Measurement of the branching fraction for psi(3770) -> gamma chi c0

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Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

branching

fraction

for

ψ (3770)

→

γ χ

c0

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

6

_,

_{X.C. Ai}

a

_,

_{O. Albayrak}

e

_,

_{M. Albrecht}

d

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_{D.J. Ambrose}

aw

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A. Amoroso

bb

,

bd

,

F.F. An

a

,

Q. An

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,

1

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J.Z. Bai

a

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R. Baldini

Ferroli

t

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Y. Ban

ag

,

D.W. Bennett

s

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J.V. Bennett

e

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M. Bertani

t

,

D. Bettoni

v

,

J.M. Bian

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F. Bianchi

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bd

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E. Boger

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4

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I. Boyko

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R.A. Briere

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H. Cai

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X. Cai

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1

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O. Cakir

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2

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A. Calcaterra

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G.F. Cao

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S.A. Cetin

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J.F. Chang

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1

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G. Chelkov

y

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4

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5

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G. Chen

a

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H.S. Chen

a

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H.Y. Chen

b

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J.C. Chen

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M.L. Chen

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1

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S.J. Chen

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X. Chen

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X.R. Chen

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Y.B. Chen

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H.P. Cheng

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G. Cibinetto

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D. Dedovich

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http://dx.doi.org/10.1016/j.physletb.2015.11.074

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a_Institute_of_High_Energy_Physics,_Beijing_100049,_People’s_Republic_of_China b_Beihang_University,_Beijing_100191,_People’s_Republic_of_China

c_Beijing_Institute_of_{Petrochemical}_Technology,_Beijing_102617,_People’s_Republic_of_China d_Bochum_{Ruhr-University,}_D-44780_Bochum,_Germany

e_Carnegie_Mellon_University,_Pittsburgh,_{PA 15213,}_USA

f_Central_China_Normal_University,_Wuhan_430079,_People’s_Republic_of_China

g_China_Center_of_Advanced_Science_and_Technology,_Beijing_100190,_People’s_Republic_of_China

h_COMSATS_Institute_of_Information_Technology,_Lahore,_Defence_Road,_Off_Raiwind_Road,₅₄₀₀₀_Lahore,_Pakistan i_G.I._Budker_Institute_of_Nuclear_Physics_SB_RAS_(BINP),_Novosibirsk_630090,_Russia

j_GSI_{Helmholtzcentre}_for_Heavy_Ion_Research_GmbH,_D-64291_Darmstadt,_Germany k_Guangxi_Normal_University,_Guilin_541004,_People’s_Republic_of_China

l_GuangXi_University,_Nanning_530004,_People’s_Republic_of_China

m_Hangzhou_Normal_University,_Hangzhou_310036,_People’s_Republic_of_China n_Helmholtz_Institute_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany o_Henan_Normal_University,_Xinxiang_453007,_People’s_Republic_of_China

p_Henan_University_of_Science_and_Technology,_Luoyang_471003,_People’s_Republic_of_China q_Huangshan_College,_Huangshan_245000,_People’s_Republic_of_China

r_Hunan_University,_Changsha_410082,_People’s_Republic_of_China s_Indiana_University,_Bloomington,_{IN 47405,}_USA

t_INFN_Laboratori_Nazionali_di_Frascati,_I-00044,_Frascati,_Italy u_INFN_and_University_of_Perugia,_I-06100,_Perugia,_Italy v_INFN_Sezione_di_Ferrara,_I-44122,_Ferrara,_Italy w_University_of_Ferrara,_I-44122,_Ferrara,_Italy

x_Johannes_Gutenberg_University_of_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany y_Joint_Institute_for_Nuclear_Research,₁₄₁₉₈₀_Dubna,_Moscow_region,_Russia

z_Justus_Liebig_University_Giessen,_II._{Physikalisches}_Institut,_{Heinrich-Buff-Ring}_16,_D-35392_Giessen,_Germany aa_KVI-CART,_University_of_Groningen,_NL-9747_AA_Groningen,_The_Netherlands

ab_Lanzhou_University,_Lanzhou_730000,_People’s_Republic_of_China ac_Liaoning_University,_Shenyang_110036,_People’s_Republic_of_China ad_Nanjing_Normal_University,_Nanjing_210023,_People’s_Republic_of_China ae_Nanjing_University,_Nanjing_210093,_People’s_Republic_of_China af_Nankai_University,_Tianjin_300071,_People’s_Republic_of_China ag_Peking_University,_Beijing_100871,_People’s_Republic_of_China ah_Seoul_National_University,_Seoul,_151-747,_Republic_of_Korea ai_Shandong_University,_Jinan_250100,_People’s_Republic_of_China

aj_Shanghai_Jiao_Tong_University,_Shanghai_200240,_People’s_Republic_of_China ak_Shanxi_University,_Taiyuan_030006,_People’s_Republic_of_China

al_Sichuan_University,_Chengdu_610064,_People’s_Republic_of_China am_Soochow_University,_Suzhou_215006,_People’s_Republic_of_China an_Sun_Yat-Sen_University,_Guangzhou_510275,_People’s_Republic_of_China ao_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China ap_Istanbul_Aydin_University,₃₄₂₉₅_Sefakoy,_Istanbul,_Turkey aq_Istanbul_Bilgi_University,₃₄₀₆₀_Eyup,_Istanbul,_Turkey ar_Uludag_University,₁₆₀₅₉_Bursa,_Turkey

as_Near_East_University,_Nicosia,_North_Cyprus,_10,_Mersin,_Turkey

(3)

au_University_of_Hawaii,_Honolulu,_{HI 96822,}_USA av_University_of_Minnesota,_Minneapolis,_{MN 55455,}_USA aw_University_of_Rochester,_Rochester,_{NY 14627,}_USA

ax_University_of_Science_and_Technology_Liaoning,_Anshan_114051,_People’s_Republic_of_China ay_University_of_Science_and_Technology_of_China,_Hefei_230026,_People’s_Republic_of_China az_University_of_South_China,_Hengyang_421001,_People’s_Republic_of_China

ba_University_of_the_Punjab,_{Lahore-54590,}_Pakistan bb_University_of_Turin,_I-10125,_Turin,_Italy

bc_University_of_Eastern_Piedmont,_I-15121,_Alessandria,_Italy bd_INFN,_I-10125,_Turin,_Italy

be_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden bf_Wuhan_University,_Wuhan_430072,_People’s_Republic_of_China bg_Zhejiang_University,_Hangzhou_310027,_People’s_Republic_of_China bh_Zhengzhou_University,_Zhengzhou_450001,_People’s_Republic_of_China

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Articlehistory:

Received4November2015

Receivedinrevisedform24November2015 Accepted30November2015

Availableonline9December2015 Editor: W.-D.Schlatter

Byanalyzingadata setof2.92 fb−1ofe+e− collisiondatatakenat√s=3.773 GeV and106.41×106

ψ(3686) decaystakenat√s₌3.686 GeV withthe BESIIIdetector attheBEPCIIcollider, wemeasure the branchingfraction andthe partialdecaywidthfor ψ(3770)→

γ χ

c0tobeB(ψ(3770)→

γ χ

c0)= (6.88±0.28±0.67)×10−3_and_[ψ(₃₇₇₀₎_→

_{γ χ}

c0]= (187±8±19)keV,respectively.Thesearethe

mostprecisemeasurementstodate.

1. Introduction

Transitions between charmonium states can be used to shed lighton variousaspects ofQuantum Chromodynamics (QCD),the theoryofthestronginteractions,inboththeperturbativeand non-perturbative regimes [1]. The

ψ(

3770

)

resonance is the lowest-mass charmonium state lying above the production threshold of open-charm DD pairs.

¯

It is assumed to be the 13_D

1 cc state

¯

witha small 23S1 admixture. Based on this S–D mixing model,

predictions have been made [2–6] for the partial widths of the

ψ(

3770

)

electric-dipole (E1) radiative transitions. These predic-tionsvaryover alargerangedepending ontheunderlyingmodel assumptions.Oneofthelargestvariationsinpredictionsisforthe partialwidth of

ψ(

3770

)

→

γ χ

c0,withpredictions ranging from 213 keVto523 keV.A precisemeasurement ofthepartial width of

ψ(

3770

)

→

γ χ

c0 provides a stringent test ofthe various the-oretical approaches, thereby providing a better understanding of

ψ(

3770

)

decays.

In 2006, the CLEO Collaboration reported the ﬁrst observa-tionof

ψ(

3770

)

→

γ χ

c0/1 andmeasured thepartialwidths[7,8].

A comparisonbetweentheir resultsandpredictionsoftraditional theorymodels[2–5]indicatesthatrelativisticandcoupled-channel effects are necessary ingredients to describe the data. A similar conclusionhasbeendrawnin

ψ(

3686

)

→

γ χ

cJ decays[9].The re-sultsofCLEOwerenormalizedtothecrosssection of

ψ(

3770

)

→

DD to

¯

obtainthetotalnumberof

ψ(

3770

)

decays,whichassumed

*

Correspondingauthor.

E-mailaddress:mahl@ihep.ac.cn(H.L. Ma).

1 _Also _at _State _Key _Laboratory _of _Particle _Detection _and _Electronics, _Beijing 100049,Hefei230026,People’sRepublicofChina.

2 _Also_at_Ankara_University,₀₆₁₀₀_Tandogan,_Ankara,_Turkey. 3 _Also_at_Bogazici_University,₃₄₃₄₂_Istanbul,_Turkey.

4 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia. 5 _Also_at _the_Functional _Electronics_Laboratory,_Tomsk _State_University,_Tomsk, 634050,Russia.

6 _Also_at_the_Novosibirsk_State_University,_Novosibirsk,_630090,_Russia. 7 _Also_at_the_NRC_“Kurchatov_{Institute”,}_PNPI,_188300,_Gatchina,_Russia. 8 _Also_at_the_{University of}_Texas_at_Dallas,_Richardson,_{TX 75083,}_USA. 9 _Also_at_Istanbul_Arel_University,₃₄₂₉₅_Istanbul,_Turkey.

thecontributionof

ψ(

3770

)

→

non-DD decays

¯

isnegligible[27]. Recently,theBESIIICollaborationpresentedanimproved measure-mentof

ψ(

3770

)

→

γ χ

c1 [10].

In this Letter, we report on an alternative and complemen-tary measurement ofthe branching fractionand partialwidth of

ψ(

3770

)

→

γ χ

c0 using

χ

c0

→

2

(

π

+

π

−

)

,K+K−

π

+

π

−,3

(

π

+

π

−

)

and K+K− decays.Theresultsofourmeasurements areobtained by taking the relative strength with respect to the well-known

ψ(

3686

)

radiative E1 transition [11]. In this way, the measure-mentwillnotdependonknowledgeofthe

χ

cJ branchingfractions tolighthadronﬁnalstates,whichhavelargeuncertainties[7].This

measurementformsanindependentandmoreprecise benchmark

that can be compared to the predictions of various theoretical models.

2. BESIIIdetectorandMonteCarlosimulation

Inthiswork, weuse2

.

92 fb−1 ofe+e−collision datatakenat

√

s

=

3

.

773 GeV[12],and106

.

41

×

106

ψ(

3686

)

decaystakenat

√

s

=

3

.

686 GeV [13] withthe BESIII detector.These are labeled the

ψ(

3770

)

and

ψ(

3686

)

datasamples,respectively, throughout thisLetter.

TheBESIIIdetector[14]hasageometricalacceptanceof93%of 4

π

andconsistsoffourmaincomponents.Inthefollowing,we de-scribeeachdetectorcomponentstartingfromtheinnermost (clos-esttotheinteraction region)tothemostoutsidelayer.Theinner threecomponentsareimmersedinthe1 T magneticﬁeldofa su-perconductingsolenoid.First,asmall-cell,helium-basedmaindrift chamber (MDC)with43layers provideschargedparticle tracking andmeasurement ofionization energy loss (dE

/

dx). The average single wire resolution is 135 μm,and the momentum resolution for1 GeVelectronsina1 T magneticfieldis0.5%.Thenext detec-toraftertheMDCisatime-of-flightsystem(TOF)usedforparticle identification. It is composed of a barrel part made of two lay-ersof88plasticscintillators,each with5 cmthicknessand2.4 m length; andtwo endcaps,eachwith96fan-shapedplastic scintil-latorsof5 cmthickness.Thetimeresolutionis80 psinthebarrel, and 110 ps in the endcaps, corresponding to a K

/

π

separation betterthan2

σ

formomentauptoabout1.0 GeV.Thethird

(4)

detec-tor componentis an electromagnetic calorimeter(EMC) made of 6240CsI(Tl) crystals arrangedin a cylindricalshape (barrel) plus two endcaps. For1.0 GeV photons, the energy resolutionis 2.5% inthebarreland5%intheendcaps,andthepositionresolutionis 6 mminthe barreland9 mminthe endcaps.Outside theEMC, amuonchamber system(MUC)isincorporatedinthereturniron ofthesuperconductingmagnet.Itismadeof1272 m2_of_resistive

platechambersarrangedin9layers inthe barreland8 layersin theendcaps.Thepositionresolutionisabout2 cm.

A GEANT4 [15] based Monte Carlo (MC) simulation software

package,whichincludesthegeometricdescriptionofthedetector andthedetectorresponse,isusedtodeterminethedetection eﬃ-ciencyofthesignal processandtoestimatethepotential peaking backgrounds.SignalMCsamplesof

ψ(

3686

)/ψ(

3770

)

→

γ χ

cJ are generatedwiththeangulardistributionthatcorrespondstoan E1

transition,andthe

χ

cJ decaystolighthadronﬁnal statesare gen-eratedaccordingtoaphase-spacemodel.Particledecaysare mod-eledusingEvtGen[16],whiletheinitialproductionishandledby theMCgeneratorKKMC[17],inwhichbothinitialstate radiation (ISR)effects[18]andﬁnalstateradiation(FSR)effects[19]are con-sidered.Forthebackgroundstudiesof

ψ(

3686

)

decays,106

×

106 MCeventsofgenericdecays

ψ(

3686

)

→

anything areproducedat

√

s

=

3

.

686 GeV. Forthe background studies of

ψ(

3770

)

decays, MCsamplesof

ψ(

3770

)

→

D0_D

¯

0_,

_ψ(

₃₇₇₀

₎

_→

_D+_D−_,

_ψ(

₃₇₇₀

₎

_→

non-DD decays,

¯

ISRproductionof

ψ(

3686

)

and J

/ψ

,QED,andqq

¯

continuumprocessesareproducedat

√

s

=

3

.

773 GeV.Theknown decay modes of the J

/ψ

,

ψ(

3686

)

and

ψ(

3770

)

are generated withbranchingfractionstakenfromthePDG[11],andthe remain-ingeventsaregeneratedwithLundcharm[20].

3. Analysis

Toselectcandidate eventsfor

ψ(

3686

)/ψ(

3770

)

→

γ χ

cJ with

χ

cJ

→

2

(

π

+

π

−

)/

K+K−

π

+

π

−

/

3

(

π

+

π

−

)/

K+K−, we require at least4

/

4

/

6

/

2 charged trackstobe reconstructedintheMDC, re-spectively.Allchargedtracksusedinthisanalysisarerequiredto be within a polar-angle(

θ

) range of

|

cos

θ

|

<

0

.

93.It is required that all charged tracks originate from the interaction region de-ﬁnedby

|

Vz

|

<

10 cm and

|

Vxy

|

<

1 cm,where

|

Vz

|

and

|

Vxy

|

are thedistancesofclosestapproachofthechargedtracktothe colli-sionpointinthebeamdirectionandintheplaneperpendicularto thebeam,respectively.

Charged particles are identiﬁed by conﬁdencelevels for kaon and pion hypotheses calculated using dE

/

dx and TOF measure-ments.Toeffectivelyseparatepionsandkaons,atrackisidentified asa pion (or kaon) only if theconfidence level for thepion (or kaon) hypothesis islarger thanthe confidencelevel forthe kaon (orpion)hypothesis.

Photons are selected by exploiting the information from the EMC. It is required that the shower time be within 700 ns of the event start time and the shower energy be greater than 25 (50) MeVin thebarrel(endcap) regiondeﬁned by

|

cos

θ

|

<

0

.

80 (0

.

86

<

|

cos

θ

|

<

0

.

92).Here,

θ

isthephotonpolaranglewith re-specttothebeamdirection.

In the selection of

γ

2

(

π

+

π

−

)

, background events from ra-diative Bhabha events in which at least two radiative photons are produced and one of them converts into an e+e− pair are suppressed by requiring the opening angle of any

π

+

π

− com-bination be larger than 10◦. For the selection of

γ

K+K−, the background events of e+e−

→

γ

e+e− are suppressed by requir-ing EEMC

<

1 GeV and EEMC/pMDC

<

0

.

8 for each charged kaon,

where EEMC and pMDC arethe energydeposited in theEMC and

themomentummeasuredbytheMDC,respectively.

In each event, there maybe several different charged and/or neutraltrackcombinationswhichsatisfy theselection criteriafor

Fig. 1. Invariant massspectraofthe(a)2(π+π−),(b)K+K−π+π−,(c)3(π+π−) and(d) K+K− combinationsfortheψ(3686)data.Thedotswitherrorbarsare fordataandthebluesolidlinesaretheﬁtresults.Thereddashedlinesarethe ﬁttedbackgrounds.Thered,pinkandbluearrowsshowtheχc0,χc1andχc2

nom-inalmasses,respectively.(Forinterpretationofthereferencestocolorinthisﬁgure legend,thereaderisreferredtothewebversionofthisarticle.)

each light hadron ﬁnal state. Each combination is subjected to a 4C kinematic ﬁt for the hypotheses of

ψ(

3686

)/ψ(

3770

)

→

γ

2

(

π

+

π

−

)

,

γ

K+K−

π

+

π

−,

γ

3

(

π

+

π

−

)

and

γ

K+K−.Foreach ﬁ-nalstate,ifmorethanone combinationsatisﬁestheselection cri-teria, onlythe combinationwiththe least

χ

2

4C isretained,where

χ

2

4C isthechi-squareofthe4C kinematicﬁt.Theﬁnalstateswith

χ

2

4C

<

25 arekeptforfurtheranalysis.

To identify the

χ

cJ decays, we examine the invariant mass spectra of the light hadron ﬁnal states. Fig. 1 shows the corre-sponding massspectra forthe

ψ(

3686

)

data, inwhich clear

χ

c0,

χ

c1 and

χ

c2 signals are observed. Since the

χ

c1 cannot decay into two pseudoscalar mesons because of spin-parity conserva-tion, the

χ

c1 signal cannot be observed in the K+K− invariant mass spectrum.Byﬁttingthesespectraseparately,we obtain the numbers of

χ

cJ observed fromthe

ψ(

3686

)

data, Nψ (3686),which

are summarized in Table 1. In the ﬁts, the

χ

cJ signals are de-scribed by the MC simulatedline-shapes convoluted byGaussian functionsfortheresolution.Backgroundsinthefourchannelsare describedby3/3/3/1-parameterpolynomialfunctions.The parame-tersoftheconvolutedGaussianfunctionsandtheChebychev poly-nomialfunctionsareallfree.

Fig. 2 shows thecorresponding mass spectra forthe

ψ(

3770

)

data, in which clear peaks can be observed for the

χ

c0 decays. Fitting to these spectra similarly, we obtain the number of

χ

cJ

(

J

=

0

,

1

)

decaysobservedfromthe

ψ(

3770

)

data,Nψ (3770),which

aresummarizedinTable 1.Duetothelimitedstatistics,thedecay

ψ(

3770

)

→

γ χ

c2 is not further considered in this analysis. The means and widths of the convoluted Gaussian functions for the

χ

c0 signalsare left free.For the

χ

c1, themeanand widthofthe convoluted Gaussian functionsareﬁxed atthe valuestakenfrom theﬁtstothe

ψ(

3686

)

data.Backgroundsinthefourchannelsare describedby6

/

2

/

6

/

2-parameterpolynomialfunctions.

The background eventsfrom e+e−

→ (

γ

ISR)ψ(3686

)

produced near

√

s

=

3

.

773 GeV have the same event topologies as those from

ψ(

3770

)

decaysandareindistinguishablefrom

ψ(

3770

)

de-cays. In theﬁts to the

ψ(

3770

)

data, the size andline-shape of

(5)

Table 1

MeasuredRcJ (%),whereNψ (3770)andNψ (3686)arethe(peakingbackgroundcorrected)

num-bersof χcJ observedfrom the ψ(3770)and ψ(3686) data, ψ (3770) and ψ (3686) arethe

detectioneﬃciencies(%).Theuncertaintiesarestatisticalonly.

χcJ→LH J=0 J=1 2(π+π−) Nψ (3770) 756±51 80±26 ψ (3770) 24.1±0.2 25.7±0.2 Nψ (3686) 59 976±318 19 712±175 ψ (3686) 24.9±0.2 26.5±0.2 RcJ 6.64±0.45 2.13±0.69 K+K−π+π− Nψ (3770) 716±54 46±24 ψ (3770) 24.0±0.2 25.4±0.2 Nψ (3686) 46 929±240 11 576±115 ψ (3686) 23.3±0.2 24.9±0.2 RcJ 7.56±0.57 2.00±1.04 3(π+π−) Nψ (3770) 502±54 76±27 ψ (3770) 18.5±0.2 20.0±0.2 Nψ (3686) 36 536±237 19 593±153 ψ (3686) 18.1±0.2 19.6±0.2 RcJ 6.86±0.74 1.94±0.69 K+K− Nψ (3770) 283±24 – ψ (3770) 32.5±0.2 – Nψ (3686) 21 452±154 – ψ (3686) 32.1±0.2 – RcJ 6.65±0.57 – Averaged RcJ 6.89±0.28 2.03±0.44

Fig. 2. Invariant massspectraofthe(a)2(π+π−),(b)K+K−π+π−,(c)3(π+π−) and(d)K+K− combinationsfor theψ(3770)data.Thedotswitherrorbarsare dataandthebluesolidlinesarethefitresults.The redsolidlinesarethefitted combinatorialbackgrounds.Thereddashedlinesarethesumsofthepeakingand fittedcombinatorialbackgrounds.Thered,pinkandbluearrowsshowtheχc0,χc1

andχc2nominalmasses,respectively.(Forinterpretationofthereferencestocolor

inthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

suchbackgroundsareﬁxedaccordingtoMCsimulations,withthe numbersofbackgroundeventsbeingdeterminedby

Nb_χ cJ

=

σ

χcJ,LH,obs

ψ (3686)

· L

ψ (3770)

· η

,

(1)

where

L

ψ (3770) isthe integratedluminosityofthe

ψ(

3770

)

data,

σ

χcJ,LH,obs

ψ (3686) is the observed cross section of e+e−

→ ψ(

3686

)

→

γ χ

cJ with

χ

cJ

→

LH, in which LH denotes 2

(

π

+

π

−

)

,

K+K−

π

+

π

−,3

(

π

+

π

−

)

andK+K−.Inthiswork,weassumethat

there is noother effectaffecting the

ψ(

3686

)

and

ψ(

3770

)

pro-ductionintheenergyrangefrom3.73to3.89 GeV.Thevariable

η

representsthe rateofmisidentifying

ψ(

3686

)

decaysas

ψ(

3770

)

decays, which is obtained by analyzing 1

.

5

×

106 MC events of

ψ(

3686

)

→

γ χ

cJwith

χ

cJ

→

LH generatedat

√

s

=

3

.

773 GeV.The

observed cross section for

ψ(

3686

)

→

γ χ

cJ with

χ

cJ

→

LH at a center-of-massenergyof

√

s isgivenby

σ

χcJ,LH,obs

ψ (3686)

=

σ

χcJ,LH

ψ (3686)

(

s

)

f

(

s

)

F

(

x

,

s

)

G

(

s

,

s

)

dsdx

,

(2)

wheres

≡

s

(

1

−

x

)

isthesquareoftheactualcenter-of-mass en-ergyofthee+e− afterradiatingphoton(s),x isthefractionofthe radiativeenergytothebeamenergy; f

(

s

)

isthephasespace fac-tor,

(

Eγ

(

s

)/

E0_γ

)

3,inwhichEγ

(

s

)

andE0_{γ are}thephotonenergies in

ψ(

3686

)

→

γ χ

cJtransitionat

√

sandatthe

ψ(

3686

)

mass, re-spectively;F

(

x

,

s

)

isthesamplingfunctiondescribingtheradiative photonenergyfractionx at

√

s[18];G

(

s

,

s

)

isaGaussianfunction describingthe distributionofthecollision energywithan energy spread

σ

E

=

1

.

37 MeV as achieved atBEPCII;

σ

χcJ,LH

ψ (3686)

(

s

)

is the

crosssectiondescribedbytheBreit–Wignerfunction

σ

χcJ,LH ψ (3686)

(

s

)

=

12π

_{ψ (}ee₃₆₈₆₎

tot_{ψ (}₃₆₈₆₎Bχ_{ψ (}cJ₃₆₈₆,LH ₎

(

s2

−

M2 ψ (3686)

)

2

+ (

ψ (tot3686)Mψ (3686)

)

2

,

(3)

in which

ee_{ψ (}₃₆₈₆₎ and

_{ψ (}tot₃₆₈₆₎ are, respectively, the leptonic width andtotal widthof the

ψ(

3686

)

, Mψ (3686) is the

ψ(

3686

)

mass,

B

χcJ,LH

ψ (3686) isthe combinedbranchingfractionof

ψ(

3686

)

→

γ χ

cJ with

χ

cJ

→

LH. Here, the upper limit of x is set at 1

−

m2

χcJ

/

s, where mχcJ is the

χ

cJ nominal mass. We determine the

branching fraction

B

χ_{ψ (}cJ₃₆₈₆,LH₎ by dividing the number of

χ

cJ de-cays of

ψ(

3686

)

by the total number of

ψ(

3686

)

and by the corresponding eﬃciency obtained in this work. The rates

η

of misidentifying

ψ(

3686

)

→

γ χ

c0/1/2 as

ψ(

3770

)

→

γ χ

c0/1/2 are

estimated to be 4

.

72

/

6

.

40

/

7

.

60

×

10−4, 4

.

40

/

6

.

27

/

7

.

57

×

10−4, 3

.

53

/

4

.

95

/

6

.

14

×

10−4 and 6

.

56

/

−/

11

.

02

×

10−4 for

χ

c0/1/2

→

2

(

π

+

π

−

)

,K+K−

π

+

π

−,3

(

π

+

π

−

)

andK+K−,respectively.These

(6)

(

γ

ISR)ψ(3686

)

to be 90

.

6

±

3

.

4

/

37

.

5

±

1

.

4

/

76

.

5

±

2

.

9, 70

.

0

±

2

.

7

/

23

.

5

±

0

.

9

/

51

.

0

±

1

.

9, 56

.

6

±

2

.

2

/

39

.

7

±

1

.

5

/

73

.

5

±

2

.

8 and 34

.

9

±

1

.

3

/

−/

11

.

1

±

0

.

4 for

ψ(

3770

)

→

γ χ

c0/1/2 with

χ

c0/1/2

→

2

(

π

+

π

−

)

, K+K−

π

+

π

−, 3

(

π

+

π

−

)

and K+K− decays, respec-tively. The errors arise from uncertainties in the

ψ(

3686

)

reso-nanceparameters, theintegratedluminosity ofthe

ψ(

3770

)

data

L

ψ (3770) and the misidentiﬁcation rates

η

. In Eq. (1), the

num-ber of background events depends on the ratio of the misiden-tiﬁcation rate

η

over the eﬃciency

ψ (3686) of reconstructing

ψ(

3686

)

→

χ

cJ. Since

η

and

ψ (3686) all contain the simulation

of

χ

cJ

→

LH,apossiblesystematicuncertaintyfromthesimulation

of

χ

cJ

→

LH iscanceledhere.

4. Results

Theratioofthebranchingfractionfor

ψ(

3770

)

→

γ χ

cJdivided bythebranchingfractionfor

ψ(

3686

)

→

γ χ

cJisdetermined chan-nelbychannelas RcJ

=

B

[ψ(

3770

)

→

γ χ

cJ

]

B

[ψ(

3686

)

→

γ χ

cJ

]

=

Nψ (3770)

·

N_{ψ (}tot₃₆₈₆₎

·

ψ (3686) Nψ (3686)

·

Nψ (tot3770)

·

ψ (3770)

,

(4) whereNψ (3686)andNψ (3770)arethenumbersof

χ

cJobservedfrom the

ψ(

3686

)

and

ψ(

3770

)

data,N_{ψ (}tot₃₆₈₆₎andNtot_{ψ (}₃₇₇₀₎arethetotal numbersof

ψ(

3686

)

and

ψ(

3770

)

decays,

ψ (3686)and

ψ (3770)are

the eﬃciencies of reconstructing

ψ(

3686

)

and

ψ(

3770

)

→

γ χ

cJ

with

χ

cJ

→

LH estimated by MC simulations, respectively. Here,

Ntot

ψ (3770) is determined by

σ

ψ (obs3770)

· L

ψ (3770), where

σ

ψ (obs3770)

=

(

7

.

15

±

0

.

27

±

0

.

27

)

nb isthecrosssectionfor

ψ(

3770

)

production

[21–23]and

L

ψ (3770) istheintegratedluminosityofthe

ψ(

3770

)

dataset[12].

Table 1 summarizesthe ratios RcJ measured via the different channels.Theresultsareconsistentwithinstatisticaluncertainties. Fromthesemeasurements,weobtainthestatistical-weighted aver-ages R

¯

c0

= (

6

.

89

±

0

.

28

±

0

.

65

)

% andR

¯

c1

= (

2

.

03

±

0

.

44

±

0

.

66

)

%, wheretheﬁrstuncertaintyisstatisticalandthesecondsystematic. InthemeasurementsofR

¯

c0/1,thesystematicuncertaintyarises

from the uncertainties in the total number (0.81%) of

ψ(

3686

)

decays (Ntot_{ψ (}₃₆₈₆₎ [13]); the integrated luminosity (1.0%) of the

ψ(

3770

)

data(Lψ (3770)[12]);thecrosssection(5.3%)for

ψ(

3770

)

(

σ

obs

ψ (3770) [21–23]);thephoton selection(1.4%),assignedbasedon

1.0% per photon [24]; the MDC tracking (2.6%/4.0%); the particle identification (2.6%/4.0%); the statistical uncertainty (1.0%)of the efficiencydueto the sizeof thesimulated eventsample;the 4C kinematic fit (1.0%), estimated by comparing the measurements with and without the kinematic fit correction; the fit to mass spectra (6.4%/31.5%), estimated by comparing the measurements with alternative fit ranges (

±

20 MeV

/

c2_), _signal _shape _(simple

Breit–Wigner function) andbackground shapes (

±

1 order ofthe polynomial functions); and the subtraction of

ψ(

3686

)

peaking background(0.5%/2.0%). The eﬃciencies ofthe MDCtracking and particleidentiﬁcationfor K+ or

π

+ areexamined by thedoubly taggedhadronic DD events.

¯

The difference betweenthe eﬃcien-cies of data and MC is assigned as an uncertainty. Then, their effects on R

¯

c0/1 are estimated to be 2.6%/4.0%. Table 2

summa-rizes these uncertainties. Adding them in quadrature, we obtain thetotalsystematicuncertaintyforR

¯

c0/1tobe9.4%/32.6%.

Multiplying R

¯

cJ by the branching fraction

B[ψ(

3686

)

→

γ χ

cJ

]

(andthetotalwidth

_{ψ (}tot₃₇₇₀₎)takenfromthePDG[11],weobtain the branching fractions (and the partial widths) for

ψ(

3770

)

→

γ χ

cJ, which are summarized in Table 3, where the ﬁrst uncer-taintyisstatisticalandthesecondsystematic.Inthemeasurement of

B[ψ(

3770

)

→

γ χ

cJ

]

(and

[ψ(

3770

)

→

γ χ

cJ

]

), the systematic uncertaintyarisesfromthe uncertainties of R

¯

c0/1 andthe

uncer-Table 2

Systematicuncertainties(%)inthemeasurementsofR¯cJ.

¯ Rc0 R¯c1 Ntot ψ (3686)[13] 0.81 0.81 σobs ψ (3770)[21–23] 5.3 5.3 Lψ (3770)[12] 1.0 1.0 MC statistics 1.0 1.0 Photon selection 1.4 1.4 MDC tracking 2.6 4.0 Particle identiﬁcation 2.6 4.0 4C kinematic ﬁt 1.0 1.0

Fit to mass spectra 6.4 31.5

Background subtraction 0.5 2.0

Total 9.4 32.6

Table 3

Comparisonsofthepartialwidthsforψ(3770)→γ χcJ(inkeV),whereBand

de-notethebranchingfractionandthepartialwidthforψ(3770)→γ χcJ,respectively.

FortheBESIIIresults,theﬁrstuncertaintyisstatisticalandthesecondsystematic. DetailedexplanationsabouttheCLEOresultscanbefoundinfootnote1.

Experiments J=0 J=1 BBESIII₍_×10−3₎ ₆_.₈₈_±₀_.₂₈_±₀_.₆₇ ₁_.₉₄_±₀_.₄₂_±₀_.₆₄ BBESIII₍_×10−3₎_[10] _– ₂_.₄₈_±₀_.₁₅_±₀_.₂₃ BESIII ₁₈₇_±₈_±₁₉ ₅₃_±₁₂_±₁₈ BESIII_[10] _– ₆₇_.₅_±₄_.₁_±₆_.₇ CLEO_[7,8] ₁₇₂_±₃₀ ₇₀_±₁₇ correctedCLEO 192±24 72±16 Theories Rosner[2](non-relativistic) 523±12 73±9 Ding–Qing–Chao[3] non-relativistic 312 95 relativistic 199 72 Eichten–Lane–Quigg[4] non-relativistic 254 183

withcoupledchannels corrections 225 59 Barnes–Godfrey–Swanson[5] non-relativistic 403 125 relativistic 213 77 NRCQM[6] 218 70

tainties of

B[ψ(

3686

)

→

γ χ

c0/1

]

of2.7/3.2%(andtheuncertainty

of

_{ψ (}tot₃₇₇₀₎of3.7%). 5. Summary

In summary, by analyzing 2

.

92 fb−1 of e+e− collision data takenat

√

s

=

3

.

773 GeV and106

.

41

×

106

ψ(

3686

)

decaystaken at

√

s

=

3

.

686 GeV with the BESIII detector at the BEPCII col-lider, we measure the branching fraction

B(ψ(

3770

)

→

γ χ

c0

)

=

(

6

.

88

±

0

.

28

±

0

.

67

)

×

10−3 _and_the _partial _width

_[ψ(

₃₇₇₀

₎

_→

γ χ

c0

]

= (

187

±

8

±

19

)

keV.Theseareobtainedbyﬁrstmeasuring theratiowithrespecttotheaccurately knownbranchingfraction for

ψ(

3686

)

→

γ χ

cJ decays. Our results are, thereby, not inﬂu-encedbytheuncertaintiesinthebranchingfractionsof

χ

cJdecays to light hadrons as done in Ref. [7]. The branching fraction and partialwidthfor

ψ(

3770

)

→

γ χ

c1measuredinthisworkare con-sistentwithourpreviousmeasurement[10]withinerrors.Table 3

comparesthe

[ψ(

3770

)

→

γ χ

c0/1

]

measuredatBESIIIwiththose

measured by CLEO [7,8]1 and the theoretical calculations from Refs. [2–6]. The partial width

[ψ(

3770

)

→

γ χ

c0

]

measured at

1 _The _CLEO_measurements _were_based _on _the_total _width

totψ (3770)= (23.6±

2.7)MeV[25]andthecrosssectionσobs

ψ (3770)→DD¯= (6.39±0.10 +0.17

−0.08)nb for de-terminingthe totalnumberofψ(3770)decays,wheretheψ(3770)→non-DD¯

(7)

BESIIIisconsistentwithin errorswiththeone measuredby CLEO withanimproved precision.These resultsunderline thefact that the traditional models [3–5] with a relativistic assumption or a coupled-channelcorrectionagreequantitativelybetterwiththe ex-perimentaldatathanthose [2–5] basedupon non-relativistic cal-culations.For thesetraditional models,the non-relativistic calcu-lationsclearlyoverestimatethepartialwidth

[ψ(

3770

)

→

γ χ

cJ

]

. The experimental data alsosupport the recent calculation based onthe non-relativisticconstituentquark model(NRCQM) [6]. To-gether with further theoretical developments, our results aim to contributetoadeeperunderstandingofthedynamicsof charmo-niumdecaysabovetheopen-charmthreshold.

Acknowledgements

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by the National Key Basic Research Program

ofChina underContract Nos.2009CB825204 and2015CB856700;

NationalNatural Science Foundation of China (NSFC) under Con-tractsNos.10935007, 11125525,11235011, 11305180, 11322544,

11335008, 11425524; the Chinese Academy of Sciences (CAS)

Large-ScaleScientiﬁc Facility Program; JointLarge-Scale Scientiﬁc FacilityFundsoftheNSFCandCASunderContractsNos.11179007,

U1232201, U1332201; CAS under Contracts Nos. KJCX2-YW-N29,

KJCX2-YW-N45; 100 Talents Program of CAS; the CAS Center

for Excellence in Particle Physics (CCEPP); INPAC and Shang-hai Key Laboratory for Particle Physics and Cosmology; German

Research Foundation DFG under Collaborative Research Center

Contract No. CRC-1044; Istituto Nazionale di Fisica Nucleare,

Italy; Ministry of Development of Turkey under Contract No.

DPT2006K-120470; Russian Foundation for Basic Research

un-der Contract No. 14-07-91152; U.S. Department of Energy

un-derContractsNos.DE-FG02-04ER41291,DE-FG02-05ER41374,

DE-FG02-94ER40823, DESC0010118; U.S. National Science

Founda-tion; University of Groningen (RuG) and the Helmholtzzentrum

fürSchwerionenforschung GmbH(GSI), Darmstadt;WCUProgram

of National Research Foundation of Korea under Contract No.

R32-2008-000-10155-0.

0.11±0.46)% and B(ψ(3686)→γ χc1)= (9.07±0.11±0.54)% to determine

B(ψ(3770)→γ χcJ)fromRef.[26].AlthoughCLEOdeterminedthebranching

frac-tionofψ(3770)→non-DD decays¯ to be(−3.3±1.4+4.8

−6.6)% andset anupper limitof9%at90%conﬁdencelevel[27],thePDGvalueforDD¯

ψ (3770)/

tot

ψ (3770)[28]

fromfour measurements at BESII[22,29–31]implied the branchingfraction for ψ(3770)→ non-DD decays¯ to be (14.7±3.2)%. At present, the PDG value for ψ (DD¯3770)/

tot

ψ (3770) gives the branching fraction of ψ(3770)→ non-DD de-¯

caystobe(7+₋89)%[11]. Therefore, for bettercomparisons,we alsolist the cor-rectedCLEO partial widths with the same input values as those used in our measurements,whichareσobs

ψ (3770)= (7.15±0.27±0.27)nb[21–23], tot ψ (3770)= (27.2±1.0)MeV,B(ψ(3686)→γ χc0)= (9.99±0.27)% andB(ψ(3686)→γ χc1)= (9.55±0.31)%[11]. References

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