only one candidate per mode per event; when multiple candidates are present, the one with the small-est
|
E|
is chosen. Since the correlation betweenE and MBC isfoundtobesmall,thiswillnotbiasthebackgrounddistribution inMBC.Weapplythemode-dependent
E requirementslistedin
Table 2.
For K+K− and
π
+π
− ST modes, ifcandidate events contain onlytwochargedtracks,thefollowingrequirementsareappliedto suppressbackgroundsfromcosmic rays andBhabhaevents.First, werequireatleastone EMCshower separatedfromthetracksof theSTwithenergylargerthan50 MeV.Second,thetwoSTtracks must not be both identified as muons or electrons, and, if they havevalidTOF times,thetime differencemustbe lessthan 5 ns. BasedonMCstudies,nopeakingbackgroundispresentinMBCin ourSTmodesexceptforthe K0Sπ
0 mode. Inthe K0S
π
0 STmode,therearefewbackgroundeventsfromD0
→
ρπ
.FromMCstudies, theestimatedfractionislessthan0.
5%;thiswillbeconsideredin thesystematicuncertainties.TheMBCdistributionsforthesixSTmodesareshownin
Fig. 2
.Unbinned maximum likelihood fits are performed to obtain the
numbersofSTyieldsexceptinthe K0S
ω
mode,forwhichabinned least-square fit is applied to the MBC distribution after subtrac-tion of theω
sidebands. In each fit, the signal shape is derived fromsimulatedsignal eventsconvoluted witha bifurcated Gaus-sianwithfreeparameterstoaccountforimperfectmodelingofthe detectorresolution andbeamenergycalibration.Backgrounds are describedby theARGUS[32] function.Themeasured STyieldsinTable 3
Yieldsand efficiencies ofallST and DTmodes, where NCP± (NCP±;l)and εCP±
(εCP±;l)denotesignalyieldsanddetectionefficienciesofD→CP±(D D→CP±;l),
respectively.Theuncertaintiesarestatisticalonly.
ST Mode NCP± εCP±(%) K+K− 54 494±251 61.32±0.18 π+π− 19 921±174 64.09±0.18 K0 Sπ0π0 24 015±236 16.13±0.08 K0 Sπ0 71 421±285 40.67±0.14 K0 Sω 20 989±243 13.44±0.07 K0 Sη 9878±117 34.39±0.13 DT Mode NCP±;l εCP±;l(%) K+K−, K eν 1216±40 39.80±0.14 π+π−, K eν 427±23 41.75±0.14 K0 Sπ 0π0, K eν 560±28 11 .05±0.07 K0 Sπ0, K eν 1699±47 26.70±0.12 K0 Sω, K eν 481±30 9.27±0.07 K0 Sη, K eν 243±17 22.96±0.11 K+K−, Kμν 1093±37 36.89±0.14 π+π−, Kμν 400±23 38.43±0.15 K0 Sπ0π0, Kμν 558±28 10.76±0.08 K0 Sπ 0, Kμν 1475±43 25 .21±0.12 K0 Sω, Kμν 521±27 8.75±0.07 K0 Sη, Kμν 241±18 21.85±0.11
thesignal regionof1
.
855 GeV/
c2<
MBC
<
1.
875 GeV/
c2 andthe correspondingefficienciesaregiveninTable 3
.2.2. Doubletagsofsemileptonicmodes
In each ST event, we search among the unused tracks and
showersforsemileptonicD
→
K e(
μ
)
ν
candidates.Werequirethat there be exactly two oppositely-charged tracks that satisfy the fiducialrequirementsdescribedabove.In searchingfor K
μν
decays,kaoncandidates are requiredto satisfyL(
K)
>
L(
π
)
.Ifthetwo trackscan passthecriterion, the track with largerL(
K)
is taken as the K± candidate, and the other track is assumed to be theμ
candidate. The energy de-posit in the EMC of theμ
candidateis required to be lessthan 0.3 GeV. We further require the Kμ
invariant mass MKμ to be lessthan 1.
65 GeV/
c2 to reject D→
Kπ
backgrounds.The total energyof remaining unmatched EMC showers, denoted as Eextra, isrequiredtobelessthan0.2 GeVtosuppress D→
Kπ π
0 back-grounds. Toreduce backgrounds from the D→
K eν
process, the ratioR
L(
e)
≡
L
(
e)/
[
L
(
e)
+
L
(
μ
)
+
L
(
π
)
+
L
(
K)
]
is required to belessthan 0.8,where thelikelihoodL
(
i)
forthehypothesis i=
e,μ
,π
or K isformed by combining EMC informationwith thedE/
dx andTOFinformation.ToselectK e
ν
events,electroncandidatesarerequiredtosatisfyL
(
e)
>
0.
001 andR
L
(
e)
>
0.
8, whereR
L(
e)
≡
L
(
e)/
[
L
(
e)
+
L
(
π
)
+
L
(
K)
]
.Ifboth trackssatisfy theserequirements,theonewithlarger
R
L(
e)
istakenastheelectron.Theremainingtrackis requiredtosatisfyL(
K)
>
L(
π
)
.The variable Umiss is used to distinguish semileptonic signal eventsfrombackground:
Umiss
≡
Emiss−
c|
pmiss|,
(7)where, Emiss
≡
Ebeam−
EK−
El,
(8)pmiss
≡ −
pK
+
pl+ ˆ
pST E2 beam/
c2−
c2m2D,
(9)Fig. 2. TheMBCdistributionsforSTD candidatesfromdata.ThesolidlineisthetotalfitandthedashedlineshowsthebackgroundcontributiondescribedbyanARGUS function.
EK(l) (
pK(l)) is the energy (three-momentum) of K∓ (l±), p
ˆ
ST is theunit vectorinthe directionofthereconstructedCP-tagged D andmD isthenominalD mass. Theuseofthebeamenergyandthe nominal D mass for the magnitude ofthe CP-tagged D
im-provesthe Umiss resolution.Since E equalsto
|
p|
c foraneutrino, thesignalpeaksatzeroinUmiss.TheUmissdistributionsareshownin
Fig. 3
,wherethetagged-D is required to be in the region of 1.
855 GeV/
c2<
MBC
<
1.
875 GeV/
c2.DTyields,obtainedbyfittingtheUmiss spectra,are listedinTable 3
.Unbinnedmaximumlikelihoodfitsareperformed forallmodesexceptformodesincludingω
.Formodesincluding anω
, binned least-square fits are performedto theω
sideband-subtracted Umiss distributions.Ineach fit,the K eν
or Kμν
signal ismodeledbytheMC-determined shapeconvolutedwitha bifur-catedGaussianwhereallparametersareallowedtovaryinthefit. BackgroundsforK eν
arewelldescribedwithafirst-order polyno-mial.However,inthe Kμν
mode,backgroundsaremorecomplex and consist of three parts. The primary background comes from D→
Kπ π
0 decay. To better control this background, we select asample of D→
Kπ π
0 in databyrequiring Eextra
>
0.
5 GeV, in whichtheUmissshapeofKπ π
0isprovedtobebasicallythesame asthatintheregionofEextra<
0.
2 GeV inMCsimulation.The se-lected Kπ π
0 sampleis usedto extractthe resolutiondifferences in the Umiss shape of Kπ π
0 inMC anddata, andto obtain the D→
Kπ π
0yieldsinEextra
>
0.
5 GeV region.Then,infitstoUmiss, theKπ π
0 isdescribedbytheresolution-correctedshapefromMC simulationsanditssizeisfixedaccordingtotherelativesimulated efficiencies ofthe Eextra>
0.
5 GeV and Eextra<
0.
2 GeV selection criteria.ThesecondbackgroundfromK eν
eventsismodeledbya MC-determined shape. Its ratioto thesignal yields is about3.5% based on MC studies andis fixed in the fits. Background in the thirdcategory includesallother backgroundprocesses,whichare welldescribedwithafirst-orderpolynomial.3. Systematicuncertainties
MostsourcesofuncertaintiesfortheSTorDTefficiencies,such astracking, PID,and
π
0,η
, K0S reconstruction, cancelout in
de-termining yCP.The main systematicuncertainties come fromthe
background veto, modeling of the signals and backgrounds, fake tagged signals, and the CP-purity of ST events, as shown in Ta-ble 4.
The cosmic and Bhabha veto is applied only for the K K and
π π
STeventswhichhaveonlytwotracks.Theeffectofthisveto isestimatedbasedonMCsimulation.Wecomparethecaseswith andwithoutthisrequirementandtheresultantrelativechangesinSTefficienciesareabout0.3%forboththeK K and
π π
modes.The resultingsystematicuncertaintyon yCP is0.001.Peaking backgroundsarestudied fordifferentSTmodes, espe-ciallyfor
ρπ
backgroundsintheK0S
π
0tagmodeandK0Sπ
+π
−π
0backgroundsintheK0S
ω
tagmode.Basedonastudyofthe inclu-sive MCsamples,thefractionofpeakingbackgroundsin K0Sπ
0 is 0.3%. Theuncertainties on yCP causedby thisisabout0.001.Un-certainties fromthesidebandsubtractionofpeakingbackgrounds fortheK0S
ω
modearestudiedbychangingthesidebandandsignal regions;changesintheefficiency-correctedyieldsarenegligible.Fits to the MBC and Umiss spectracould inducesystematic er-rorsbythemodelingofthesignalandbackgroundshape.The MC-determined signal shapesconvoluted with a Gaussian are found to describe the data well, and systematic uncertainties from the modeling ofthe signal are assumedto be negligible.Toestimate uncertaintiesfrommodelingofbackgrounds,differentmethodsare considered. For the CP ST yields, we include an additional back-groundcomponenttoaccountforthe
ψ(
3770)
→
D D processwith a shapedetermined byMC simulationwhoseyieldis determined in the fit. The uncertainties in the fits to MBC are uncorrelated among different tag modes, and the obtained change on yCP is0.001. For the DT semileptonic yields, the polynomial functions that areused todescribe backgroundsinournominalfitsare
re-placed by a shape derived from MC simulations. For the K
μν
mode,thesizeofthemainbackgroundK
π π
0 isfixedinour nom-inal fit,so the statisticaluncertainties of the numberof selected Kπ π
0 eventsintroduces asystematicerror.Toestimatethe asso-ciateduncertainty,wevaryitssizeby±
1standarddeviationbased on the selected Kπ π
0 samples. Systematic uncertainties due to the Umiss fits aretreatedaspositively correlatedamongdifferent tag modes. We take the maximum change on the resultant yCP,thatis0.006,assystematicuncertainty.
The DT yields are obtainedfrom the fit to the Umiss spectra. However,onealsohastoconsidereventsthatpeakatUmissbutare backgroundsintheMBCspectra,theso-calledfaketaggedsignals. This issue is examined by fitting to the MBC versus Umiss two-dimensionalplots.Fromthisstudy,thefaketaggedsignal compo-nentisprovedtobeverysmall.Theresultingdifferenceon yCP is
0.002andassignedasasystematicuncertainty.
WestudytheCP-puritiesofSTmodesbysearchingforsame-CP DTsignalsindata.AssumingCP conservationinthecharmsector, the same-CP process is prohibited, unless the studied CP modes are notpure ortheinitial C -odd D0D0 systemisdiluted. TheCP modes involving K0S are not pure due to the existence of small CPV in K0–K0 mixing[6].However, thissmalleffectisnegligible
Fig. 3. FittotheUmissdistributionsforselectedDTeventsfromdata.Ineachplot,thesolidlineisthetotalfit,thedashedlineinK eνshowsthecontributionofpolynomial backgrounds,andthedash-dottedlineinKμνshowsthecontributionofthemainKπ π0backgrounds.
Table 4
Summaryofsystematicuncertainties.Relativesystematicuncertaintiesarelistedforeachtagmodeinpercent,whiletheresultingabsoluteuncertaintiesonycpareshown
inthelastcolumn.Negligibleuncertaintiesaredenotedby“–”.
K+K− π+π− K0 Sπ0π0 K0Sπ0 K0Sω K0Sη ycp Background 0.3 0.3 – 0.3 – – 0.001 MBCfit 0.4 0.1 2.4 0.4 0.1 1.4 0.001 Umissfit (K eν) 1.8 1.3 2.4 1.6 8.1 1.2 0.006 Umissfit (Kμν) 3.2 7.0 4.6 2.5 1.7 1.7 Fake tag (K eν) 0.2 1.4 0.9 1.2 3.1 0.4 0.002 Fake tag (Kμν) 1.0 0.7 0.5 0.9 4.8 0.4 CP-purity – – 0.4 – 0.2 0.2 0.001
withourcurrentsensitivity.Hence, K0S
π
0isassumedtobeaclean CP mode, as its background level is very low. As a conservative treatment,westudyDTyieldsof(K0S
π
0, K0Sπ
0) toverifyits pureCP-oddeigenstatenatureandtheCP-oddenvironmentoftheD0D0 pair.TheobservednumbersofthisDTsignalsarequitesmall,and weestimatethedilutionofthe C -oddinitialstatetobelessthan 2%at90%confidencelevel.ThisaffectsourmeasurementofyCP by
lessthan0.001.Thepurityofthe KS0
π
0modeisfoundtobelarger than99%.Duetothecomplexityoftheinvolvednon-resonantand resonantprocessesin K0S
π
0π
0 and K0Sω
,theCP-purities ofthesetagmodescouldbe contaminated.Wetakethemode K+K− asa cleanCP-eventagtotestK0S
π
0π
0,andtake K0S
π
0totest KS0ω
andK0
S
η
. TheCP-purities of K0Sπ
0π
0, K0Sω
andK0Sη
areestimatedtobelarger than89.4%, 93.3%and93.9%,respectively. Based onthe
obtained CP purities, the corresponding maximum effect on the determined yCP isassignedassystematicuncertainty.
Systematicuncertainties fromdifferentsourcesareassumedto
be independent and are combined in quadrature to obtain the
overall yCP systematic uncertainties. The resultant total yCP
sys-tematicuncertaintiesis0.007.
4. Results
ThebranchingratiosofK∓e±
ν
andK∓μ
±ν
aresummedto ob-tainBD
CP∓→l=
BD
CP∓→K eν+
BD
CP∓→Kμν .Tocombineresultsfrom differentCP modes,thestandardweightedleast-squaremethodis utilized[6].TheweightedsemileptonicbranchingfractionBD
˜
CP±→lTable 5
ValuesofbranchingratioofDCP±→l obtainedfromdifferenttagmodesandthe
combinedbranchingratio.Theerrorsshownarestatisticalonly.
Tag mode BDCP−→K eν(%) BDCP−→Kμν(%) BDCP−→l(%) K+K− 3.44±0.12 3.33±0.12 6.77±0.17 π+π− 3.29±0.18 3.35±0.20 6.64±0.27 K0 Sπ0π0 3.40±0.18 3.48±0.18 6.89±0.26 ˜ BDCP−→l 3.40±0.09 3.37±0.09 6.77±0.12 Tag mode BDCP+→K eν(%) BDCP+→Kμν(%) BDCP+→l(%) K0 Sπ0 3.62±0.10 3.33±0.10 6.96±0.15 K0 Sω 3.32±0.21 3.81±0.21 7.14±0.30 K0Sη 3.68±0.26 3.84±0.29 7.52±0.40 ˜ BDCP+→l 3.58±0.09 3.46±0.09 7.04±0.13
χ
2=
α˜
BD
CP±→l−
B
αDCP±→l 2σ
α CP± 2,
(10)where
α
denotesdifferentCP-tagmodesandσ
αCP±isthestatistical
errorof
B
αDCP±→l forthegiventag mode.The branchingfractions
of
BD
CP±→l andtheobtainedBD
˜
CP±→l arelistedinTable 5
.Finally,yCP iscalculatedusingEq.(3),with
BD
CP±→l replacedbyBD
˜
CP±→l.Weobtain yCP
= (−
2.
0±
1.
3±
0.
7)
%, wherethefirst uncertaintyisstatisticalandthesecondissystematic.
5. Summary
Using quantum-correlated D0D0 pairs produced at
√
s=
3
.
773 GeV, we employ a CP-tagging technique to obtain the yCPparameterof D0–D0 oscillations.Underthe assumptionofno di-rect CPV in the D sector, we obtain yCP
= (−
2.
0±
1.
3(
stat.)
±
0
.
7(
syst.))
%. Thisresultiscompatiblewiththeprevious measure-ments[18,33–35]withinabouttwostandarddeviations.However, theprecision isstill statisticallylimitedandlessprecise thanthe currentworldaverage[6].Futureeffortsusingaglobalfit[36]may betterexploittheBESIIIdata,leadingtoamorepreciseresult.Acknowledgements
TheBESIIICollaboration thanksthestaffofBEPCIIandtheIHEP computingcenterfortheirstrongsupport.Thisworkissupported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; Joint Funds of the National Natu-ral Science Foundation of China under Contracts Nos. 11079008, 11179007,U1232201,U1332201;NationalNaturalScience Founda-tion of China (NSFC) under Contracts Nos. 11125525, 11235011,
11275266,11322544,11335008, 11425524;the ChineseAcademy
ofSciences (CAS) Large-ScaleScientific Facility Program; CAS
un-der Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents
Program of CAS;INPAC andShanghai Key Laboratory forParticle
Physics andCosmology; GermanResearch Foundation DFG under
ContractNo.CollaborativeResearchCenterContractNo. CRC-1044; IstitutoNazionalediFisicaNucleare,Italy;MinistryofDevelopment
of Turkey under Contract No. DPT2006K-120470; Russian
Foun-dation for Basic Research under Contract No. 14-07-91152; U.S. Department ofEnergy under Contracts Nos.DE-FG02-04ER41291,
DE-FG02-05ER41374,DE-FG02-94ER40823,DESC0010118;U.S.
Na-tionalScience Foundation;UniversityofGroningen(RuG)andthe HelmholtzzentrumfuerSchwerionenforschungGmbH(GSI), Darm-stadt;WCUProgramofNationalResearchFoundationofKorea un-derContractNo.R32-2008-000-10155-0.
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