Measurements of cross section of e(+)e(-) -> p(p)over-bar pi(0) at center-of-mass energies between 4.008 and 4.600 GeV

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurements

of

cross

section

of

e

+

e

−

→

p

¯

π

0 at

center-of-mass

energies

between

4.008 and

4.600 GeV

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

5

,

S. Ahmed

n

,

X.C. Ai

a

,

∗

,

O. Albayrak

e

,

M. Albrecht

d

,

D.J. Ambrose

aw

,

A. Amoroso

bb

,

bd

,

F.F. An

a

,

Q. An

ay

,

1

,

J.Z. Bai

a

,

R. Baldini Ferroli

t

,

Y. Ban

ag

,

D.W. Bennett

s

,

J.V. Bennett

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,

N. Berger

x

,

M. Bertani

t

,

D. Bettoni

v

,

J.M. Bian

av

,

F. Bianchi

bb

,

bd

,

E. Boger

y

,

3

,

I. Boyko

y

,

R.A. Briere

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,

H. Cai

bf

,

X. Cai

a

,

1

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O. Cakir

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,

A. Calcaterra

t

,

G.F. Cao

a

,

S.A. Cetin

aq

,

J. Chai

bd

,

J.F. Chang

a

,

1

,

G. Chelkov

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,

3

,

4

,

G. Chen

a

,

H.S. Chen

a

,

J.C. Chen

a

,

M.L. Chen

a

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1

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S. Chen

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S.J. Chen

ae

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X. Chen

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1

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X.R. Chen

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Y.B. Chen

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http://dx.doi.org/10.1016/j.physletb.2017.05.033

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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-Universitaet}_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

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ao_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China ap_Ankara_University,₀₆₁₀₀_Tandogan,_Ankara,_Turkey aq_Istanbul_Bilgi_University,₃₄₀₆₀_Eyup,_Istanbul,_Turkey ar_Uludag_University,₁₆₀₅₉_Bursa,_Turkey

as_Near_East_University,_Nicosia,_North_Cyprus,_Mersin_10,_Turkey

at_University_of_Chinese_Academy_of_Sciences,_Beijing_100049,_People’s_Republic_of_China 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

ZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina

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Articlehistory:

Received17January2017

Receivedinrevisedform26April2017 Accepted11May2017

Availableonline15May2017 Editor: V.Metag

Keywords: Hadrons

Crosssectionmeasurements Y(4260)

Based one+e− annihilationdata samples collectedwith the BESIII detectorat the BEPCIIcollider at 13center-of-massenergiesfrom4.008to4.600GeV,measurementsoftheBorncrosssectionofe+e−_→ pp¯

π

0_are_performed._No_signiﬁcant_resonant_structure_is_observed_in_the_measured_energy_dependence_of

thecrosssection.TheupperlimitontheBorncrosssectionofe+e−→Y(4260)→p¯p

π

0_at_the_90%_C.L.

isdeterminedtobe0.01pb.Theupperlimitontheratioofthebranchingfractions _B₍B_Y₍(₄₂₆₀Y(4260₎_→π)→+p_πp¯−π0J/ψ)) atthe90%C.L.isdeterminedtobe0.02%.

1. Introduction

TheBorncross sectionofe+e−

→

pp

¯

π

0 _in_the _vicinity_of_the

ψ(

3770

)

hasbeenmeasuredrecentlybyBESIII[1].Informationon thecrosssection ofe+e−

→

pp

¯

π

0 _at_higher_energies_is _however

stilllacking.Theexperimentaldataonthecrosssectionofe+e−

→

hadrons canbeusedasaninputtocalculatethehadronicvacuum polarizationviadispersionintegrals[2–5].

The charmonium-like state Y

(

4260

)

was ﬁrst observed in its decayto

π

+

π

−J

/ψ

[6].Sofar,thereisnoevidenceoftheY

(

4260

)

in the measured open charm decay channels [7,8] and R value

scans[9–15].Manytheoreticalmodelshavebeenproposed to in-terpretthenatureofY

(

4260

)

,e.g. asatetraquarkstate[16],aD1D

¯

or D0D

¯

∗ hadronic molecule [17], a hybrid charmonium [18,19],

ora baryonium state [20]. Searchesfor newdecaymodes ofthe

Y

(

4260

)

mayprovideinformationthatcanshedlightonitsnature. Inparticular,thehybridmodel[18]predictsasizablecoupling be-tweentheY

(

4260

)

andcharmlessdecays.

*

Correspondingauthor.

E-mailaddress:aixc@ihep.ac.cn(X.C. Ai).

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

2 _Also_at_Bogazici_University,₃₄₃₄₂_Istanbul,_Turkey.

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

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

9 _Also_at_Goethe_University_Frankfurt,₆₀₃₂₃_Frankfurt_am_Main,_Germany.

In thisanalysis, we report measurements of thecross section of e+e−

→

pp

¯

π

0 _based _on _the _e+_e− _annihilation _samples

col-lected with the BESIII detector at 13 center-of-mass energies in therange

√

s

=

4

.

008–4

.

600 GeV asshownin Table 1.Results of the measurements can be used to estimate the cross section of

pp

¯

→

Xc¯c

π

0 [21], which is of high importance for the planned PANDAexperiment[22]atFAIRinDarmstadt,Germany.

2. BESIIIdetectorandMonte-Carlosimulation

TheBESIIIdetector[23]isamagneticspectrometeroperatingat BEPCII, a double-ring e+e− colliderwith center-of-massenergies between2.0and4.6GeVandapeakluminosityof1033cm−2s−1 near the

ψ(

3770

)

mass.The cylindrical coreof the BESIII detec-torconsistsofahelium-basedmaindriftchamber(MDC),aplastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromag-neticcalorimeter(EMC)thatareallenclosedinasuperconducting solenoidal magnet providinga 1.0 Tmagnetic field. The solenoid issupported byanoctagonal flux-returnyokewithresistiveplate counter muon identifier modules interleaved withsteel. The ac-ceptanceforchargedparticlesandphotonsis93%ofthe4

π

solid angle,andthe charged-particle momentum resolution is0.5% for transversemomentaof1 GeV

/

c.Theenergyresolutionforshowers intheEMC is2.5(5%) for1 GeVphotonsin thebarrel(endcaps) region.

A geant4-based [24] Monte Carlo (MC) simulation software

package isused to optimizetheevent selectioncriteria, estimate backgrounds anddetermine thedetectioneﬃciency.Foreach en-ergy point, we generate 200,000 signal MC events of e+e−

→

pp

¯

π

0 _uniformly _in _phase _space. _Effects _of _initial _state _radiation

(ISR) are simulatedwith kkmc [25],where the lineshape of the productioncrosssectionofe+e−

→

pp

¯

π

0_is_taken_from_results_of

(4)

themeasured crosssection iteratively.Effects ofﬁnal state radia-tionoffchargedparticlesaresimulatedwith photos[26].

To study possible backgrounds, a MC sample of inclusive

Y

(

4260

)

decays, equivalent to an integrated luminosity of 825

.

6 pb−1, is also generated at

√

s

=

4

.

26 GeV. In these simu-lations,theY

(

4260

)

isallowedtodecaygenerically,withthemain

known decay channels being generated using evtgen [27] with

branchingfractions settoworld averagevalues[28].The remain-ingeventsassociatedwithcharmoniumdecaysaregeneratedwith lundcharm [29], while the continuum hadronic events are gen-erated with pythia[30].QED events(e+e−

→

e+e−,

μ

+

μ

−, and

γ γ

)aregeneratedwith kkmc[25].Thesourcesofbackgroundsat otherenergypointsareassumedtobesimilar.

3. Eventselection

The ﬁnal state in this decay is characterized by two charged tracksandtwophotons. Twochargedtrackswithopposite charge arerequired.Eachtrackisrequiredtohaveitspointofclosest ap-proachtothebeamaxiswithin10cmoftheinteractionpointin thebeamdirectionandwithin1cmofthebeamaxisintheplane perpendiculartothebeam.Thepolarangleofthetrackisrequired tobewithintheregionof

|

cos

θ

|

<

0.93.

The time of ﬂight and the speciﬁc energy loss dE

/

dx of a particlemeasured in theMDC are combinedto calculateparticle identiﬁcationprobabilities forpion,kaon,andprotonhypotheses. Foreachtrack,theparticletype yieldingthelargestprobability is assigned.Inthisanalysis,onechargedtrackisrequiredtobe iden-tiﬁedasaprotonandtheotheroneasanantiproton.

Photon candidates are reconstructed using clusters of energy depositedintheEMC.The energydepositedinnearbyTOF coun-tersisincludedinEMCmeasurementstoimprovethe reconstruc-tion eﬃciency and the energy resolution. Photon candidates are selectedbyrequiringaminimumenergydeposition of25MeV in thebarrelEMC(

|

cos

θ

|

<

0.8)or50MeVintheendcapEMC(0.86

<

|

cos

θ

|

<

0.92).To reject photonsradiatedfrom charged parti-cles, the angle between the photon candidate and the proton is required to be greater than 10 degrees. A more stringent cut of 30 degrees betweenthe photon candidate and the antiproton is applied to exclude the large numberof photons fromantiproton annihilation.

Forevents with one proton, one antiproton, and atleast two photons, a kinematicﬁt (4C) with the total four-momenta of all particlesconstrainedtotheenergyandthree-momentum compo-nentsoftheinitiale+e− systemisapplied.Whenmorethantwo photons are found in an event, all possible pp

¯

γ γ

combinations are considered andtheone yielding the smallest

χ

2

4C is retained

forfurtheranalysis. The

χ

2

4C isrequired tobe lessthan 30.After

selectingthe pp

¯

γ γ

candidate,the

π

0 _candidates_are _selected_by

requiring

|

M

(γ γ

)

−

_mπ0

|

<

15 MeV

/

c2,wheremπ0 isthenominal

π

0 _mass_[28]_.

The Dalitzplot fortheeventspassing the above selection cri-teriafordataat

√

s

=

4

.

258 GeV isshowninFig. 1(a).The corre-spondinginvariant mass spectraof pp,

¯

p

π

0 _and _p

_¯

_π

0 _are _shown

inFig. 1(b),(c)and(d),respectively.

The potential backgrounds for e+e−

→

pp

¯

π

0 _are _studied

us-ingtheinclusiveMC sampleat

√

s

=

4

.

26 GeV. Afterimposingall eventselectionrequirements,theremainingbackgroundeventsare foundtohavetheﬁnal statetopologies e+e−

→

γ

pp,

¯

γ γ

pp and

¯

γ γ γ

pp.

¯

No other background survives. The non-

π

0 _background

eventscanbeevaluated fromeventsinthe

π

0 _sidebands._The

_π

0

sidebandregionsaredeﬁnedas0

.

07

<

M

(γ γ

)

<

0

.

10 GeV

/

c2 _and

0

.

17

<

M

(γ γ

)

<

0

.

20 GeV

/

c2_._The _background_{contamination}

es-timatedusing

π

0 _sidebands_at

√

_s

₌

₄

_.

_{258 GeV is}_0.3%._The

back-groundcontributionsareneglectedinthesubsequentanalysis.

Fig. 1. (a)Dalitzplotfortheselectede+e−→p¯pπ0_candidates_of_data_and invari-antmassspectraof(b)p¯p,(c)pπ0_and_(d)_p_¯_π0_at√_s₌₄_._{258 GeV.}_In_(b),_(c)_and (d),thepointswitherrorbarsshowdataandtheredhistogramsshowMC projec-tionsofthepartialwaveanalysisﬁtdescribedinthetext.(Forinterpretationofthe referencestocolorinthisﬁgurelegend,thereaderisreferredtothewebversionof thisarticle.)

4. Studyofintermediatestructuresbypartialwaveanalysis As shown in Fig. 1, a prominent structure nearthe threshold inthepp mass

¯

spectrumisvisible.Structuresarealsoseeninthe

p

π

0 _and _p

_¯

_π

0 _mass_spectra._To_evaluate _the_detection_eﬃciencies

ofthedecaye+e−

→

pp

¯

π

0_properly,_a_partial_wave_analysis_(PWA)

is performedwiththe e+e−

→

pp

¯

π

0 _candidates _to_study_the

in-termediatestatespresent.

For the process e+e−

→

pp

¯

π

0_, _the _isospin _of _the _p_p

_¯

_π

0

sys-temcan be I

=

0 or I

=

1. Thequasi-two-body decayamplitudes in the sequentialdecay processes e+e−

→

pN

¯

∗

(

pN

¯

∗

)

, N∗

( ¯

N∗

)

→

p

π

0

₍

_p

_¯

_π

0

₎

_, _e+_e−

_→

_p

_¯

∗

₍

_p

_¯

∗

₎

_,

∗

_{( ¯}

∗

₎

_→

_p

_π

0

₍

_p

_¯

_π

0

₎

_, _e+_e−

_→

ρ

∗

(ω

∗

)π

0_,

_ρ

∗

_(ω

∗

₎

_→

_p_{p are}

_¯

_constructed_in _the _covariant _tensor formalism[31,32].All1−−and3−−statesabovepp threshold,

¯

N∗

and

∗ states withspin up to 5/2,listed inthe summary tables ofthe PDG[28], areconsidered inthisanalysis. Accordingto the frameworkofsoft

π

mesontheory[33],theoff-shelldecayprocess shouldbeincluded.Thus, N

(

940

)

withamassof940 MeV

/

c2and zero widthrepresenting a virtual proton which could emit a

π

0

isconsidered asapossiblecomponent. Noisoscalarvectormeson isconsidered, sincethereisnocandidateabovethe pp threshold

¯

in thesummary tables ofthe PDG.The

ρ

∗ states are parameter-izedbyaconstant-widthrelativisticBreit–Wigner(BW)propagator withbarrierfactorsincluded.TheN∗ and

∗statesare parameter-ized byaBW propagatorasdescribed inRef.[31].Theresonance parametersarefixedaccordingtopreviousmeasurements[28]due tolimitedstatistics.Thecomplexcoefficientsoftheamplitudesare determinedbyanunbinnedmaximumlikelihoodfit.Thedetailsof thelikelihoodfunctionconstructioncanbefoundinRef.[34].

For

ρ

∗ states with J

=

1, the pp ﬁnal

¯

state interaction (FSI) effect using the Jülich model [35] is taken into consideration by factorizing the partial wave amplitude into the amplitude with-out the FSI effect and the S wave pp scattering

¯

amplitude in the scattering length approximation given in Ref. [35]. The di-rect process of e+e−

→

pp

¯

π

0 _can _be _modeled _by ₁−− _or ₃−− phase space ofthe pp system

¯

(1−− or 3−− PHSP). All combina-tionsofthecomponentsinRef.[36]areevaluated.Theresonances parameters are ﬁxed to the PDG world average values [28]. We

(5)

Table 1

Theresultsone+e−→pp¯π0_._Shown_in_the_table_are_the_integrated_luminosity_L_,_the_radiative_correction_factor

(1+ δr₎_,_the_vacuum_polarization_factor₍₁_{+ δ}v₎_,_the_number_of_observed_events_Nobs_,_the_detection_efficiency andtheBorncrosssectionσB₍_e+_e−_→_p_p_¯_π0₎_at_each_energy_point._The_errors_of_are_from_the_PWA_fit._The_first errorsofσB_are_statistical,_and_the_second_ones_are_systematic.

√ s (GeV) L[pb−1_] (1+ δr ) (1+ δv ) Nobs _[_%_] _σB_[_pb_] 4.008 482.0 0.967 1.044 1074±33 43.9±0.9 5.09±0.18+0.26 −0.24 4.085 52.6 0.992 1.052 106±11 43.7±1.4 4.47±0.46+₋00..2721 4.189 43.1 1.025 1.056 75±9 44.7±1.0 3.64±0.43+0.18 −0.19 4.208 54.6 1.031 1.057 93±10 44.9±1.6 3.52±0.39+0.17 −0.22 4.217 54.1 1.034 1.057 82±10 43.4±1.3 3.24±0.37±0.18 4.226 1047.3 1.037 1.056 1611±41 45.2±0.5 3.15±0.08±0.14 4.242 55.6 1.042 1.056 89±9 44.6±1.1 3.30±0.36+₋00..1915 4.258 825.6 1.048 1.054 1203±35 43.4±0.5 3.08±0.10+0.14 −0.15 4.308 44.9 1.063 1.053 53±8 46.0±1.4 2.32±0.33+₋00..1510 4.358 539.8 1.081 1.051 668±26 44.7±1.1 2.48±0.11+0.13 −0.12 4.387 55.2 1.087 1.051 57±8 47.5±1.8 1.92±0.26±0.10 4.416 1028.9 1.098 1.053 1133±34 44.6±0.6 2.16±0.10+₋00..1011 4.600 566.9 1.124 1.055 474±22 43.8±0.8 1.63±0.08±0.08

do not have the sensitivity to test the larger number of narrow resonancesreportedinRef.[37].Thechangesinthenegative log-likelihood (NLL) and the number of free parameters in the fit with and without a resonance are used to evaluate its statisti-calsignificance.Resonanceswithsignificancegreater than5

σ

are retainedin the PWA solution. The selection of PWA components isperformedat the energypoints withthe highstatistics, i.e.at

√

s

=

4

.

008, 4.226, 4.258 and 4.416 GeV, as shown in Table 1. The selected components are used to describe the data atother nearbyenergypoints. The data at

√

s

=

4

.

189–4

.

600 GeV can be describedbythe N

(

1440

)

,

ρ

(

2150

)

,

ρ

3(1990

)

and1−−PHSP am-plitudes. Thedataat

√

s

=

4

.

008–4

.

085 GeV canbe described by the N

(

1520

)

, N

(

2570

)

,

ρ

(

2150

)

,

ρ

3(1990

)

and 1−− PHSP ampli-tudes.The N

(

940

)

isnotincludedintheﬁtssinceitssigniﬁcance islessthan5

σ

.IfweperformanalternativePWAﬁtwithN

(

1440

)

,

ρ(

2150

)

,

ρ

3(1990

)

and 1−− PHSP at

√

s

=

4

.

008 GeV, the NLL worsensby37.8.Thechangeofefficiencydeterminedwiththe al-ternative fit with respect to the nominal value is considered as a source of systematicuncertainty. Comparisons of the dataand thefitprojection(weightedbyMCefficiencies)intermsofthe in-variantmassspectraof pp,

¯

p

π

0 _and_p

_¯

_π

0 _at

√

_s

₌

₄

_.

_{258 GeV are}

showninFig. 1(b),(c)and(d),respectively.The

χ

2 _over_the

num-berofbinsisdisplayedinthoseﬁgures. 5. Crosssectionfore+e−

→

pp

¯

π

0

TheBorncrosssectionfore+e−

→

pp

¯

π

0 _is_determined_as

σ

B

=

N

obs

L

· (

1

+ δ

r

₎

_{· (}

₁

_{+ δ}

v

₎

_·

_B

π0

,

(1)

whereNobs isthenumberofobservedevents;

L

istheintegrated luminosity;

is the detectioneﬃciency derived fromMC events generatedaccordingtothe resultsofthe PWAﬁt;

(

1

+ δ

r

₎

_is_the radiativecorrection factor,whichistakenfroma QEDcalculation takingtheline shape ofthe crosssection e+e−

→

pp

¯

π

0 _of_data

asinput inan iterativeprocedure;

(

1

+ δ

v

₎

_is _the_vacuum polar-izationfactor,includingleptonicandhadroniccontributions,taken froma QED calculation with an accuracy of 0.5% [38]; and

B

_π0

isthe branching fractionof

π

0 _decaying_to

_{γ γ}

_according_to _the

PDG[28]. The measured Born cross section of e+e−

→

pp

¯

π

0 _at

eachenergypointislistedinTable 1.Themeasuredcrosssection ofe+e−

→

pp

¯

π

0 _is_much _larger _than _that _of_e+_e−

_→

_p_{p at}

_¯

_the sameenergy[39].

UncorrelatedsystematicuncertaintiesintheBorncrosssection measurements mainly originate from the

π

0 _mass _window

re-quirement, kinematicﬁtandtheintermediate statesinPWA.The systematicuncertaintyfromtherequirementonthe

π

0 _signal

re-gionisestimatedbysmearingtheinvariantmassofthe

γ γ

pairin thesignalMCwithaGaussianfunctiontocompensateforthe reso-lutiondifferencebetweendataandMC.Theparametersfor smear-ingaredeterminedbyﬁttingthe

π

0 _distribution_of_data_with_the

MC shapeconvoluted withaGaussian function.The difference in thedetectionefficiencybetweensignalMCsampleswithand with-outtheextrasmearingistakenasthesystematicuncertainty.The systematicuncertaintyduetothekinematicfitisestimatedby cor-rectingthe helix parameters ofcharged tracks forthe signal MC sample according the method described in Ref. [40]. The differ-enceinthedetectionefficiencybetweentheMCsampleswithand withoutthiscorrectionistakenasthesystematicuncertainty.The systematic uncertainty from the intermediate states in PWA in-cludes thosefromtheBW parametrization, resonanceparameters andextraresonances. UncertaintiesfromtheBW parametrization ofintermediatestatesareestimatedbyreplacingtheBW formula of N

(

1440

)

and N

(

1520

)

as used in Ref. [31] with a constant BW formula andreplacing those of

ρ

(

2150

)

and

ρ

3(1990

)

with the BW formula with the Gounaris–Sakurai (GS) model [41]. In thePWA fit,the resonanceparameters arefixed accordingto the previous measurements [42,43]. Alternativefits are performed in whichtheresonanceparametersaresetasfreeparametersandthe changes in the resultsare takenassystematic uncertainties. Un-certaintiesfromadditionalresonancesareestimatedbyaddingthe mostsignificant additionalresonanceamongeach JP assignment inRef.[36]intothePWAsolutionindividually,andtheirinfluences onthecrosssectionmeasurementsaretakenasthesystematic un-certainties.

Correlatedsystematicuncertaintiesamongthedifferentenergy points include those from luminosity measurement (1.0%) [44], MDC tracking (2% for two charged tracks) [45], particle identiﬁ-cation(2%in totalforprotonandantiproton)[46],photon detec-tion eﬃciency (2%) [47] and radiative correction. The difference in

(

1

+ δ

r

₎

_between _the _third _and _fourth _iteration _is _taken _as the systematicuncertaintydueto theradiative correction, asthe radiative-correction-dependent quantity

(

1

+ δ

r

)

converges after threeiterations.

Thetotal systematicuncertaintyofthedifferentenergypoints iscalculated byadding theindividual uncertainties inquadrature asshowninTable 2.

(6)

Table 2

SummaryofsystematicuncertaintiesontheBorncrosssectionofe+e−→pp¯π0_(%).

Sources/√s (GeV) 4.008 4.085 4.189 4.208 4.217 4.226 4.242 4.258 4.308 4.358 4.387 4.416 4.600 Luminosity 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 MDC tracking 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 PID 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Photon detection 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 Kinematic ﬁt 2.1 1.9 1.8 1.6 1.7 1.6 1.6 2.1 1.5 1.8 1.5 1.8 1.6 π0_{mass resolution} _0.2 _0.2 _0.2 _0.2 _0.2 _0.3 _0.2 _0.4 _0.6 _0.4 _0.3 _0.4 _0.4 Radiative correction 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9

Intermediate states in PWA +2.4

−1.3 + 4.1 −1.3 + 2.1 −2.6 + 2.2 −4.4 + 3.3 −3.5 + 1.0 −1.1 + 3.8 −1.0 + 0.4 −1.9 + 4.8 −0.9 + 2.8 −1.7 + 3.1 −2.3 + 0.9 −2.1 ±1.9 Total +5.2 −4.8 + 6.1 −4.7 + 4.9 −5.2 + 4.9 −6.2 + 5.5 −5.6 ±4.5 + 5.8 −4.5 + 4.6 −5.0 + 6.5 −4.5 + 5.3 −4.8 + 5.4 −4.9 + 4.6 −4.9 ±4.8

Fig. 2. Fittoσ(e+e−→pp¯π0₎_with_resonance_and_continuum_(solid_line),_or_only continuumterm(dashedline).DotswitherrorbarsarethemeasuredBorncross sections.Theuncertaintiesarestatisticalonly.

6. UpperlimitonY(4260

)

→

pp

¯

π

0_decay

Fig. 2showsthemeasuredBorncrosssectionofe+e−

→

pp

¯

π

0

intheenergyregion studiedinthiswork.No signiﬁcantresonant structureisobserved.TheupperlimitontheBorncrosssectionof

e+e−

→

Y

(

4260

)

→

pp

¯

π

0 _is_determined_by_a_{least-squares}_ﬁt_of

σ

(

s

)

=

√

σ

con

+

√

σ

Y m

s

−

m2

₊

_im

exp

(

i

φ)

2

,

(2)

tothecalculatedcross sections.InEq.(2),

σ

con and

σ

Y represent the continuum cross section and resonant cross section, respec-tively,and

σ

con canbe described by afunction ofs,

σ

con

=

C

/

sλ,

wherethe exponent

λ

isapriori unknown.The parameter

φ

de-scribes the phase between resonant and continuum production

amplitudes. The mass m and width

of the Y

(

4260

)

are ﬁxed to the PDG values [28]. The values of C ,

λ

,

σ

Y, and the inter-ference phase

φ

are free in the fit. The uncorrelated systematic uncertaintiesinthe Borncrosssectionmeasurements aredirectly considered in the fit and the effect of the correlated systematic uncertainties on the final results is estimated by the method in Ref.[48],inwhichtheerrorpropagationisdeterminedfrom shift-ing the data by the aforementioned correlated uncertainties and addingthedeviationsinquadrature.Inaddition,theuncertainties for the beam energy measurements of all the data points taken from Ref. [49] are considered in the fit. The best fit function is showninFig. 2asthesolidline.Thedashedlinerepresentsthefit with

σ

Y

=

0. The optimal value of

σ

Y is

(

1

.

6

±

5

.

9

)

×

10−3 pb with a statistical signiﬁcance of 0.5

σ

. The signiﬁcance is calcu-lated based on the changes in the

χ

2 _value _and _the _number

of free parameters in the ﬁt with and without the assumption of existence of the Y

(

4260

)

resonance. The result for the phase

between resonant and continuum production amplitudes is

φ

=

3

.

4

±

1

.

0.The parameters describing the slope ofthe continuum crosssectionare C

= (

5

.

4

±

5

.

3

)

·

105 GeV2λpb and

λ

=

4

.

2

±

0

.

4. The upper limit on

σ

Y at the 90% C.L.,

σ

Yup, is determined by

σ_Yup

0 G

(σ

Y

,

σ

σY

)

dx

/

_∞

0 G

(σ

Y

,

σ

σY

)

dx

=

0

.

9, where G

(σ

Y

,

σ

σY

)

is a

Gaussian functionwithmeanvalue

σ

Y

=

1

.

6

×

10−3 pb and stan-dard deviation

σ

σY

=

5

.

9

×

10−3 pb.The uncertaintiesfrommass

andwidthoftheY

(

4260

)

areconsideredby varyingthemby one standarddeviationaccordingtothePDGvalues[28]andthemost conservative

σ

_Yup is taken as the ﬁnal result. The obtained up-per limit is 0.01 pb. Comparedto the measured cross section of

e+e−

→

Y

(

4260

)

→

π

+

π

−J

/ψ

[50,51],theupperlimitonthe ra-tioofthe branchingfractions _B(B(_Y₍₄₂₆₀Y(4260₎_→)_π→+p_πp¯−π0J/ψ )) atthe 90%C.L.

isdeterminedtobe0.02%.

X

(

4360

)

and

ψ(

4415

)

are also searched for. The ﬁtted cross sectionforX

(

4360

)

and

ψ(

4415

)

are

(

0

.

8

±

2

.

9

)

×

10−3_{pb with}_a

signiﬁcanceof0.5

σ

and

(

0

.

7

±

1

.

6

)

×

10−2 pb withasigniﬁcance of 1.1

σ

, respectively. The upper limit on

σ

(

e+e−

→

X

(

4360

)

→

pp

¯

π

0

₎

_and

_σ

₍

_e+_e−

_{→ ψ(}

₄₄₁₅

₎

_→

_p_p

_¯

_π

0

₎

_at_the_90% _C.L._are

de-terminedtobe0.01pband0.08pb,respectively. 7. Summary

Basedon13datasamplesbetween

√

s

=

4

.

008 and4.600GeV collected with the BESIII detector, the process e+e−

→

pp

¯

π

0 _is

studied.TheBorncrosssectionofe+e−

→

pp

¯

π

0 _is_measured._No

resonant structure isobserved in the shape of the cross section. The upperlimitontheBorn crosssectionofe+e−

→

Y

(

4260

)

→

pp

¯

π

0 _at_the_90% _C.L._is_estimated_to _be_0.01 _pb._The_upper_limit

ontheratioofthebranchingfractions _B(_YB(₍₄₂₆₀Y(4260₎_→)_π→+p_πp¯−π0J/ψ )) atthe

90%C.L.isdeterminedtobe0.02%. Acknowledgements

The BESIII collaboration thanks the staff of BEPCII and the IHEPcomputingcenterfortheirstrongsupport.Thisworkis sup-ported in part by National Key Basic Research Program ofChina underContractNo.2015CB856700;NationalNaturalScience Foun-dationofChina(NSFC)underContractsNos.11235011,11305178,

11322544, 11335008, 11375204, 11425524, 11635010; the

Chi-neseAcademyofSciences(CAS)Large-ScaleScientiﬁc Facility Pro-gram; the CAS Center for Excellence in Particle Physics (CCEPP); the Collaborative Innovation Center for Particles andInteractions (CICPI); Joint Large-Scale Scientiﬁc Facility Funds of the NSFC

and CAS under Contracts Nos. U1232201, U1332201, U1532257,

U1532258; CAS under Contracts Nos.KJCX2-YW-N29,

KJCX2-YW-N45; 100 Talents Program of CAS; National 1000 Talents

Pro-gram of China; INPAC and Shanghai Key Laboratory for Particle

Physics and Cosmology; German Research Foundation DFG

un-der Contracts Nos. Collaborative Research Center CRC 1044, FOR 2359;IstitutoNazionalediFisicaNucleare,Italy;Koninklijke

Neder-landseAkademievanWetenschappen(KNAW)underContractNo.

530-4CDP03; Ministry of Development of Turkey under Contract

No. DPT2006K-120470; The Swedish Resarch Council; U. S.

(7)

DE-SC-0010504, DE-SC0010118,DE-SC0012069; U.S. NationalScience Foundation;UniversityofGroningen(RuG)andthe

Helmholtzzen-trum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU

ProgramofNationalResearchFoundation ofKorea underContract No.R32-2008-000-10155-0.

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