Measurement of higher-order multipole amplitudes in $\psi(3686)\rightarrow\gamma\chi_{c1,2}$ with $\chi_{c1,2}\to\gamma J/\psi$ and search for the transition $\eta_{c}(2S)\to\gamma J/\psi$

0.42 MB·

by  M. Ablikim

Measurement ofhigher-order multipoleamplitudes inψ(3686) → γχc1,2 withχc1,2 → γJ/ψ
andsearch forthetransitionη (2S) → γJ/ψ
c
M.Ablikim1,M.N.Achasov9,e,X.C.Ai1,O.Albayrak5,M.Albrecht4,D.J.Ambrose44,A.Amoroso49A,49C,F.F.An1,Q.An46,a,
J.Z.Bai1,R.BaldiniFerroli20A,Y.Ban31,D.W.Bennett19,J.V.Bennett5,M.Bertani20A,D.Bettoni21A,J.M.Bian43,F.Bianchi49A,49C,
E.Boger23,c,I.Boyko23,R.A.Briere5,H.Cai51,X.Cai1,a,O. Cakir40A,A.Calcaterra20A,G.F.Cao1,S.A.Cetin40B,J.F.Chang1,a,
G.Chelkov23,c,d,G.Chen1,H.S.Chen1,H.Y.Chen2,J.C.Chen1,M.L.Chen1,a,S.Chen41,S.J.Chen29,X.Chen1,a,X.R.Chen26,
Y.B.Chen1,a,H.P.Cheng17,X.K.Chu31,G.Cibinetto21A,H.L.Dai1,a,J.P.Dai34,A.Dbeyssi14,D.Dedovich23,Z.Y.Deng1,
A.Denig22,I.Denysenko23,M.Destefanis49A,49C,F.DeMori49A,49C,Y.Ding27,C.Dong30,J.Dong1,a,L.Y.Dong1,M.Y.Dong1,a,
Z.L.Dou29,S.X.Du53,P.F.Duan1,J.Z.Fan39,J.Fang1,a,S.S.Fang1,X.Fang46,a,Y.Fang1,R.Farinelli21A,21B,L.Fava49B,49C,
O.Fedorov23,F.Feldbauer22,G.Felici20A,C.Q.Feng46,a,E.Fioravanti21A,M. Fritsch14,22,C.D.Fu1,Q.Gao1,X.L.Gao46,a,
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1 F.A.Harris42,K.L.He1,T.Held4,Y.K.Heng1,a,Z.L.Hou1,C.Hu28,H.M.Hu1,J.F.Hu49A,49C,T.Hu1,a,Y.Hu1,G.S.Huang46,a,
0 J.S.Huang15,X.T.Huang33,X.Z.Huang29,Y.Huang29,Z.L.Huang27,T.Hussain48,Q.Ji1,Q.P.Ji30,X.B.Ji1,X.L.Ji1,a,
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] H.H.Liu16,H.H.Liu1,H.M.Liu1,J.Liu1,J.B.Liu46,a,J.P.Liu51,J.Y.Liu1,K.Liu39,K.Y.Liu27,L.D.Liu31,P.L.Liu1,a,Q.Liu41,
x S.B.Liu46,a,X.Liu26,Y.B.Liu30,Z.A.Liu1,a,ZhiqingLiu22,H.Loehner25,X.C.Lou1,a,g,H.J.Lu17,J.G.Lu1,a,Y.Lu1,Y.P.Lu1,a,
e C.L.Luo28,M.X.Luo52,T.Luo42,X.L.Luo1,a,X.R.Lyu41,F.C.Ma27,H.L.Ma1,L.L. Ma33,M.M.Ma1,Q.M.Ma1,T.Ma1,
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e J.G.Messchendorp25,G.Mezzadri21B,J.Min1,a,R.E.Mitchell19,X.H.Mo1,a,Y.J.Mo6,C.MoralesMorales14,N.Yu.Muchnoi9,e,
h H.Muramatsu43,Y.Nefedov23,F.Nerling14,I.B.Nikolaev9,e,Z.Ning1,a,S.Nisar8,S.L.Niu1,a,X.Y.Niu1,S.L.Olsen32,Q.Ouyang1,a,
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0 X.P.Xu37,L.Yan49A,49C,W.B.Yan46,a,W.C.Yan46,a,Y.H.Yan18,H.J.Yang34,H.X.Yang1,L.Yang51,Y.X.Yang11,M.Ye1,a,
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i Y.Zhang1,Y.H.Zhang1,a,Y.N.Zhang41,Y.T.Zhang46,a,YuZhang41,Z.H.Zhang6,Z.P.Zhang46,Z.Y.Zhang51,G.Zhao1,
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r Y.B.Zhao1,a,Z.G.Zhao46,a,A.Zhemchugov23,c,B.Zheng47,J.P.Zheng1,a,W.J.Zheng33,Y.H.Zheng41,B.Zhong28,L.Zhou1,a,
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Y.S.Zhu1,Z.A.Zhu1,J.Zhuang1,a,L.Zotti49A,49C,B.S.Zou1,J.H.Zou1
(BESIIICollaboration)
1InstituteofHighEnergyPhysics,Beijing100049,People’sRepublicofChina
2BeihangUniversity,Beijing100191,People’sRepublicofChina
3BeijingInstituteofPetrochemicalTechnology,Beijing102617,People’sRepublicofChina
4BochumRuhr-University,D-44780Bochum,Germany
5CarnegieMellonUniversity,Pittsburgh,Pennsylvania15213,USA
6CentralChinaNormalUniversity,Wuhan430079,People’sRepublicofChina
7ChinaCenterofAdvancedScienceandTechnology,Beijing100190,People’sRepublicofChina
8COMSATSInstituteofInformationTechnology,Lahore,DefenceRoad,OffRaiwindRoad,54000Lahore,Pakistan
9G.I.BudkerInstituteofNuclearPhysicsSBRAS(BINP),Novosibirsk630090,Russia
10GSIHelmholtzcentreforHeavyIonResearchGmbH,D-64291Darmstadt,Germany
11GuangxiNormalUniversity,Guilin541004,People’sRepublicofChina
12GuangXiUniversity,Nanning530004,People’sRepublicofChina
13HangzhouNormalUniversity,Hangzhou310036,People’sRepublicofChina
14HelmholtzInstituteMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany
2
15HenanNormalUniversity,Xinxiang453007,People’sRepublicofChina
16HenanUniversityofScienceandTechnology,Luoyang471003,People’sRepublicofChina
17HuangshanCollege,Huangshan245000,People’sRepublicofChina
18HunanUniversity,Changsha410082,People’sRepublicofChina
19IndianaUniversity,Bloomington,Indiana47405,USA
20(A)INFNLaboratoriNazionalidiFrascati,I-00044,Frascati,Italy;(B)INFNandUniversityofPerugia,I-06100,Perugia,Italy
21(A)INFNSezionediFerrara,I-44122,Ferrara,Italy;(B)UniversityofFerrara,I-44122,Ferrara,Italy
22JohannesGutenbergUniversityofMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany
23JointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia
24Justus-Liebig-UniversitaetGiessen,II.PhysikalischesInstitut,Heinrich-Buff-Ring16,D-35392Giessen,Germany
25KVI-CART,UniversityofGroningen,NL-9747AAGroningen,TheNetherlands
26LanzhouUniversity,Lanzhou730000,People’sRepublicofChina
27LiaoningUniversity,Shenyang110036,People’sRepublicofChina
28NanjingNormalUniversity,Nanjing210023,People’sRepublicofChina
29NanjingUniversity,Nanjing210093,People’sRepublicofChina
30NankaiUniversity,Tianjin300071,People’sRepublicofChina
31PekingUniversity,Beijing100871,People’sRepublicofChina
32SeoulNationalUniversity,Seoul,151-747Korea
33ShandongUniversity,Jinan250100,People’sRepublicofChina
34ShanghaiJiaoTongUniversity,Shanghai200240,People’sRepublicofChina
35ShanxiUniversity,Taiyuan030006,People’sRepublicofChina
36SichuanUniversity,Chengdu610064,People’sRepublicofChina
37SoochowUniversity,Suzhou215006,People’sRepublicofChina
38SunYat-SenUniversity,Guangzhou510275,People’sRepublicofChina
39TsinghuaUniversity,Beijing100084,People’sRepublicofChina
40(A)AnkaraUniversity,06100Tandogan,Ankara,Turkey;(B)IstanbulBilgiUniversity,34060Eyup,Istanbul,Turkey;(C)Uludag
University,16059Bursa,Turkey;(D)NearEastUniversity,Nicosia,NorthCyprus,Mersin10,Turkey
41UniversityofChineseAcademyofSciences,Beijing100049,People’sRepublicofChina
42UniversityofHawaii,Honolulu,Hawaii96822,USA
43UniversityofMinnesota,Minneapolis,Minnesota55455,USA
44UniversityofRochester,Rochester,NewYork14627,USA
45UniversityofScienceandTechnologyLiaoning,Anshan114051,People’sRepublicofChina
46UniversityofScienceandTechnologyofChina,Hefei230026,People’sRepublicofChina
47UniversityofSouthChina,Hengyang421001,People’sRepublicofChina
48UniversityofthePunjab,Lahore-54590,Pakistan
49(A)UniversityofTurin,I-10125,Turin,Italy;(B)UniversityofEasternPiedmont,I-15121,Alessandria,Italy;(C)INFN,I-10125,Turin,
Italy
50UppsalaUniversity,Box516,SE-75120Uppsala,Sweden
51WuhanUniversity,Wuhan430072,People’sRepublicofChina
52ZhejiangUniversity,Hangzhou310027,People’sRepublicofChina
53ZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina
aAlsoatStateKeyLaboratoryofParticleDetectionandElectronics,Beijing100049,Hefei230026,People’sRepublicofChina
bAlsoatBogaziciUniversity,34342Istanbul,Turkey
cAlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia
dAlsoattheFunctionalElectronicsLaboratory,TomskStateUniversity,Tomsk,634050,Russia
eAlsoattheNovosibirskStateUniversity,Novosibirsk,630090,Russia
f AlsoattheNRC”KurchatovInstitute,PNPI,188300,Gatchina,Russia
gAlsoatUniversityofTexasatDallas,Richardson,Texas75083,USA
hAlsoatIstanbulArelUniversity,34295Istanbul,Turkey
Using 106 million ψ(3686) events collected with the BESIII detector, we measure multipole amplitudes
for the decay ψ(3686) γχ γγJ/ψ beyond the dominant electric-dipole (E1) amplitudes. The
c1,2
→ →
normalized magnetic-quadrupole (M2) amplitude for ψ(3686) γχ γγJ/ψ and the normalized
c1,2
→ →
electric-octupole (E3) amplitudes for ψ(3686) γχ , χ γJ/ψ are determined. The M2 ampli-
c2 c2
→ →
tudes for ψ(3686) γχ and χ γJ/ψ are found to differ significantly from zero and are consis-
c1 c1,2
→ →
tentwiththeoretical predictions. Wealsoobtain theratiosof M2 contributions of ψ(3686) and J/ψ decays
to χ , b1/b2 = 1.35 0.72 and a1/a2 = 0.617 0.083, which agree well with theoretical expecta-
c1,2 2 2 ± 2 2 ±
tions. By considering the multipole contributions of χ , we measure the product branching fractions for
c1,2
the cascade decays ψ(3686) γχ γγJ/ψ and search for the process η (2S) γJ/ψ through
c0,1,2 c
→ → →
ψ(3686) γη (2S). The product branching fraction for ψ(3686) γχ γγJ/ψ is 3σ larger than
c c0
→ → →
publishedmeasurements,whilethoseofψ(3686) γχ γγJ/ψareconsistent.Nosignificantsignalfor
c1,2
→ →
thedecayψ(3686) γη (2S) γγJ/ψisobserved,andtheupperlimitoftheproductbranchingfractionat
c
→ →
3
the90%confidencelevelisdetermined.
PACSnumbers:14.40.Pq,13.20.Gd,13.40.Hq
I. INTRODUCTION tweenthe quarks,L , anddifferentintrinsic spins, S . M1
cc¯ cc¯
radiative transitionsare importantbecause they allow access
The processes ψ(3686) γ1χc1,2, and χc1,2 γ2J/ψ tospin-singletstatesine+e−colliders,suchasηcandηc(2S),
are dominated by electric-d→ipole (E1) amplitudes,→but allow whichcannotbeproduceddirectlyine+e− annihilation. Lit-
forhighermultipoleamplitudesaswell,suchasthemagnetic tleexperimentalinformationisavailableontheM1transitions
quadrupole(M2) and electric octupole(E3) transitions. The due to their weak transition rates. Although several experi-
contributionsofthesehighermultipoleamplitudesgiveinfor- mentshavepreviouslymeasuredtheM1transitionratesinthe
mation on the anomalous magnetic moment κ of the charm charmonium system, such as for ψ(3686) γηc(ηc(2S)),
→
quark[1,2]andontheadmixtureofS-andD-wavestates[3]. J/ψ γηc, these results are notconsistent[18–20]. Theo-
→
ThenormalizedM2contributionsforψ(3686) γ χ and retically, the M1 transitionrates have been calculated by us-
1 c1,2
χ γ J/ψ, which are referred to as b1,2→and a1,2 with ing various models [16, 21–23], and the corresponding par-
c1,2 → 2 2 2 tialwidthsarefoundtobemuchlargerthantheexperimental
thesuperscriptrepresentingχ , arepredictedtoberelated
c1,2
values. Alatticequantumchromodynamics(LQCD)calcula-
tothemassofthecharmquark,m ,andκ[1,2,4].Byassum-
c
ingmc = 1.5 GeV/c2 andignoringthemixingofS-andD- tionpredictsthatthepartialwidthforthetransitionηc(2S)→
γJ/ψ is largerthanthatforthe decayψ(3686) γη [23].
wavestates, thecontributionsb1,2 anda1,2, correctedtofirst → c
2 2 The process of η (2S) γJ/ψ has not been observed yet.
order in Eγ1,2/mc, where Eγ1,2 is the energy of γ1,2 in the Anexperimentalcobserv→ationandameasurementofitsdecay
restframeofthemothercharmoniumstate, arepredicted[4]
ratewillbehelpfultotestthedifferentmodels.
tobe
In this paper, we report on a measurement of the higher-
b12= Eγ1[ψ(3648m6)c→γ1χc1](1+κ)=0.029(1+κ), order multipole amplitudes in the processes of ψ(3686) →
γ χ ,χ γ J/ψ, where the J/ψ is reconstructedin
a12=−Eγ2[χc14m→cγ2J/ψ](1+κ)=−0.065(1+κ), (1) mit1sadkcee1c,ua2syemocf1o,td2hee→sjJoi/nψ2td→istrℓi+buℓ−tio(nℓs=ofeth/eµ)fi.vTehheelmiceitaysuarnegmleesnitns
b22= √35Eγ1[ψ(3648m6)c→γ1χc2](1+κ)=0.029(1+κ), thefinal-state. Usingtheinvariantmassofγ2J/ψ,weobtain
the productbranchingfractions of ψ(3686) γ χ
a22=−√35Eγ2[χc24m→cγ2J/ψ](1+κ)=−0.096(1+κ), γ1γ2J/ψ andsearchforηc(2S) → γ2J/ψ pr→oduc1edc0th,1r,o2u→gh
ψ(3686) γ η (2S). In the measurement of the product
respectively.TheratiooftheM2contributionsofψ(3686) 1 c
→
→ branching fractions of ψ(3686) γ χ γ γ J/ψ,
γ χ toψ(3686) γ χ (χ γ J/ψtoχ γ J/ψ) 1 c0,1,2 1 2
1 c1 1 c2 c1 2 c2 2 → →
→ → → themultipolecontributionsofχ areconsideredforthefirst
isindependentofthem andκofthecharmquarktofirstor- c1,2
c
der in E /m and predicted to be b1/b2 = 1.000 0.015 time. The results presentedin this manuscriptsupersede the
and a1/aγ2 =c 0.676 0.071, respe2ctiv2ely [5], wh±ere the ones in Ref. [24]. The analyses are based on a sample of
2 2 ± 156 pb−1 taken at a center-of-mass energy 3.686 GeV, cor-
dominant uncertainties come from ignoring contributions of
higher-order in (E /m )2. Higher-order multipole ampli- responding to 106 million ψ(3686) [25]. A 928 pb−1 data
γ c sample taken at 3.773 GeV [26] and a 44 pb−1 data sample
tudes can be obtained by investigating the angular distribu-
takenat3.65GeVareusedtoestimatethebackgroundsfrom
tionsofthefinal-stateparticles[1,6,7]. Severalexperiments
QCDprocesses.
have searched for higher-order multipole amplitudes [5, 8–
12]. TheCLEOexperimentreportedsignificantM2contribu-
tions in ψ(3686) γ χ and χ γ J/ψ by analyz-
1 c1 c1,2 2
ing 24 million ψ(3→686) decays [5]. Re→cently, BESIII found II. BESIIIDETECTORANDMONTECARLO
evidence for the M2 contribution in ψ(3686) γχ with SIMULATION
c2
χ π+π−/K+K−[12]. →
c2
→
The experimentallyobservedcharmoniumstates and their The BESIII detector is described in detail in Ref. [27]. It
decay can be reproduced reasonably well by calculations is an approximately cylindrically symmetric detector which
basedonapotentialmodelandbyperturbativequantumchro- covers93%ofthesolidanglearoundthecollisionpoint. The
modynamics(pQCD)[13].However,fortheE1radiativetran- detector consists of four main components: (a) A 43-layer
sitionsofψ(3686) γ χ ,therearesignificantdiscrep- maindriftchamber(MDC)providesamomentumresolution
1 c0,1,2
→
ancies between different model predictions [14–16] and the of 0.5% for charged tracks at 1 GeV/c in a 1 T magnetic
Particle Data Group(PDG) average[17]. The partialwidths field;(b)atime-of-flightsystem(TOF)isconstructedofplas-
ofψ(3686) γ χ arepredictedtobe26,29and24keV tic scintillators with a time resolution of 80 ps (110 ps) in
1 c0,1,2
→
respectively, by using the Godfrey-Isgur model [16], which the barrel (endcaps); (c) a 6240 cell CsI(Tl) crystal electro-
deviate by (13 3.5)%, (1.4 4.6)%, (11.8 3.9)% magnetic calorimeter (EMC) provides an energy resolution
− ± ± − ±
fromtheaveragesofexperimentalmeasurements[17]. for photons of 2.5% (5%) at 1 GeV in the barrel (endcaps);
Magnetic dipole (M1) radiative transitions occur only be- (d)amuoncounter(MUC)consistingof9(8)layersofresis-
tween states having the same orbital angularmomentumbe- tive plate chambers in the barrel (endcaps) within the return
4
yoke of the magnet with a position resolution of 2 cm pro- with the smallest χ2 value is kept. The χ2 is required to
4C 4C
videsmuon/pionseparation. A GEANT4 [28] based detector be χ2 < 60, where the requirementis determinedby opti-
4C
simulationpackagehasbeendevelopedtomodelthedetector mizingthe statistical significanceS/√S+B forthe η (2S)
c
responseusedinMonteCarlo(MC)generatedevents. channel. Here, S is the numberof eventsin the η (2S) sig-
c
A MC simulated sample of 106 million generic ψ(3686) nalregion3.60<M4C(γ ℓ+ℓ−)<3.66GeV/c2(γ denotes
2 2
decays(‘inclusiveMC’)isusedforgeneralbackgroundstud- thephotonwithlargerenergy,M4Cistheinvariantmasswith
ies. The ψ(3686) resonances are produced by the event theenergiesandmomentaupdatedwiththe4Ckinematicfit)
generator KKMC [29]. The known decays are generated obtained from the exclusive MC sample and B is the num-
by BESEVTGEN [30] with branching fractions taken from berofcorrespondingbackgroundeventsdeterminedfromthe
PDG[17], whiletheremainingdecaysaregeneratedaccord- 106millioninclusiveMCsampleandacontinuumdatasam-
ing to the LUNDCHARM model [31]. Exclusive MC sam- plecollectedatacenter-of-massenergyof3.65GeV.Thelat-
ples for signal decays are generated to optimize the selec- terisnormalizedtothe luminosityoftheψ(3686)datasam-
tion criteria and to determine the detection efficiencies. The ple. Thebranchingfractionofthedecayη (2S) γ J/ψis
c 2
→
ψ(3686) γχ γγJ/ψ decays are generated with assumedtobe1%.
c0,1,2
→ →
angulardistributionsdeterminedfromdata,andtheη (2S)
c
→ To select events including the J/ψ intermediate state, the
γJ/ψ decay is generated according to the HELAMP model
invariant mass of the lepton pair is required to be in the re-
in EVTGEN [30]. To estimate the backgroundcontributions
gion of 3.08 < M4C(ℓ+ℓ−) < 3.12 GeV/c2. In addition,
fromψ(3686)decays,theexclusiveMCsamplesψ(3686)
ηJ/ψ,π0J/ψ,π0π0J/ψ,γγJ/ψ are generated according→to to removeψ(3686) π0J/ψ and ψ(3686) ηJ/ψ back-
→ →
grounds, events with an invariantmass of the photon pair in
the HELAMP, JPIPI [30] and PHSP models, respectively. To
theregions0.11<M4C(γγ)<0.15GeV/c2orM4C(γγ)>
investigate QED processes backgrounds, radiative Bhabha
and di-muonevents(e+e− e+e−/µ+µ−) simulated with 0.51 GeV/c2 are rejected. A MC study shows that this re-
→ moves 97.9% of the π0J/ψ events and almost 100% of the
BABAYAGA V3.5 [32], as well as ψ(3770) γχcJ and
γISRψ(3686) γχcJ,π0J/ψ producedby KK→MC [29], are ηJ/ψ events, while the efficiencies of the signal channels
→ for χ ,χ ,χ and η (2S) are 74.7%, 90.0%, 93.9%, and
usedtogetherwiththeexperimentaldataat3.773GeV. c0 c1 c2 c
88.0%,respectively.
III. EVENTSELECTION
The signal decay ψ(3686) γ χ (η (2S))
1 c0,1,2 c
γ γ J/ψ, J/ψ ℓ+ℓ− (ℓ = e,→µ)consistsof two charg→ed
1 2 → IV. MEASUREMENTOFHIGHER-ORDERMULTIPOLE
tracks and two photons. Events with exactly two oppositely
AMPLITUDES
chargedtracksandfromtwouptofourphotoncandidatesare
selected. Charged tracks are required to originate from the
run-dependentInteractionPoint(IP)within1cminthedirec- Figure 1 shows the M4C(γ ℓ+ℓ−) invariant
2
tionperpendiculartoandwithin 10cmalongthebeamaxis, mass distribution for the selected χ candidates.
± c1,2
and should lie within the polar angular region of cosθ < The signal regions for χ and χ are defined
| | c1 c2
0.93. The momentum p of each track must be larger than as 3.496 < M4C(γ ℓ+ℓ−) <3.533 GeV/c2 and
2
1 GeV/c. The energy deposit E in the EMC and E/p of 3.543 < M4C(γ ℓ+ℓ−) < 3.575 GeV/c2, respectively.
2
each track are used to identify muon or electron candidates.
We find 163922 χ candidates and 89409 χ candidates.
c1 c2
TrackswithE <0.4GeVaretakenasmuons,andthosewith Thebackgroundisestimated fromthe inclusiveMCsample.
E/p > 0.8 c are identified as electrons. Events with both The total number of backgroundevents is found to be 1016
tracks identified as muons or electrons are accepted for fur-
(0.7%)withintheχ signalregionand883(1.0%)intheχ
c1 c2
theranalysis.Photonsarereconstructedfromisolatedshowers
region. For theχ (χ ) channel,thedominantbackground
c1 c2
in the EMC, where the angle between the positions in EMC
is the contamination from χ (χ ). Some backgrounds
c2 c1
of the photonand the closest chargedtrack is requiredto be stem from ψ(3686) γγJ/ψ and π0π0J/ψ decays. The
largerthan 10 degrees. The energydepositedin the EMC is QEDprocesse+e− →ℓ+ℓ−γ contributesabout109
ISR/FSR
corrected by the energy loss in nearby TOF counters to im- →
eventsforχ and135eventsforχ . Non-J/ψbackground
c1 c2
provethereconstructionefficiencyandtheenergyresolution.
isnegligiblysmallaccordingtothesidebandanalysis.
Theenergyofeachphotonshowerisrequiredtobelargerthan
25 MeV. The shower timing informationis requiredto be in Events in the signal regions are used to determine
coincidence with the event start time with a requirement of the higher-order multipole amplitudes in the ψ(3686)
→
0 t 700 ns to suppress electronic noise and showers γ1χc1,2 γ1γ2J/ψ radiative transitions. The normalized
unr≤elate≤dtotheevent. M2 contr→ibutions for the channels ψ(3686) γ1χc1,2 and
→
A four-constraint (4C) kinematic fit is performed for the χ γ J/ψaredenotedasb1,2 anda1,2,respectively. In
c1,2 → 2 2 2
two lepton candidatesand all possible two photon combina- the χ decays, the E3 transitionis also allowed. The corre-
c2
tionswiththeinitialψ(3686)four-momentumasaconstraint. spondingnormalizedE3amplitudesareindicatedasb2anda2
3 3
If more than onecombinationis foundin one event, the one forψ(3686) γ χ andχ γ J/ψ,respectively.
1 c2 c2 2
→ →
5
data
105 Background
2eV/c 104 χc1,2 signal MC (cid:18)AA1011(cid:19)=(cid:18)√√00..55 −√√00.5.5(cid:19)(cid:18)aa1112(cid:19),
M
2 103 B01 = √0.5 √0.5 b11 ,
vents / 102 (cid:18)BA1120(cid:19) (cid:18)√10.5 −√√30.5√(cid:19)1(cid:18)5b12(cid:19)2√3 a21 (3)
E 10 AA212= √303√32 √√510 √−42aa222,
1  2  −  3
3.46 3.48 3.5 3.52 3.54 3.56 3.58 3.6 B2 √3 √15 2√3 b2
M4C(γ l+l-) (MeV/c2) B02= 1  3 √5 4b12,
2 B12 √30 3√2 √10 √−2 b22
 2  −  3
FIG. 1. (color online). Mass distributions of M4C(γ ℓ+ℓ−) for
2
events in the χc1,2 region. Black dots correspond to data and red where B|Jν| and B|Jνe| [33] are the helicity amplitudes for
histogramsareobtained fromthesignalMC samplesscaledbythe ψ(3686) γ χ , AJ and AJ [33] are those for χ
maximumbin.Thegreendashedhistogramisthebackgroundcontri- → 1 cJ |ν| |νe| cJ →
γ J/ψ. (a1)2+(a1)2 = 1, (a2)2+(a2)2+(a2)2 = 1,
butionobtainedfromtheinclusiveMCsamples. Thearrowsdenote 2 1 2 1 2 3
thesignalregions. and simiplarly for bJ s. The copefficientsa (n=1,...,9forχc1 )
|ν| n n=1,...,36forχc2
are functions of θ ,θ ,φ ,θ ,φ . For the normalization,
1 2 2 3 3
high-statisticsphase-space(PHSP)MCsamplesaregenerated.
IV.A. Fitmethod Thenormalizationfactorisexpressedas
Weperformanunbinnedmaximumlikelihoodfittoobtain W (aJ ,bJ )
χcJ 2,3 2,3
the higher-order multipole amplitudes following the proce-
NP W (θ (i),θ (i),φ (i),θ (i),φ (i),aJ ,bJ )
dure as described in Ref. [12]. The log-likelihood function = i=1 χcJ 1 2 2 3 3 2,3 2,3
is builtasln = ln ln , where N F (i) P NP
Ls L− Lb L ≡ i=1 χc1,2
denotestheproductofprobabilitydensitiesforQallcandidates = anAJ|ν|AJ|νe|B|Jν′|B|Jνe′|,
inthesignalregion,N isthenumberofthecandidates,andF Xn
istheprobabilitydensityfunctions(PDF).Thecontributionto (4)
thelikelihoodfrombackgroundevents, ,isestimatedusing
b
theinclusiveMCsampleandcontinuumLdata. whereNP isthenumberofselectedevents. Insuchway,the
detectorefficiencyisconsideredinthenormalization.
The PDF F for the joint angular distribu-
tions of the χ decay sequences are defined as
c1,2
WχcJ(θ1,θ2,φ2,θ3,φ3,aJ2,3,bJ2,3). The term in the numerator, IV.B. Fitresults
WχcJ(aJ2,3,bJ2,3)
W (θ ,θ ,φ ,θ ,φ ,aJ ,bJ ), is derived from the he-
χcJ 1 2 2 3 3 2,3 2,3
licity amplitudesand the Clebsch-Gordanrelation [1], while Byminimizing ln s,thebestestimatesofthehigh-order
− L
W (aJ ,bJ ) is used for the normalization. θ is the multipoleamplitudescanbeobtained. Tovalidatethefitpro-
χcJ 2,3 2,3 1 cedure,checksareperformedwithMCsamplesforχ ,re-
polar angle of γ in the ψ(3686) rest frame with the z-axis c1,2
1 spectively, where the MC samples are generated based on a
in the electron-beam direction. θ and φ are the polar and
2 2 pure E1 transition model (a1,2 = 0, b1,2 = 0) or an arbi-
azimuthalangles of γ in the χ rest frame with the z-axis 2,3 2,3
2 cJ
intheγ1directionandφ2 =0intheelectron-beamdirection. traryhigher-ordermultipoleamplitude(a21,,32 6= 0, b12,,23 6= 0).
θ and φ are the polar and azimuthal angles of ℓ+ from The fit values are consistent with the input valueswithin 1σ
3 3
J/ψ ℓ+ℓ− intheJ/ψ restframewiththez axisaligned of statistical uncertainty. An unbinned maximum likelihood
tothe→γ directionandφ =0intheγ directio−n. fit to the joint angular distribution for data is performedand
2 3 1
TheformulaW (θ ,θ ,φ ,θ ,φ ,aJ ,bJ )forthehe- the corresponding angle distributions are depicted in Fig. 2
χcJ 1 2 2 3 3 2,3 2,3
licity amplitudeshasbeen discussedin Refs. [5, 11, 12, 33]. togetherwith therelativeresidualspectra. Thefit resultsare
Using the same method as reported in Refs. [5, 11, 12], the listedinTableI,wherethefirstuncertaintiesarestatistical,the
jointangulardistributionsW canbeexpressedintermsof secondonesaresystematicalasdescribedinSectionVI.
χcJ
aJ andbJ as The statistical significance of a non-pure E1 transition is
2,3 2,3
calculatedtobe24.5σ(13.5σ)forχ (χ )bytakingthedif-
c1 c2
ference of the log-likelihood values for the fits with higher-
WχcJ(θ1,θ2,φ2,θ3,φ3,aJ2,3,bJ2,3) ordermultipoleamplitudesincludedandfitsbasedona pure
(2) E1 transition, taking the change in the number of degrees
= a AJ AJ BJ BJ ,
n |ν| |νe| |ν′| |νe′| of freedom, ∆ndf = 2 (4), into consideration. Similarly,
Xn
the statistical significance of the E3 contribution for χ is
c2
with 2.3σ, as obtained by comparing the log-likelihood values
6
TABLEI.FitresultsforaJ andbJ fortheprocessofψ(3686) γ χ γ γ J/ψ,thefirstuncertaintyisstatisticalandthesecond
2,3 2,3 → 1 c1,2 → 1 2
systematic.TheρJ arethecorrelationcoefficientsbetweenaJ andbJ .
a2,3b2,3 2,3 2,3
a1= 0.0740 0.0033 0.0034,b1 =0.0229 0.0039 0.0027
χc1 2 − ± ± 2 ± ±
ρ1 =0.133
a2b2
a2 = 0.120 0.013 0.004,b2 =0.017 0.008 0.002
2 − ± ± 2 ± ±
χc2 a23 =−0.013±0.009±0.004,b23 =−0.014±0.007±0.004
ρ2 = 0.605,ρ2 =0.733,ρ2 = 0.095
a2b2 − a2a3 a2b3 −
ρ2 = 0.422,ρ2 =0.384,ρ2 = 0.024
a3b2 − b2b3 a3b3 −
between the nominal fit and a fit based on the assumption γ µ+µ−), a three-constraint(3C) kinematic fit is ap-
ISR/FSR
that E3 contribution is zero. A Pearson-χ2 test [34] is per- plied,inwhichtheenergyofthesoftphoton(γ )isleftfreein
1
formedtovalidatethefitresult. Eachangulardimension(i.e., thefit. ThedetailMCstudiesindicatethatthe3Ckinematicfit
cosθ ,cosθ ,φ ,cosθ ,φ ) is divided equally into 8 bins. donotchangethepeakpositionofinvariantmassforsignals
1 2 2 3 3
Thisleadstoatotalof85 =32768cells. Theχ2isdefinedas andthecorrespondingresolutionsaresimilartothosewith4C
kinematicfit.
(nDT nBKG nMC)2
χ2 = i − i − i , (5)
nDT+nBKG
Xi i i
V.A. Backgroundstudy
where nDT is the number of events in the i-th cell for data,
i
nBiKG is the number of backgroundcontribution determined Thebackgroundsmainlycomefromψ(3686)transitionsto
byinclusiveMCsample,andnMi Cisthenumberofeventsfor J/ψ and from e+e− ℓ+ℓ−nγISR/FSR(ℓ = e/µ). The
theluminosity-normalizedMCsampleproducedaccordingto otherbackground,inclu→dingψ(3686) ηJ/ψ,γ J/ψand
ISR
the best fit values for aJ2,3 and bJ2,3. The number of events non-J/ψ backgrounds, is only 0.3%→of that from ψ(3686),
of the MC sample is 40 times larger than of the data. For whichisneglected.
cells with fewer than 10 events, events in adjacent bins are
The backgrounds from ψ(3686) transitions to J/ψ in-
combined. The test resulted in χ2/ndf = 9714.7/9563 = clude ψ(3686) γγJ/ψ,π0π0J/ψ,π0J/ψ. High statis-
1.02 for χ and χ2/ndf = 5985.2/5840 = 1.02 for χ →
c1 c2 tics MC samples of these decays are generated to deter-
demonstratingthatthefitgivesanexcellentrepresentationof
mine their distributions and contributions. With the pub-
thedata.
lished branching fractions [17], which have been measured
accuratelybydifferentexperiments,theestimatednumberof
events for ψ(3686) π0π0J/ψ,π0J/ψ and the efficiency
→
V. MEASUREMENTOF for ψ(3686) γγJ/ψ are obtained as summarized in Ta-
B(ψ(3686) →γχCJ →γγJ/ψ)ANDSEARCHFORTHE bleII. →
PROCESSηc(2S)→γJ/ψ The second major source of background in-
cludes radiative Bhabha and di-muon processes,
With theselected e+e− γ γ J/ψ candidates,we mea- e+e− ℓ+ℓ−γ (γ ) and ψ(3686)
1 2 ISR/FSR ISR/FSR
→ → →
suretheproductbranchingfractionsofthedecayψ(3686) ℓ+ℓ−γ (γ )(l=e/µ). Topreciselydescribetheshape,
→ FSR FSR
γ1χc0,1,2 γ1γ2J/ψ andsearchfor the processηc(2S) the backgroundis divided up into two parts: ℓ+ℓ− with one
γ2J/ψ. F→or the J/ψ e+e− channel, additional requir→e- radiative photon and ℓ+ℓ− with two radiative photons. For
→
mentsare appliedto suppressthe backgroundfromradiative thebackgroundfromψ(3686) ℓ+ℓ−γ (γ ),theratio
FSR FSR
Bhabha events (e+e− → γISR/FSRe+e−, where γISR/FSR ofeventyieldsbetweenthetwo→parts(Nℓ+ℓ−γγ/Nℓ+ℓ−γ)are
denotesthe initial/final-state radiative (ISR/FSR) photon(s)). obtainedbyaMCsimulation.Forthebackgroundfromradia-
Since the electron (positron) from radiative Bhabha tends to tive Bhabha/di-muon processes, the ratio Nℓ+ℓ−γγ/Nℓ+ℓ−γ
have a polar angle cosθe+(e−) close to +1 (-1), we apply a is obtained by a fit to a 928 pb−1 data sample taken at a
requirementofcosθe+ < 0.3andcosθe− > −0.3. Thesere- center-of-massenergyof3.773GeV.Aftertheeventselection
quirementssuppress77%oftheBhabhaeventswithareduc- imposedonthedata,theremainingeventsaremainlyradiative
tionofthesignalefficiencybyonethird. Thecorresponding Bhabha/di-muon events, and a small contribution originates
MC-determinedefficienciesarelistedinTableII. from ψ(3770) γχ and decays of ψ(3686) produced
cJ
→
A4Ckinematicfithasthedefectthattheenergyofafake in ISR process. In the fit, the shapes of the M3C(γ ℓ+ℓ−)
2
and soft photon will be modified according to the topology distributions for the Bhabha/di-muon processes are deter-
ofasignaleventduetorelativelylargeuncertainty,whichre- mined from a ψ(3686) ℓ+ℓ−γ (γ ) MC sample
FSR FSR
sultsinapeakingbackgroundsignatureintheM4C(γ J/ψ) by shifting the M3C(γ ℓ→+ℓ−) from ψ(3686) to ψ(3770)
2 2
invariant-massspectrum.Toremovethepeakingbackground, according to formula m′ = a (m m ) + m , where
0 0
such as radiative Bhabha and radiative di-muon (e+e− m = 3.097 GeV/c2 is the ma∗ss thr−eshold of γJ/ψ, and
0
→
7
4000
3000
2000
Data Data Data Data Data
1000 Fit MC Fit MC Fit MC Fit MC Fit MC
5
χ 0
-5
-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 10 1 2 3 4 5 6 0 1 2 3 4 5 6
2500
2000
1500
1000
Data Data Data Data Data
500 Fit MC Fit MC Fit MC Fit MC Fit MC
5
χ 0
-5
-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 10 1 2 3 4 5 6 0 1 2 3 4 5 6
cosθ cosθ cosθ φ φ
1 2 3 2 3
FIG.2.(coloronline).Resultsofthemulti-dimensionalfitonthejointangulardistributionandtheprojectionsoncosθ ,cosθ ,cosθ ,φ ,φ
1 2 3 2 3
ofthefinal-stateparticles. Theuppertenplotsshowtheangulardistributionsfortheχ channelandtheloweronesarefortheχ channel.
c1 c2
Theblackdotswitherrorbarsrepresentdatasubtractedbybackgroundandtheredhistogramsarethefitresults. Thelowerplotsdepictthe
relativeresidualχ=(N N )/√N ofthefit.
data fit data
−
TABLEII.Detectionefficiencies(ǫ)forchannelsofψ(3686) γχ ,γη (2S),γγJ/ψandthenumber(N)ofestimatedbackgroundfor
c0,1,2 c
channelsψ(3686) π0J/ψ,π0π0J/ψscaledbythedecayb→ranchingfractionandthetotalψ(3686)number.
→
Channel ǫχc0 (%) ǫχc1 (%) ǫχc2 (%) ǫηc(2S)(%) ǫγγJ/ψ (%) Nπ0J/ψ Nπ0π0J/ψ
e+e− 15.1 20.1 20.3 16.9 17.1 26.8 0.7 246.5 4.5
µ+µ− 32.7 44.1 44.0 37.0 38.0 65.2±1.7 500.9±9.1
± ±
the coefficient a = (3.773 m )/(3.686 m ) = 1.15 served. No evidentη (2S) signature is found. A simultane-
0 0 c
− −
shifts the events from 3.686 GeV to 3.773 GeV. The ousunbinnedmaximumlikelihoodfit isperformedto obtain
shapes of the backgrounds are based on MC simula- thesignalyields.ThecommonparameterforthetwoJ/ψde-
tion, while the amplitude of each component is set as a cay channels is the product branching fraction ( product) of
B
free parameter. Thus, the cross-section weighted ratio thecascadedecaysψ(3686) γχ (η (2S)) γγJ/ψ.
c0,1,2 c
→ →
of the backgrounds e+e− ℓ+ℓ−γISR/FSR(γISR/FSR) Thenumberof signaleventsforeachchannelis Nψ(3686)
and ψ(3686) ℓ+ℓ−γ →(γ ) for the two parts is product (J/ψ ℓ+ℓ−) ǫ. In the fit, the branch×-
FSR FSR
N0.6e+8e9−γγ/0N.0e4+4e)−→fγor=th1e.2e0+3e−±(0µ.0+8µ1−()Ncµh+aµn−nγeγl./NTµh+eµ−quγan=- Bibnegrofrfaψct(i3o×6n8sB6f)oervJen/tψ→sa→refiex+ede−×to/µth+eµv−aluaensdinthReetfo.t[a1l7n]uamnd-
±
titative results and shapes will be used in the simultaneous Ref.[25], respectively. Theefficiencyǫis obtainedfromthe
fit. signalMCsamplewiththehigher-ordermultipoleamplitudes
consideredaslistedinTableII. Thefitcontainsthreeχ
c0,1,2
components,theη (2S),andthebackground.Thesignalline-
c
V.B. SimultaneousfittoM3C(γ2ℓ+ℓ−) shapesoftheχc0,1,2areparameterizedas
(E3 E3 (BW(m) R ǫ(m))) G(µ,σ), (6)
Figure 3 shows the M3C(γ ℓ+ℓ−) distributions for se- γ1× γ2× ⊗ × ⊗
2
lected candidates of the two channels of J/ψ e+e− and whereBW(m) is the Breit-Wignerfunctionfor χ with
c0,1,2
J/ψ µ+µ−, where clear signals of χ →can be ob- themassesandwidthsfixedattheirworldaveragevalues[17].
c0,1,2
→
8
Rrepresentsthemassresolution,andǫ(m)isthemassdepen- isdeterminedbyaBayesianapproachusingauniformprior,
dentefficiency. The product(BW(m) R ǫ(m)) can be i.e.,findingthevaluescorrespondingto90%oftheprobability
⊗ ×
directly determinedfrom the MC simulation, where the MC distributioninthepositivedomain.
eventsaregeneratedwithsimpleBreit-Wignerfunctionusing
the higher-order multipole amplitudes with the angular dis-
tributions of the final state particles. E is the energy of VI. SYSTEMATICUNCERTAINTIES
γ1
theradiativephotonγ ofψ(3686) γ χ intheψ(3686)
1 1 cJ
→
restframe,andEγ2 istheenergyoftheγ2 ofχcJ γ2J/ψ The main sources of systematic uncertainty for the mea-
→
in the χcJ rest frame. The factor Eγ31,2 stems fromthe two- surements of higher-order multipole amplitudes are the un-
bodyPHSPandtheE1-transitionfactor,andtheBreit-Wigner certainties in the efficiency, the kinematic fit procedure, the
functionmodifiedbytheEγ31,2 factorisfortheχcJ invariant fitprocedureofthecombinedangulardistributions,statistical
mass distribution. The lineshape is convolutedwith a Gaus- fluctuationsoftheMCsample,andthebackgroundcontami-
sianfunction(denotedasG)accountingfordifferencesinthe nation.
invariantmass and massresolutionbetweenthe data and the A simulated sample of events distributed uniformly in
MCsimulation. Themeanµandstandarddeviationσ ofthe phase space PHSP is used to normalize the function Wχc1,2.
Gaussian functions are obtained from the fit to the data in a AdifferenceofdetectionefficienciesbetweentheMCsample
region of (3.36 < M3C(γ2ℓ+ℓ−) < 3.61 GeV/c2) by as- and the data will resultin a shiftin the measurement, which
suming no dependence between the e+e− and µ+µ− decay is taken as the systematic uncertainty. From the studies of
modes as well as between χc0,1,2. The results indicate µ thetrackingefficiencyforelectronsandmuonswiththecon-
0.35 MeV/c2 and σ 0.73 MeV/c2. Similarly, the sign≤al trolsamplesofψ(3686) π+π−J/ψ,J/ψ e+e−/µ+µ−
lineshapeoftheηc(2S≤)isdescribedby decays, and the photon→efficiency with the→control samples
fromψ(3686) 2(π+π−)π0 decaysandradiativedi-muon
(Eγ31×Eγ72×(B(m)⊗R×ǫ(m)))⊗G(µ,σ), (7) events,thediffe→renceinthedetectionefficienciesbetweenthe
data and MC is found to be polar angle dependent with the
where Eγ31 represents the two-body PHSP and the M1- largest value 0.006 0.003, which may change the helicity
transition factor for ψ(3686) γ η (2S) and E7 is the angulardistribution.±Thecorrespondingeffectonthehigher-
→ 1 c γ2
two-bodyPHSPandhinderedM1transitionfactor[16,21]for ordermultipolemeasurementisestimatedbyvaryingtheeffi-
η (2S) γ J/ψ.The(B(m) R ǫ(m))isalsodetermined ciencywithanasymmetricfunctionofcosθ andcosθ as
c → 2 ⊗ × ℓ+ γ1
byMCsimulationwiththemassandwidthofη (2S)setting p(cosθ ,cosθ )=(1.0+0.003cosθ 0.006cos2θ )
c γ1 ℓ+ γ1 γ1
totheworldaveragevalues[17]. Sincethemassofη (2S)is (1.0+0.003cosθ 0.006cos2θ )(w−hichcorresponds×to
c ℓ+− ℓ+
closetothoseofχ ,theµandσoftheGaussianarefixedto a0.9%(0.3%)differenceforcosθ = 1(1),θ isthepolar
cJ γ1
−
thevaluesobtainedfromafittotheχ signalsonly. angle for one photon, θ is for one charged track). Twice
c0,1,2 ℓ+
The shapes of backgrounds ψ(3686) thedifferencewithrespecttothenominalresultistakenasa
π0J/ψ,π0π0J/ψ,γγJ/ψ and e+e−( ψ(3686)) → systematic uncertainty. For the kinematic fit, the track helix
ℓ+ℓ−γ (γ ) are taken→from MC sim→- parametersare corrected to reduce the differencein the χ2
ISR/FSR ISR/FSR 4C
ulations. The numbers of ψ(3686) π0J/ψ and distributionbetweenthedataandtheMCsimulationaccord-
ψ(3686) π0π0J/ψ events are fixed→to the expec- ingtotheproceduredescribedinRefs.[35,36]. These PHSP
tations as →given in Table II. For the background from MCsampleswithoutandwiththehelixcorrectionareusedto
Ne+ℓe+−ℓ−(γ→γ/Nψℓ+(3ℓ−6γ86a))re →fixedℓ+toℓ−1n.2γ0IS3R/foFrSRt,hethee+er−atiocshaonf- tnaokremnaalsizteheWsχycs1t,e2mreastipceuctnicveerlyta,ianntyd.theresultantdifferenceis
nel and to 0.689 for the µ+µ− channel as described Toestimatetheuncertaintyfromthefitprocedure,200MC
above. In the fit for the final results in the region samplesusingthehigh-ordermultipoleamplitudesaregener-
(3.36 < M3C(γ ℓ+ℓ−) < 3.71 GeV/c2), the parame- ated,followedbyacompletedetectorsimulation. Eachsam-
2
ters of the smearing Gaussians for χc0,1,2 and ηc(2S) are plehas165k(90k)selectedeventsforχc1(χc2),andthesame
fixed, while the numbers of events for χ and η (2S), multipoleanalysisprocedureisappliedforeachsample. The
c0,1,2 c
ψ(3686) γγJ/ψ, e+e− ℓ+ℓ−γISR/FSR(γISR/FSR) differencesin a12, b12 (a22, a23, b22, b23) betweentheinputand
are free p→arameters. Figure→3 shows the M3C(γ ℓ+ℓ−) fittedvaluesareGaussiandistributed.Themeanvaluesofthe
2 Gaussiansareµ =(2 3) 10−4,µ =( 6 3) 10−4
distributions,theresultsoftheunbinnedmaximumlikelihood a12 ± × b12 − ± ×
fit,andtherelativeresiduals. Theχ2/ndf ofthefitis1.88for (µa22 = (17±13)×10−4, µa23 = (−4±8)×10−4, µb22 =
theµ+µ− channeland1.83forthee+e− channel. (16 6) 10−4, µ = ( 32 7) 10−4) and are taken
± × b23 − ± ×
The product branching fractions from the fit are (15.8 asthesystematicuncertainty.ThestatisticsoftheMCsample
0.3) 10−4,(351.8 1.0) 10−4and(199.6 0.8) 10−±4 forthenormalization,about3.6(1.8)Mevents,mayaffectthe
× ± × ± ×
forχ withstatisticaluncertaintyonly,respectively. The fitresults.Forthenormalizationfunction,Eq.(4),thevariance
c0,1,2
branchingfractionofψ(3686) γγJ/ψisdeterminedtobe fora (n=1,...,9forχc1 )is
(3.2 0.6) 10−4. Allmeasure→dbranchingfractionsarecon- n n=1,...,36forχc2
sisten±twith×thepreviousmeasurementofBESIII[24]. Since V(a )= 1 ΣNi=1a2n(i) [ΣNi=1an(i)]2 .
no significant η (2S) signal is found, an upper limit at the n N{ N − N }
c
90%confidencelevel(C.L.)ontheproductbranchingfraction The standard deviation for each coefficient is σ(a ) =
n
9
data data
22 110055 χFcit0t,i1n,2g,η rce(2sSu)lts Fχcit0t,i1n,2g,η rce(2sSul)ts
cc ψ(3686)→ γγJ/ψ ψ(3686)→ γγJ/ψ
V/V/110044 ψ(3686)→π0J/ψ ψ(3686)→π0J/ψ
ee
MM ψ(3686)→π0π0J/ψ ψ(3686)→π0π0J/ψ
s / 5s / 5110033 ee++ee--γγFFSSRRγFSR µµ++µµ--γγFFSSRRγFSR
ntnt
ee110022
vv
EE
1100
5
a
at
D
N
0
N/
∆
-5
3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.4 3.45 3.5 3.55 3.6 3.65 3.7
M3C(γ e+e-) (GeV/c2) M3C(γ µ+µ-) (GeV/c2)
2 2
FIG.3.(coloronline).Theresultsofasimultaneousmaximumlikelihoodfit(top)andcorrespondingrelativeresidual(N N )/√N
data fit data
(bottom). Theleftpanel forthee+e− channel, whilerightonefortheµ+µ− channel. Theblackdotsaredata, thebluec−urvesarethefit
results, the red long-dashed lines are for χ 0,1,2 signals. The grey dashed, orange dot-dashed, pink dotted lines are for backgrounds of
c
ψ(3686) γγJ/ψ, π0J/ψ, π0π0J/ψ,respectively. Thelight-bluedot-dot-dashedandgreendot-long-dashed linesareforbackgrounds
withfinal→stateparticlescomposedofℓ+ℓ−γandℓ+ℓ−γγ.
V(a ). The largest change in parameters a1 and b1 by sameprocedureasdescribedinthemultipoleamplitudemea-
n 2 2
pvanardybin2g, bth2efocrotehffiecχientcbhyan±ne1lσ)isfotraktheneaχsc1thcehsaynsnteeml (aati22c,uan23- smuaressmreenqtusi.reTmoenets,taimcoatnetrtohlesaumncpelertianintthyecχausedregbiyonth3e.4J9/<ψ
2 3 c2 c1,2
certainty. M4C(γℓ+ℓ−) < 3.58 GeV/c2 is used. For data, the only
The main backgrounds for the χ channel come from background is from ψ(3686) π0π0J/ψ, which is deter-
c1 →
ψ(3686) γχ ,γχ ,π0π0J/ψ,γγJ/ψ,whichcontribute minedinfittingwiththeexclusiveMCshape. Theefficiency
c0 c2
about0.7%→ofthecandidatesaccordingtoaMCstudy.Forthe of selection M4C(ℓ+ℓ−) (3.08,3.12) GeV is evaluated by
∈
comparingthenumberofsignaleventsbeforeandafterthere-
χ channel, the main backgroundscome from ψ(3686)
c2
γχ ,γχ ,π0π0J/ψ,γγJ/ψ and the contribution is abo→ut quirement,thecorrespondingdifferencebetweenthedataand
c0 c1
1%. Inthenominalfit,thecontributionofbackgroundisesti- MC sample is 0.6% for e+e− channel, and 0.1% for µ+µ−
channel. To beconservative,we take0.6%asthe systematic
matedbytheinclusiveMCsamples. Toestimatethesystem-
uncertainty. Withthesamesample,thesystematicuncertain-
atic uncertainty,high-statisticsMC samplesforbackgrounds
are generatedto re-determinethe shape and the contribution tiesrelatedtotheselectioncriteriaNγ 4,π0 andη vetoes,
≤
leptonsidentificationarealsodetermined. Theoveralldiffer-
accordingtopreviousmeasurements[17,24,37]. Thediffer-
ence in the efficiency between the data and MC sample for
enceinthefitresultsistakenasthesystematicuncertainty.All
thesecriteriais1.6%andistakenasasystematicuncertainty.
thesystematicuncertaintiesaresummarizedinTableIII.The
The additional systematic uncertainty due to the polar angle
totalsystematicuncertaintiesarecalculatedbyaddingthein-
dividualvaluesinquadrature,thereby,assumingthattheyare selectionfore+e−channelisdeterminedbyvaryingtheselec-
independent. tionwith 0.05andfittingsimultaneouslyagain. Thelargest
±
changes on the fit results are taken as the systematic uncer-
The systematic uncertainties of the branching fractions
tainty.
measurement include uncertainties from the number of
ψ(3686)events(0.9%)[25],thetrackingefficiency(0.1%per To estimate the possible uncertaintyfrom the interference
lepton) [38], the photon detection efficiency (1.0% per pho-
between ψ(3686) γγJ/ψ and ψ(3686) γχ
c0
ton) [39], the kinematicfit, the J/ψ mass window,the other γγJ/ψ, we repeat →the simultaneous fit, taking→the interfe→r-
selection criteria (Nγ 4, veto π0 and η, particle identifi- ence into account. The interference phase is found to be
≤
cation, cosθe+ < 0.3&&cosθe− > −0.3), the branching 1.58 0.05. The changes in the signal yields are taken as
fraction of J/ψ e+e−/µ+µ− (0.6%) [17], the interfer- the sy±stematic uncertainty. Since the signal shapes are de-
→
ence between ψ(3686) χc0 γγJ/ψ and non-resonant terminedfrom MC simulation, the correspondingsystematic
→ →
ψ(3686) γγJ/ψprocess,thefittingprocedure. uncertainty is estimated by alternative fit with varying the
→
The uncertaintyfrom the kinematic fit is estimated by the massandwidthofχ with 1σoftheworldaverageval-
c0,1,2
±
10
TABLEIII.Thedifferentsourcesofsystematicuncertaintiesforthemeasurementofhigher-ordermultipoleamplitudesfortheχ channels.
c1,2
χ χ
Source a1( 10−4)c1b1( 10−4) a2( 10−4) b2( 10−4)ca22( 10−4) b2( 10−4)
2 × 2 × 2 × 2 × 3 × 3 ×
EfficiencyofPHSPMC 17 14 2 4 27 18
Kinematicfit 8 12 20 9 10 3
Fittingprocedure 2 6 17 16 4 32
StatisticsofPHSPMC 2 3 4 2 3 4
Background 28 18 23 4 26 4
Total 34 27 36 20 40 38
ues [17] for signal MC shape. To estimate the uncertainty TheratiosofM2contributionsofχ toχ areindependent
c1 c2
duetothebackgroundofψ(3686) π0J/ψ,π0π0J/ψ and ofthemassm andtheanomalousmagneticmomentκofthe
c
→
theratioofNℓ+ℓ−γγ/Nℓ+ℓ−γ forBhabhaanddi-muonback- charmquarkatleadingorderinEγ/mc. Theyaredetermined
grounds,alternativefits are performedinwhich thenumbers tobe
ofexpectedbackgroundevents(seeTableII)andtheratioof
b1/b2 =1.35 0.72,
Nγγℓ+ℓ−/Nγℓ+ℓ− arevariedby 1σ. Forχc0,1,2,thelargest 2 2 ± (8)
differences in the signal yields f±rom the nominal values are a1/a2 =0.617 0.083.
2 2 ±
taken as the systematic uncertainty. For the η (2S) case, to
c
be conservative,theonecorrespondingto largestupperlimit The corresponding theory predictions are (b12/b22)th =
itshetadkieffneraesntthseoufirnceasl raerseusltu.mAmlalriszyesdteimnaTtiacbluenIcVer.taTinhteietsotoafl 1th.0e0m0o±st0p.0re1c5isaenmd(eaa12su/rae22m)tehnt=o0f.t6h7e6M±20a.0m7p1li[t5u]d.eBsya12usainndg
systematic uncertainties are obtained by adding the individ- by takingmc = 1.5 0.3GeV/c2, the anomalousmagnetic
±
ualonesinquadrature,thereby,assumingallthesesourcesare momentκcanbeobtainedfromEq.(1),
independent.
4m
1+κ= c a1
− Eγ2[χc1 →γ2J/ψ] 2 (9)
TABLEIV.Summaryofallsystematicuncertaintiesforthebranch- =1.140 0.051 0.053 0.229,
ingfractionsmeasurement. ± ± ±
wherethefirstuncertaintyisstatistical,thesecondissystem-
Source χ (%) χ (%) χ (%) η (2S)(%)
c0 c1 c2 c
Nψ(3686) 0.9 0.9 0.9 0.9 atic,andthethirduncertaintyisfrommc =1.5±0.3GeV/c2.
Trackingefficiency 0.2 0.2 0.2 0.2 Based on the multipole analysis, we measure the product
Photondetection 2.0 2.0 2.0 2.0 branchingfractionsforψ(3686) γχ γγJ/ψtobe
c0,1,2
Kinematicfit 0.6 0.5 0.5 0.4 (15.8 0.3 0.6) 10−4,(351.→8 1.0 12→.0) 10−4and
J/ψmasswindow 0.6 0.6 0.6 0.6 (199.6± 0.8± 7.0×) 10−4,respe±ctively±,where×thefirstun-
Otherselection 2.4 2.2 2.3 2.4 certaint±yissta±tistical×andsecondissystematic. InFig.5,the
(J/ψ e+e−/µ+µ−) 0.6 0.6 0.6 0.6 productbranchingfractionsarecomparedtopreviousresults
B →
Interference 0.7 - - -
from BESIII [24], CLEO [40], and the world average [17].
Signalshape 0.7 0.9 1.0 -
The world average refers to product of the average branch-
Background 0.1 0.1 0.1 -
ing fraction of ψ(3686) γ χ and the average branch-
Total 3.6 3.4 3.5 3.4 → 1 cJ
ing fraction of χ γ J/ψ, where the results of BESIII
cJ 2
→
andCLEOarenotincludedintheworldaveragevalues. For
allχ ,ourresultsexceedtheprecisionofthepreviousmea-
cJ
surements. Compared to the previous BESIII result, the re-
VII. RESULTANDSUMMARY sults are consistent within 1σ, but we have considered the
higher-ordermultipoleamplitudesandimprovedthe system-
Based on 106 million ψ(3686) decays, we measure the aticuncertaintyduetoamoreprecisemeasurementoftheto-
higher-ordermultipoleamplitudesforthedecaysψ(3686) talnumberofproducedψ(3686)[25]. Inaddition,ourmea-
→
γ χ γ γ J/ψ channels. Thestatisticalsignificanceof surementfortheχ channelis3σlargerthantheresultfrom
1 c1,2 1 2 c0
→
non-pureE1transitionis24.3σand13.4σfortheχ andχ CLEOand3σ largerthantheworldaveragevalue,whilefor
c1 c2
channel, respectively. The normalized M2 contribution for the χ , our results are consistent with previous measure-
c1,2
χ andthenormalizedE3contributionsforχ arelistedin ments.Therearetheoreticalpredictionforthebranchingfrac-
c1,2 c2
TableI.Figure4showsacomparisonofourresultswithpre- tionψ(3686) γχ byseveraldifferentmodels[14–16]
c0,1,2
→
viouslypublishedmeasurementsandwiththeoreticalpredic- without consideration of higher-order multipole amplitudes,
tionswithm = 1.5GeV/c2 andκ = 0. Theresultsarecon- whichagreewitheachotherpoorly. Theresultsinthismea-
c
sistentwith andmoreprecise thanthoseobtainedbyCLEO- surementwill providea guidanceforthe theoreticalcalcula-
c[5]andconfirmtheoreticalpredictions[1,2]. TheM2con- tions.
tributions for ψ(3686) γ χ (b1), χ γ J/ψ (a1), We also search for the decay η (2S) γJ/ψ through
andχ γ J/ψ(a2)→arefo1uncd1to2besigcn1ifi→cant2lynonze2ro. ψ(3686) γη (2S). No statisticcally si→gnificant signal is
c2 → 2 2 → c