• No results found

Measurement of cross sections of the interactions e(+)e(-) -> phi phi omega and e(+)e(-) -> phi phi phi at center-of-mass energies from 4.008 to 4.600 GeV

N/A
N/A
Protected

Academic year: 2021

Share "Measurement of cross sections of the interactions e(+)e(-) -> phi phi omega and e(+)e(-) -> phi phi phi at center-of-mass energies from 4.008 to 4.600 GeV"

Copied!
9
0
0

Loading.... (view fulltext now)

Full text

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

cross

sections

of

the

interactions

e

+

e

→ φφ

ω

and

e

+

e

→ φφφ

at

center-of-mass

energies

from

4.008

to

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

,

O. Bakina

y

,

R. Baldini Ferroli

t

,

Y. Ban

ag

,

D.W. Bennett

s

,

J.V. Bennett

e

,

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

e

,

H. Cai

bf

,

X. Cai

a

,

1

,

O. Cakir

ap

,

A. Calcaterra

t

,

G.F. Cao

a

,

S.A. Cetin

aq

,

J. Chai

bd

,

J.F. Chang

a

,

1

,

G. Chelkov

y

,

3

,

4

,

G. Chen

a

,

H.S. Chen

a

,

J.C. Chen

a

,

M.L. Chen

a

,

1

,

S. Chen

at

,

S.J. Chen

ae

,

X. Chen

a

,

1

,

X.R. Chen

ab

,

Y.B. Chen

a

,

1

,

X.K. Chu

ag

,

G. Cibinetto

v

,

H.L. Dai

a

,

1

,

J.P. Dai

aj

,

10

,

A. Dbeyssi

n

,

D. Dedovich

y

,

Z.Y. Deng

a

,

A. Denig

x

,

I. Denysenko

y

,

M. Destefanis

bb

,

bd

,

F. De Mori

bb

,

bd

,

Y. Ding

ac

,

C. Dong

af

,

J. Dong

a

,

1

,

L.Y. Dong

a

,

M.Y. Dong

a

,

1

,

Z.L. Dou

ae

,

S.X. Du

bh

,

P.F. Duan

a

,

J.Z. Fan

ao

,

J. Fang

a

,

1

,

S.S. Fang

a

,

X. Fang

ay

,

1

,

Y. Fang

a

,

R. Farinelli

v

,

w

,

L. Fava

bc

,

bd

,

F. Feldbauer

x

,

G. Felici

t

,

C.Q. Feng

ay

,

1

,

E. Fioravanti

v

,

M. Fritsch

n

,

x

,

C.D. Fu

a

,

Q. Gao

a

,

X.L. Gao

ay

,

1

,

Y. Gao

ao

,

Z. Gao

ay

,

1

,

I. Garzia

v

,

K. Goetzen

j

,

L. Gong

af

,

W.X. Gong

a

,

1

,

W. Gradl

x

,

M. Greco

bb

,

bd

,

M.H. Gu

a

,

1

,

Y.T. Gu

l

,

Y.H. Guan

a

,

A.Q. Guo

a

,

L.B. Guo

ad

,

R.P. Guo

a

,

Y. Guo

a

,

Y.P. Guo

x

,

Z. Haddadi

aa

,

A. Hafner

x

,

S. Han

bf

,

X.Q. Hao

o

,

F.A. Harris

au

,

K.L. He

a

,

F.H. Heinsius

d

,

T. Held

d

,

Y.K. Heng

a

,

1

,

T. Holtmann

d

,

Z.L. Hou

a

,

C. Hu

ad

,

H.M. Hu

a

,

T. Hu

a

,

1

,

Y. Hu

a

,

G.S. Huang

ay

,

1

,

J.S. Huang

o

,

X.T. Huang

ai

,

X.Z. Huang

ae

,

Z.L. Huang

ac

,

T. Hussain

ba

,

W. Ikegami Andersson

be

,

Q. Ji

a

,

Q.P. Ji

o

,

X.B. Ji

a

,

X.L. Ji

a

,

1

,

L.W. Jiang

bf

,

X.S. Jiang

a

,

1

,

X.Y. Jiang

af

,

J.B. Jiao

ai

,

Z. Jiao

q

,

D.P. Jin

a

,

1

,

S. Jin

a

,

T. Johansson

be

,

A. Julin

av

,

N. Kalantar-Nayestanaki

aa

,

X.L. Kang

a

,

X.S. Kang

af

,

M. Kavatsyuk

aa

,

B.C. Ke

e

,

P. Kiese

x

,

R. Kliemt

j

,

B. Kloss

x

,

O.B. Kolcu

aq

,

8

,

B. Kopf

d

,

M. Kornicer

au

,

A. Kupsc

be

,

W. Kühn

z

,

J.S. Lange

z

,

M. Lara

s

,

P. Larin

n

,

H. Leithoff

x

,

C. Leng

bd

,

C. Li

be

,

Cheng Li

ay

,

1

,

D.M. Li

bh

,

F. Li

a

,

1

,

F.Y. Li

ag

,

G. Li

a

,

H.B. Li

a

,

H.J. Li

a

,

J.C. Li

a

,

Jin Li

ah

,

K. Li

m

,

K. Li

ai

,

Lei Li

c

,

P.R. Li

g

,

at

,

Q.Y. Li

ai

,

T. Li

ai

,

W.D. Li

a

,

W.G. Li

a

,

X.L. Li

ai

,

X.N. Li

a

,

1

,

X.Q. Li

af

,

Y.B. Li

b

,

Z.B. Li

an

,

H. Liang

ay

,

1

,

Y.F. Liang

al

,

Y.T. Liang

z

,

G.R. Liao

k

,

D.X. Lin

n

,

B. Liu

aj

,

10

,

B.J. Liu

a

,

C.X. Liu

a

,

D. Liu

ay

,

1

,

F.H. Liu

ak

,

Fang Liu

a

,

Feng Liu

f

,

H.B. Liu

l

,

H.H. Liu

a

,

H.H. Liu

p

,

H.M. Liu

a

,

J. Liu

a

,

J.B. Liu

ay

,

1

,

J.P. Liu

bf

,

J.Y. Liu

a

,

K. Liu

ao

,

K.Y. Liu

ac

,

L.D. Liu

ag

,

P.L. Liu

a

,

1

,

Q. Liu

at

,

S.B. Liu

ay

,

1

,

X. Liu

ab

,

Y.B. Liu

af

,

Y.Y. Liu

af

,

Z.A. Liu

a

,

1

,

Zhiqing Liu

x

,

H. Loehner

aa

,

Y.F. Long

ag

,

X.C. Lou

a

,

1

,

7

,

H.J. Lu

q

,

J.G. Lu

a

,

1

,

Y. Lu

a

,

Y.P. Lu

a

,

1

,

C.L. Luo

ad

,

M.X. Luo

bg

,

T. Luo

au

,

X.L. Luo

a

,

1

,

X.R. Lyu

at

,

F.C. Ma

ac

,

H.L. Ma

a

,

L.L. Ma

ai

,

M.M. Ma

a

,

Q.M. Ma

a

,

T. Ma

a

,

X.N. Ma

af

,

X.Y. Ma

a

,

1

,

Y.M. Ma

ai

,

F.E. Maas

n

,

M. Maggiora

bb

,

bd

,

Q.A. Malik

ba

,

Y.J. Mao

ag

,

Z.P. Mao

a

,

S. Marcello

bb

,

bd

,

J.G. Messchendorp

aa

,

G. Mezzadri

w

,

J. Min

a

,

1

,

T.J. Min

a

,

R.E. Mitchell

s

,

X.H. Mo

a

,

1

,

Y.J. Mo

f

,

C. Morales Morales

n

,

G. Morello

t

,

N.Yu. Muchnoi

i

,

5

,

H. Muramatsu

av

,

P. Musiol

d

,

Y. Nefedov

y

,

F. Nerling

j

,

I.B. Nikolaev

i

,

5

,

Z. Ning

a

,

1

,

S. Nisar

h

,

S.L. Niu

a

,

1

,

E-mailaddress:liupl@ihep.ac.cn(P.L. Liu).

http://dx.doi.org/10.1016/j.physletb.2017.09.021

0370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

(2)

X.Y. Niu

a

,

S.L. Olsen

ah

,

Q. Ouyang

a

,

1

,

S. Pacetti

u

,

Y. Pan

ay

,

1

,

P. Patteri

t

,

M. Pelizaeus

d

,

H.P. Peng

ay

,

1

,

K. Peters

j

,

9

,

J. Pettersson

be

,

J.L. Ping

ad

,

R.G. Ping

a

,

R. Poling

av

,

V. Prasad

a

,

H.R. Qi

b

,

M. Qi

ae

,

S. Qian

a

,

1

,

C.F. Qiao

at

,

L.Q. Qin

ai

,

N. Qin

bf

,

X.S. Qin

a

,

Z.H. Qin

a

,

1

,

J.F. Qiu

a

,

K.H. Rashid

ba

,

C.F. Redmer

x

,

M. Ripka

x

,

G. Rong

a

,

Ch. Rosner

n

,

X.D. Ruan

l

,

A. Sarantsev

y

,

6

,

M. Savrié

w

,

C. Schnier

d

,

K. Schoenning

be

,

W. Shan

ag

,

M. Shao

ay

,

1

,

C.P. Shen

b

,

P.X. Shen

af

,

X.Y. Shen

a

,

H.Y. Sheng

a

,

W.M. Song

a

,

X.Y. Song

a

,

S. Sosio

bb

,

bd

,

S. Spataro

bb

,

bd

,

G.X. Sun

a

,

J.F. Sun

o

,

S.S. Sun

a

,

X.H. Sun

a

,

Y.J. Sun

ay

,

1

,

Y.Z. Sun

a

,

Z.J. Sun

a

,

1

,

Z.T. Sun

s

,

C.J. Tang

al

,

X. Tang

a

,

I. Tapan

ar

,

E.H. Thorndike

aw

,

M. Tiemens

aa

,

I. Uman

as

,

G.S. Varner

au

,

B. Wang

af

,

B.L. Wang

at

,

D. Wang

ag

,

D.Y. Wang

ag

,

K. Wang

a

,

1

,

L.L. Wang

a

,

L.S. Wang

a

,

M. Wang

ai

,

P. Wang

a

,

P.L. Wang

a

,

W. Wang

a

,

1

,

W.P. Wang

ay

,

1

,

X.F. Wang

ao

,

Y. Wang

am

,

Y.D. Wang

n

,

Y.F. Wang

a

,

1

,

Y.Q. Wang

x

,

Z. Wang

a

,

1

,

Z.G. Wang

a

,

1

,

Z.H. Wang

ay

,

1

,

Z.Y. Wang

a

,

Zongyuan Wang

a

,

T. Weber

x

,

D.H. Wei

k

,

P. Weidenkaff

x

,

S.P. Wen

a

,

U. Wiedner

d

,

M. Wolke

be

,

L.H. Wu

a

,

L.J. Wu

a

,

Z. Wu

a

,

1

,

L. Xia

ay

,

1

,

L.G. Xia

ao

,

Y. Xia

r

,

D. Xiao

a

,

H. Xiao

az

,

Z.J. Xiao

ad

,

Y.G. Xie

a

,

1

,

Y.H. Xie

f

,

Q.L. Xiu

a

,

1

,

G.F. Xu

a

,

J.J. Xu

a

,

L. Xu

a

,

Q.J. Xu

m

,

Q.N. Xu

at

,

X.P. Xu

am

,

L. Yan

bb

,

bd

,

W.B. Yan

ay

,

1

,

W.C. Yan

ay

,

1

,

Y.H. Yan

r

,

H.J. Yang

aj

,

10

,

H.X. Yang

a

,

L. Yang

bf

,

Y.X. Yang

k

,

M. Ye

a

,

1

,

M.H. Ye

g

,

J.H. Yin

a

,

Z.Y. You

an

,

B.X. Yu

a

,

1

,

C.X. Yu

af

,

J.S. Yu

ab

,

C.Z. Yuan

a

,

Y. Yuan

a

,

A. Yuncu

aq

,

2

,

A.A. Zafar

ba

,

Y. Zeng

r

,

Z. Zeng

ay

,

1

,

B.X. Zhang

a

,

B.Y. Zhang

a

,

1

,

C.C. Zhang

a

,

D.H. Zhang

a

,

H.H. Zhang

an

,

H.Y. Zhang

a

,

1

,

J. Zhang

a

,

J.J. Zhang

a

,

J.L. Zhang

a

,

J.Q. Zhang

a

,

J.W. Zhang

a

,

1

,

J.Y. Zhang

a

,

J.Z. Zhang

a

,

K. Zhang

a

,

L. Zhang

a

,

S.Q. Zhang

af

,

X.Y. Zhang

ai

,

Y. Zhang

a

,

Y. Zhang

a

,

Y.H. Zhang

a

,

1

,

Y.N. Zhang

at

,

Y.T. Zhang

ay

,

1

,

Yu Zhang

at

,

Z.H. Zhang

f

,

Z.P. Zhang

ay

,

Z.Y. Zhang

bf

,

G. Zhao

a

,

J.W. Zhao

a

,

1

,

J.Y. Zhao

a

,

J.Z. Zhao

a

,

1

,

Lei Zhao

ay

,

1

,

Ling Zhao

a

,

M.G. Zhao

af

,

Q. Zhao

a

,

Q.W. Zhao

a

,

S.J. Zhao

bh

,

T.C. Zhao

a

,

Y.B. Zhao

a

,

1

,

Z.G. Zhao

ay

,

1

,

A. Zhemchugov

y

,

3

,

B. Zheng

n

,

az

,

J.P. Zheng

a

,

1

,

W.J. Zheng

ai

,

Y.H. Zheng

at

,

B. Zhong

ad

,

L. Zhou

a

,

1

,

X. Zhou

bf

,

X.K. Zhou

ay

,

1

,

X.R. Zhou

ay

,

1

,

X.Y. Zhou

a

,

K. Zhu

a

,

K.J. Zhu

a

,

1

,

S. Zhu

a

,

S.H. Zhu

ax

,

X.L. Zhu

ao

,

Y.C. Zhu

ay

,

1

,

Y.S. Zhu

a

,

Z.A. Zhu

a

,

J. Zhuang

a

,

1

,

L. Zotti

bb

,

bd

,

B.S. Zou

a

,

J.H. Zou

a

aInstituteofHighEnergyPhysics,Beijing100049,People’sRepublicofChina bBeihangUniversity,Beijing100191,People’sRepublicofChina

cBeijingInstituteofPetrochemicalTechnology,Beijing102617,People’sRepublicofChina dBochumRuhr-University,D-44780Bochum,Germany

eCarnegieMellonUniversity,Pittsburgh,PA 15213,USA

fCentralChinaNormalUniversity,Wuhan430079,People’sRepublicofChina

gChinaCenterofAdvancedScienceandTechnology,Beijing100190,People’sRepublicofChina

hCOMSATSInstituteofInformationTechnology,Lahore,DefenceRoad,OffRaiwindRoad,54000Lahore,Pakistan iG.I.BudkerInstituteofNuclearPhysicsSBRAS(BINP),Novosibirsk630090,Russia

jGSIHelmholtzcentreforHeavyIonResearchGmbH,D-64291Darmstadt,Germany kGuangxiNormalUniversity,Guilin541004,People’sRepublicofChina

lGuangxiUniversity,Nanning530004,People’sRepublicofChina

mHangzhouNormalUniversity,Hangzhou310036,People’sRepublicofChina nHelmholtzInstituteMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany oHenanNormalUniversity,Xinxiang453007,People’sRepublicofChina

pHenanUniversityofScienceandTechnology,Luoyang471003,People’sRepublicofChina qHuangshanCollege,Huangshan245000,People’sRepublicofChina

rHunanUniversity,Changsha410082,People’sRepublicofChina sIndianaUniversity,Bloomington,IN 47405,USA

tINFNLaboratoriNazionalidiFrascati,I-00044,Frascati,Italy uINFNandUniversityofPerugia,I-06100,Perugia,Italy vINFNSezionediFerrara,I-44122,Ferrara,Italy wUniversityofFerrara,I-44122,Ferrara,Italy

xJohannesGutenbergUniversityofMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany yJointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia

zJustus-Liebig-UniversitaetGiessen,II.PhysikalischesInstitut,Heinrich-Buff-Ring16,D-35392Giessen,Germany aaKVI-CART,UniversityofGroningen,NL-9747AAGroningen,TheNetherlands

abLanzhouUniversity,Lanzhou730000,People’sRepublicofChina acLiaoningUniversity,Shenyang110036,People’sRepublicofChina adNanjingNormalUniversity,Nanjing210023,People’sRepublicofChina aeNanjingUniversity,Nanjing210093,People’sRepublicofChina afNankaiUniversity,Tianjin300071,People’sRepublicofChina agPekingUniversity,Beijing100871,People’sRepublicofChina ahSeoulNationalUniversity,Seoul,151-747RepublicofKorea aiShandongUniversity,Jinan250100,People’sRepublicofChina

ajShanghaiJiaoTongUniversity,Shanghai200240,People’sRepublicofChina akShanxiUniversity,Taiyuan030006,People’sRepublicofChina

(3)

alSichuanUniversity,Chengdu610064,People’sRepublicofChina amSoochowUniversity,Suzhou215006,People’sRepublicofChina anSunYat-SenUniversity,Guangzhou510275,People’sRepublicofChina aoTsinghuaUniversity,Beijing100084,People’sRepublicofChina apAnkaraUniversity,06100Tandogan,Ankara,Turkey aqIstanbulBilgiUniversity,34060Eyup,Istanbul,Turkey arUludagUniversity,16059Bursa,Turkey

asNearEastUniversity,Nicosia,NorthCyprus,Mersin10,Turkey

atUniversityofChineseAcademyofSciences,Beijing100049,People’sRepublicofChina auUniversityofHawaii,Honolulu,HI 96822,USA

avUniversityofMinnesota,Minneapolis,MN 55455,USA awUniversityofRochester,Rochester,NY 14627,USA

axUniversityofScienceandTechnologyLiaoning,Anshan114051,People’sRepublicofChina ayUniversityofScienceandTechnologyofChina,Hefei230026,People’sRepublicofChina azUniversityofSouthChina,Hengyang421001,People’sRepublicofChina

baUniversityofthePunjab,Lahore-54590,Pakistan bbUniversityofTurin,I-10125,Turin,Italy

bcUniversityofEasternPiedmont,I-15121,Alessandria,Italy bdINFN,I-10125,Turin,Italy

be

UppsalaUniversity,Box516,SE-75120Uppsala,Sweden bfWuhanUniversity,Wuhan430072,People’sRepublicofChina bgZhejiangUniversity,Hangzhou310027,People’sRepublicofChina bhZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received23June2017

Receivedinrevisedform12August2017 Accepted9September2017

Availableonline14September2017 Editor:L.Rolandi

Keywords: e+e−annihilation Triplequarkonia Crosssection

UsingdatasamplescollectedwiththeBESIIIdetectorattheBEPCIIcollideratsixcenter-of-massenergies between4.008and4.600 GeV,weobservetheprocessese+e→ φφ

ω

ande+e→ φφφ.TheBorncross sectionsaremeasuredandtheratioofthecrosssections

σ

(e+e→ φφ

ω

)/

σ

(e+e→ φφφ)isestimated tobe1.75±0.22±0.19 averagedoversixenergypoints,wherethefirstuncertaintyisstatisticalandthe secondissystematic.Theresultsrepresentfirstmeasurementsoftheseinteractions.

©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

The experimental understanding of hadron production in

electron–positron annihilation has been achieved with the mea-surement of the total inclusive hadronic cross sections, the so-calledRmeasurement

[1]

,andtheexclusivemeasurementoffinal states involving pions, kaons and other light hadrons at various center-of-mass (c.m.) energies [2,3]. The tools for describing the

e+e−annihilationtohadronsprocessgenerallyincludetheuseof theKKMCgenerator

[4]

,whichincludesinitialandfinalstate radi-ation,andthePythia

[5]

programbasedontheLundStringmodel orPartonShowermodelthathadronizesthefinal-statequarks.The KKMC-Pythiacombinationisnotexpectedtocorrectlydescribethe processeswithmorethantwovectormesonsinthefinalstate,as

theycorrespondtohigherorderQuantumChromodynamics(QCD)

1 Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049,Hefei230026,People’sRepublicofChina.

2 AlsoatBogaziciUniversity,34342Istanbul,Turkey.

3 AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia. 4 Alsoatthe FunctionalElectronicsLaboratory,Tomsk StateUniversity,Tomsk, 634050,Russia.

5 AlsoattheNovosibirskStateUniversity,Novosibirsk,630090,Russia. 6 AlsoattheNRC“KurchatovInstitute”,PNPI,188300,Gatchina,Russia. 7 AlsoatUniversityofTexasatDallas,Richardson,TX 75083,USA. 8 AlsoatIstanbulArelUniversity,34295Istanbul,Turkey.

9 AlsoatGoetheUniversityFrankfurt,60323FrankfurtamMain,Germany. 10 AlsoatKeyLaboratoryforParticlePhysics,AstrophysicsandCosmology, Min-istryofEducation;Shanghai KeyLaboratoryfor ParticlePhysicsand Cosmology; Institute ofNuclearand Particle Physics,Shanghai 200240, People’sRepublic of China.

processes andare generally associatedwith multiplegluons. The experimentalresultsprovidemoreconstraintsonthehigher-order QCDcalculation.

The BaBar and Belle collaborations reported the observation ofsignificant doublecharmoniumproductione+e

J

cc and

¯

foundtheratio

σ

(

e+e

J

cc

¯

)/

σ

(

e+e

J

X

)

tobe

0

.

6

[6], whichindicates that a surprisinglylarge fraction ofe+e

J

X events are produced by the e+e

J

cc process.

¯

This experimental resulthasstimulatedmuchtheoretical interest. Var-ious theoretical approaches, such asNRQCD factorization[7]and the light cone method [8], have been proposed to make correc-tions tothelowratiopredictedbythenon-relativisticcalculation, which predicts amuch lower value forthecross section [9]. The validityofthetheoreticalinvestigations canbetestedoverawide kinematicalrangewithdoubleortriplequarkonia(s

¯

s,cc,

¯

bb)

¯

pro-duced ine+e− annihilations. In particular, strangeonia ss are

¯

lo-cated in the region of transition between perturbative QCD and non-perturbativeQCD.Thee+e− annihilationtomultiples

¯

s states

may provide an important experimental opportunity in the low-energyregion.

Inthispaper,we report onthefirstmeasurement oftheBorn crosssectionsofe+e

→ φφ

ω

ande+e

→ φφφ

processesatc.m. energies Ecm

=

4

.

008

,

4

.

226

,

4

.

258

,

4

.

358

,

4

.

416 and 4

.

600 GeV [10]. The data samples were collected by the BESIII detector at theBEPCIIcollider

[11]

.

Additionally, we also measure the ratio

σ

(

e+e

→ φφ

ω

)/

σ

(

e+e

→ φφφ)

,wheremanyofthesystematicuncertainties are canceled. The mixing angle of

ω

and

φ

is expectedto be small anditseffectontheratiocanbeneglected.Inthee+e− annihila-tion process,withoutconsideringthe intermediateresonance,the

(4)

Fig. 1. Feynman graphs for (a) e+e−→γgg→3(s¯s). (b) e+e−→3γ∗→3(s¯s).

final

φφφ

states wouldbe generatedvia one virtual photon and two gluons orthree virtual photons, as illustrated in Fig. 1. The productionviatwovirtualphotonsandonegluonisforbidden, be-causethegluoncarriescolorwhilethefinalstateiscolorneutral. By replacing s

(

7

)

¯

s

(

8

)

with

(

uu

¯

+

dd

¯

)/

2 in Fig. 1(a), we obtain theratio σ(e+e−→γgg→2(s¯s)+(uu¯+dd¯)/ √ 2) σ(e+e−→γgg→3(s¯s))

(4 9+19)/2 1 9

=

2

.

5,because thevertex“A”isproportionaltothechargesquaredofthequarks. If, on the other hand,

(

uu

¯

+

dd

¯

)/

2 is substituted for s

(

3

)

¯

s

(

4

)

ors

(

5

)

s

¯

(

6

)

,the ratiowould be about1 since thestrong interac-tionvertexonlyreliesonthemassofthequarks.Consideringthe abovetwocasesin

Fig. 1

(a)andneglectingthesmallcontribution from

Fig. 1

(b), σ(e+e−→γgg→2(s¯s)+(uu¯+dd¯)/

2)

σ(e+e−→γgg→3(s¯s)) wouldrangefrom1

to2.5, depending onthe ratioofthetwo casesabove. The study of

σ

(

e+e

→ φφ

ω

)/

σ

(

e+e

→ φφφ)

canthereforehelpto under-standtheproductionmechanismofe+e− annihilationtomultiple quarkonia.

2. DetectorandMonteCarlosimulation

TheBESIIIdetector,asdescribedindetailinRef.[12],hasa geo-metricalacceptanceof93%ofthesolidangle.Asmall-cell, helium-basedmaindriftchamber(MDC)immersedina1 Tmagneticfield measuresthemomentumofchargedparticleswitharesolutionof 0.5% at1 GeV/c, andprovides energy loss (dE/dx) measurements witharesolutionbetterthan6%forelectronsfromBhabha scatter-ing.Theelectromagneticcalorimeter(EMC)detectsphotonswitha resolution of2.5% (5%) atan energyof 1 GeV inthe barrel (end cap)region.Atime-of-flightsystem(TOF)assistsinparticle identi-fication(PID)withatimeresolutionof80 ps(110 ps)inthebarrel (endcap)region.

A geant4-based [13] Monte Carlo (MC) simulation software,

whichincludesthegeometricdescriptionoftheBESIIIdetectorand thedetectorresponse,isusedtooptimizetheeventselection cri-teria,determinethedetectionefficiencyandestimatebackground contributions.Thesimulationincludesthebeamenergyspreadand initial-stateradiation(ISR)modeledwith kkmc[4].Inthisanalysis, 0.5million events of e+e

→ φφ

ω

and e+e

→ φφφ

are gener-ated individually at different c.m. energies corresponding to the experimentalvalues.Both processesaresimulatedwithauniform distributioninphasespace(PHSP).Theobservedcrosssectionsfor

e+e

→ φφ

ω

and e+e

→ φφφ

at the sixenergy values in this analysis are used as the inputs in the KKMC simulation for ISR effects.Inlinewiththepartialreconstructiontechniquethatis im-plementedintheanalysis,thesignalprocesse+e

→ φφ

ω

is sim-ulatedwithboth

φ

decayingintoK+K− andthe

ω

decayinginto all possible final states, whilein the simulation of e+e

→ φφφ

events,allthree

φ

aregeneratedtodecayviaallpossiblemodes. 3. Eventselection

The candidateevents for e+e

→ φφ

ω

and

φφφ

are selected with a partial reconstruction method to get higher efficiencies.

We reconstruct two

φ

mesons with their prominent K+K

de-caymodeandidentifytheremaining

ω

or

φ

mesonwiththemass recoilingagainstthereconstructed

φφ

system.

Foreachchargedtrack,thepolarangleintheMDCmustsatisfy

|

cos

θ

|

<

0

.

93,andthepoint ofclosest approach tothe e+e− in-teractionpointmustbewithin

±

10 cminthebeamdirectionand within1 cmintheplaneperpendiculartothebeamdirection.We identifycharged kaoncandidates usingthe dE/dx andTOF infor-mation. The probabilities

L(

π

)

and

L(

K

)

are determinedfor the

π

andK hypothesis,respectively.Kaonsareidentifiedbyrequiring

L(

K

)

>

L(

π

)

.

The

φ

candidates are formed from pairs of identified kaons

withopposite charges. Theirinvariant massis requiredto satisfy 1

.

01

<

M

(

K+K

)

<

1

.

03 GeV/c2. At least two

φ

candidates with nosharedtracksarerequiredineachevent.Iftherearemorethan two

φ

candidatesinoneevent,onlythe

φφ

combinationwiththe minimum

M is keptfor furtheranalysis, andthe two

φ

candi-datesare randomlylabeledas

φ

1 or

φ

2.Themassdifference

M

is defined as



(

1

(

K+K

)

M

(φ))

2

+ (

2

(

K+K

)

M

(φ))

2,

where M

(φ)

isthenominalmassofthe

φ

mesontakenfromthe particledatagroup(PDG)

[14]

.

Fig. 2 (a) depicts the scatter plot of 1

(

K+K

)

versus 2

(

K+K

)

bycombiningthe datasamplesat sixc.m.energies.

A clear accumulation of events is observed around the intersec-tionofthe

φ

1 and

φ

2massregions,whichindicates e+e

→ φφ

X

signals.Themassofthesystemrecoilingagainstthereconstructed

φφ

iscalculatedwithR M

(φφ)

=



(

Ecm

Eφφ

)

2

p2φφ,whereEcm

is the c.m. energy obtained by analyzing the di-muon process

e+e

γ

ISR/FSR

μ

+

μ

−, with a precision of 0.02% [10]. Eφφ and pφφ arethe energyandmomentum ofthereconstructed

φφ

pair

inthee+e−restsystem.Asshownbythesolidpointsin

Fig. 2

(b), we obtain two clear peaks in the vicinities of

ω

and

φ

in the

R M

(φφ)

distribution,whichindicates theprocessese+e

→ φφ

ω

and

φφφ

,respectively.

4. StudyofbackgroundsinR M

(φφ)

To ensure that the observed

ω

and

φ

signal in the R M

(φφ)

distribution originatefrom theprocesses e+e

→ φφ

ω

and

φφφ

,

we perform a study of the potential peaking backgrounds. The

two dimensional (2D) sidebandsillustrated in Fig. 2(a) are used to studythepotential backgroundwithout a

φφ

pairin thefinal state, where the

φ

sidebands are definedas0

.

99

<

M

(

K+K

)

<

1

.

00 GeV/c2 and 1

.

04

<

M

(

K+K

)

<

1

.

06 GeV/c2. The non-

φ

1

and/or non-

φ

2 processes are estimated by the weighted sum of

the events in the horizontal and vertical sideband regions, with the entries in the diagonal sidebands subtracted to compensate for the double counting of the background without any

φ

in fi-nalstate.Theweightingfactorforthe

φ

2 butnon-

φ

1eventsinthe

horizontalsidebandsistheratioofthenumberof

φ

2 butnon-

φ

1

events under the signal region (nsigbkg) to the number of

φ

2 but

non-

φ

1eventsinthehorizontalsidebands(nsdbbkg).n sig

(5)

Fig. 2. (a)Scatterplotof1(K+K)versus2(K+K).Thecentralboxisthesignalregionwhiletheboxesaroundarethetwo-dimensionalsidebands.(b)Therecoil

massdistributionsofφφforeventsinthesignalregion(solidpoints)orsidebands(circles).Allsixdatasamplesarecombined.

determined from the 2D fit to 1

(

K+K

)

versus 2

(

K+K

)

.

Theweighting factorforthe

φ

1 butnon-

φ

2 (non-

φ

1 andnon-

φ

2)

events in the vertical (diagonal) sidebands are determined sim-ilarly. The 2D probability density functions for the components

φ

1

φ

2,

φ

1 butnon-

φ

2,non-

φ

1 but

φ

2,non-

φ

1 andnon-

φ

2 are

con-structed by the product of two one-dimensional functions. The

φ

peak is described with a MC-derived shape convoluted with

a Gaussian function to take into account the resolution

differ-encebetween dataand MC simulation.The non-

φ

componentis

described withsecond-orderpolynomial functions. The estimated

R M

(φφ)

distributionwithweighted2Dsidebandseventsisshown as the open circles in Fig. 2 (b). Since the

φ

signal is close to theK+K−productionthreshold,wearenotabletoobtaina side-bandwhichisfarenoughawayfromthesignalregionatthelower side of M

(

K+K

)

. Thus, the small

ω

and

φ

signalsobserved in

R M

(φφ)

estimatedwiththe2D sidebandarefromtheleakageof thereale+e

→ φφ +

ω

signals.FromstudiesofsignalMC sam-ples,the ratioofthe signalevents inthe2D sidebandregions to thoseinthesignalregionisestimatedtobe3%

5%.

Wealsoestimate thepeakingbackgroundinthe R M

(φφ)

dis-tributionfortheprocess e+e

→ φφφ

withthe MCsamples.The dominantpeakingbackgroundsisfromthee+e

K+K

φφ

and

e+e

K+KK+K

φ

processes. When the directly produced

K+K(K+KK+K−) isreconstructedas

φ

(

φφ

),thesetwo pro-cesses would contribute as peaking backgrounds in the R M

(φφ)

distribution. The contamination rate of the e+e

K+K

φφ

(e+e

K+KK+K

φ

) events to e+e

→ φφφ

is estimatedto be

1

.

0% (0.1%) at each energy point withthe assumption that the c.m. energy dependent cross section for e+e

K+K

φφ

(e+e

K+KK+K

φ

) is the same as for e+e

→ φφφ

. We take 1.0% as the uncertainty on the size of the peaking back-grounds of e+e

→ φφφ

. Similarly, the dominant peaking back-grounds of e+e

→ φφ

ω

is from the e+e

K+K

φ

ω

and

e+e

K+KK+K

ω

processes. For e+e

→ φφ

ω

, the uncer-taintyfromthepeakingbackgroundsisdeterminedtobe1.0%. 5. FitstotheR M

(φφ)

spectrumandcrosssectionresults

Thereconstructionefficiencies andyields ofe+e

→ φφ

ω

and

φφφ

signalsaredeterminedbythefittothe R M

(φφ)

distribution forMCsimulationanddata,respectively.

5.1. CorrectiontoR M

(φφ)

ComparedwiththevaluesinthePDG,themeasuredmassesof the

ω

and

φ

mesonsintheR M

(φφ)

distributiondeviatetotheleft with

4.5 MeV.Thisdeviationmaybeinduced byISR,theenergy

loss ofthereconstructed kaonsandfinal state radiation(FSR), or the uncertaintyof Ecm.The overalleffect isconsidered asashift

on Ecm,

Ecm.

We estimate

Ecm by studying the process e+e

→ φ

K+K

withpartiallyreconstructingone

φ

mesonandonechargedkaon. The recoil mass against the reconstructed

φ

K is calculated with

R M

K

)

=



(

Ecm

EφK

)

2

pφ2K, where EφK and pφK are the

energy and momentum of the reconstructed

φ

K in the system

of e+e−.

Ecm is estimated with

Ecm

=

ER Mcm−(φEKφ K)

×

R M

K

)

,

where R M

K

)

isapproximatelym

(

K

)

fromPDGandEφK isthe

average over all

φ

K+K− events. R M

(φφ)

for each event is then corrected by subtracting

R M

(φφ)

in thedata andMC samples, where

R M

(φφ)

=

Ecm−Eφφ

R M(φφ)

×

Ecm.Asa consequence,the

mea-sured masses of the

ω

and

φ

mesons obtained by fitting the

R M

(φφ)

distributionsareconsistentwiththevaluesinthePDG.

5.2. FitstotheR M

(φφ)

spectrum

An unbinnedmaximumlikelihood fitisperformedto the cor-rected R M

(φφ)

distributions. The signal distribution is modeled by theMC-derived signalshape. The studyof theselected

φ

sig-nal indicates that themass resolution differencefor the

φ

signal is very small.Therefore,we assume the resolutionof R M

(φφ)

is thesamebetweendataandMCsimulation,andthecorresponding systematic uncertaintywill be considered.The background shape isdescribed byathird-orderChebyshevpolynomialfunctionwith parameters fixed tothevaluesobtainedby fittingall samples to-gether,sincesomesampleshavesmallstatistics.Thecorresponding fit resultsare shown in

Fig. 3

.The statisticalsignificances of the

ω

signalsare examinedusingthe differencesin likelihood val-uesoffitswithandwithoutan

ω

signalcomponentincludedin thefits.Both

ω

and

φ

signalsareseenwithstatisticalsignificances ofmorethan3

σ

foreachdatasample,andthesignificancesof

ω

and

φ

are both largerthan 10

σ

ifall sixdatasamples are com-bined.Theyields of

ω

and

φ

signal eventsandthecorresponding statisticalsignificancesforeachsamplearesummarizedin

Table 1

and

Table 2

,respectively.

5.3. Reconstructionefficiency

Thee+e

→ φφ

ω

and

φφφ

signalMCsamplesaresimulatedby assumingauniformdistributioninphasespace.Thereconstruction efficiencyofthetworeconstructed

φ

sdependsontheirproduction angles.Thecomparisonofthecosineofthepolarangles

θ

forthe

two reconstructed

φ

mesons betweendataandMC simulation is

(6)

Fig. 3. FitstothecorrectedR M(φφ)distributionfordatasamplesatEcm=(a)4.008,(b)4.226,(c)4.258,(d)4.358,(e)4.416and(f)4.600 GeV.Ineachplot,thepointswith errorbararedata,thedashedcurveisthebackgroundcontributionandthesolidlineshowsthetotalfit.

Table 1

Summaryofthemeasurementsofthee+e→ φφωprocess.Listedinthetablearethec.m.energyEcm,theintegratedluminosityLint,thenumberoftheobservedevents Nobs,thereconstructionefficiency,thevacuumpolarizationfactor(1+ δv),theradiativecorrectionfactor(1+ δr),themeasuredBorncrosssectionσB,andstatistical significance.ThefirstuncertaintyoftheBorncrosssectionisstatistical,andthesecondissystematic.

Ecm(GeV) Lint(pb−1) Nobs (%) (1+ δv) (1+ δr) σB(fb) Significance

4.008 482.0 36.0±7.6 22.7 1.044 0.888 1485±312±138 7.3σ 4.226 1091.7 82.6±11.8 25.3 1.057 0.940 1260±180±94 10.6σ 4.258 825.7 41.0±9.6 25.2 1.054 1.159 674±158±56 5.8σ 4.358 539.8 23.5±7.1 25.8 1.051 1.062 633±191±47 4.6σ 4.416 1073.6 44.1±10.1 25.6 1.053 1.054 605±138±50 5.9σ 4.600 566.9 24.1±6.6 26.3 1.055 0.995 643±177±50 5.3σ Table 2

Summaryofthemeasurementsofthee+e→ φφφprocess.Listedinthetableare thec.m.energyEcm,thenumberoftheobservedeventsNobs,thereconstruction efficiency,theradiativecorrectionfactor(1+ δr),themeasuredBorncross

sec-tionσB,andstatisticalsignificance.ThefirstuncertaintyoftheBorncrosssection isstatistical,andthesecondissystematic.TheintegratedluminosityLintandthe vacuumpolarizationfactor(1+ δv

)aresamewiththoseinTable 1.

Ecm(GeV) Nobs (%) (1+ δr) σB(fb) Significance

4.008 17.9±6.5 59.8 0.876 284±104±28 3.5σ 4.226 82.6±12.1 68.3 0.876 500±73±55 9.7σ 4.258 63.9±10.8 69.2 0.886 501±85±56 8.4σ 4.358 31.2±8.8 70.4 0.983 332±94±40 4.6σ 4.416 68.4±11.9 71.6 0.932 379±66±45 7.7σ 4.600 39.2±8.2 73.7 0.942 395±83±49 6.9σ

fittingthe R M

(φφ)

distributionforeventswithcos

θ

ingivenbins. All the data samplesare combined,assuming the cos

θ

distribu-tionsdonot dependonthec.m. energy.Totake intoaccountthe deviationincos

θ

distributionsbetweenthedataandthePHSPMC samples,thereconstructionefficienciesaredeterminedwithPHSP MC samples incorporating the re-weighting correction according tothe2Ddistributionofcos

θ

1versuscos

θ

2 ofdataandPHSPMC

samples.

5.4.Crosssectionresults

TheBorncrosssectioniscalculatedby

σ

B

=

Nobs

L

int

· (

1

+ δ

r

)

· (

1

+ δ

v

)

·

·

B

2

(1)

where Nobs is the numberof observed signal events,

L

int is the

integrated luminosity,

(

1

+ δ

r

)

is the radiative correction factor,

(

1

+ δ

v

)

isthe vacuumpolarization factor,

isthe detection ef-ficiencyincludingreconstructionandallselectioncriteria,and

B

is thebranchingfractionof

φ

K+K−.Thevacuumpolarization fac-toristakenfromaQEDcalculation.Withtheinputoftheobserved c.m.energydependent

σ

(

e+e

→ φφ

ω

)

and

σ

(

e+e

→ φφφ)

,and usingalinearinterpolationtoobtainthecrosssectionsinthefull range, the radiative correction factor is calculated in QED [15]. Since the radiative correction factor and the detection efficiency bothdependonthelineshapeoftheinputcrosssection,theBorn crosssections ofe+e

→ φφ

ω

ande+e

→ φφφ

aredetermined withfouriterations untilconvergencehasbeen reached.The val-uesofallvariablesusedinthecalculationof

σ

(

e+e

→ φφ

ω

)

and

σ

(

e+e

→ φφφ)

arelistedin

Table 1

and

Table 2

,respectively.

Fig. 5 (a) and (b) show the measured Born cross sections

σ

(

e+e

→ φφ

ω

)

and

σ

(

e+e

→ φφφ)

,respectively.The statistical-weighted average ofthe measurements at differentc.m. energies isshownastheflatline.Variationswithinonestandarddeviation ofthestatisticaluncertaintyareshownwiththedashedlines.The measuredBorncrosssectionsofe+e

→ φφφ

arecompatiblewith a flatdistribution, with

χ

2

/

D O F

=

5

.

1

/

5, whilefor thee+e

φφ

ω

processthecompatibilityispoorwith

χ

2

/

D O F

=

15

.

4

/

5.

6. Systematicuncertaintiesofcrosssections

Several sources of systematic uncertainties are considered in the measurement of the Born cross sections. These include dif-ferences betweenthe data and the MC simulation for the

(7)

track-Fig. 4. Comparisonofthecosθdistributionsindata(points)andPHSPMCsimulation(triangles),for e+e→ φφω(topplots)ande+e→ φφφ(bottomplots)signals, combiningalldatasamples.ThecosθdistributionsareobtainedbyfittingtheR M(φφ)distributionforeventswithcosθingivenbins.

Fig. 5. Borncrosssectionsof(a)e+e→ φφωand(b)e+e→ φφφatsixenergypoints.(c)Ratiosσ(e+e→ φφω)/σ(e+e→ φφφ).Thelinesshowthestatistical-weighted averageswithanerrorbandcorrespondingtoonestandarddeviationofthestatisticaluncertainty.

ing efficiency, PID efficiency, mass window requirement, the MC

simulation ofthe radiative correction factorandthe vacuum po-larization factor. We also consider the uncertainties from the fit procedure,thepeakingbackgrounds,thesimulationmodelaswell asuncertainties ofthe branchingfraction of

φ

K+K− andthe integratedluminosity.

a. Trackingefficiency. Thedifferenceintrackingefficiencyforthe kaonreconstructionbetweenthedataandtheMCsimulation isestimatedtobe1.0%pertrack

[16]

.Therefore,4.0%istaken asthesystematicuncertaintyforfourkaons.

b. PIDefficiency. PID is required for the kaons, and the uncer-tainty is estimatedto be 1.0% per kaon [16]. Hence, 4.0% is takenas the systematic uncertaintyof the PID efficiency for fourkaons.

c.

φ

masswindow. Amass window requirementon the K+K

invariant mass might introduce a systematic uncertainty on the efficiency.The reconstructed

φ

signalsare fit witha MC shapeconvolutedwithaGaussianfunctionthat describesthe disagreementbetweendataandMCsimulation.Themeanand widthofthe Gaussian functionare left free inthe fit,which turnout tobe close to 0within 3times ofuncertainty. The systematicuncertaintyfromthe M

(

K+K

)

requirementis ig-nored.

d. Fitprocedure. Forthesixdatasamples,theyieldsofe+e

φφ

ω

and

φφφ

eventsareobtainedbyafittothedistribution

ofthemassrecoilingagainstthereconstructed

φφ

system.The followingtwoaspectsareconsideredwhenevaluatingthe sys-tematicuncertaintyassociatedwiththefitprocedure.(1) Sig-nalshape.—Inthe nominalfit,the signalshapesaredescribed bytheMCshapeobtainedfromMCsimulation.Analternative

fit with the MC shape convoluted with a Gaussian function

forthe

ω

signal shapeisperformed,wheretheparameters of theGaussian functionare free. The resulting difference in theyield withrespectto thenominalfitisconsideredasthe systematicuncertaintyfromthesignalshape.Thisuncertainty isnegligible comparedtothe statisticaluncertainty. (2)

Back-groundshape.—Inthenominalfit,thebackgroundshapeis de-scribedwithathird-orderChebyshevpolynomialfunction.The fitwithafourth-orderChebyshevpolynomialfunctionforthe background shape is performed to estimate the uncertainty duetothebackgroundparametrization.

e. Peakingbackgrounds. Theuncertaintyistakenas1.0%,as de-scribedinSec.4.

f. Lineshapeofcrosssection. Thelineshapeofthee+e

→ φφ

ω

and

φφφ

crosssections affectsthe radiativecorrection factor and the reconstruction efficiency. The corresponding uncer-taintyisestimatedbychangingtheinputoftheobservedline shapewithinonestandarddeviation.

g. vacuumpolarizationfactor. TheQEDcalculationusedto deter-mine thevacuumpolarization factor hasan accuracyof 0.5%

(8)

Table 3

Summaryofsystematicuncertainties(%)inthemeasurementofσ(e+e→ φφω).

Ecm(GeV) Tracking PID Background

shape Peaking backgrounds Line shape δv Simulation model Lint B Total 4.008 4.0 4.0 1.9 1.0 0.9 0.5 6.6 1.0 2.0 9.3 4.226 4.0 4.0 2.3 1.0 0.5 0.5 3.8 1.0 2.0 7.5 4.258 4.0 4.0 3.7 1.0 0.6 0.5 4.2 1.0 2.0 8.3 4.358 4.0 4.0 2.5 1.0 0.5 0.5 3.4 1.0 2.0 7.4 4.416 4.0 4.0 3.4 1.0 0.2 0.5 4.1 1.0 2.0 8.2 4.600 4.0 4.0 2.5 1.0 3.4 0.5 2.6 1.0 2.0 7.8 Table 4

Summaryofsystematicuncertainties(%)inthemeasurementofσ(e+e→ φφφ).

Ecm(GeV) Tracking PID Background

shape Peaking backgrounds Line shape δv Simulation model Lint B Total 4.008 4.0 4.0 3.7 1.0 0.1 0.5 7.0 1.0 2.0 10.0 4.226 4.0 4.0 1.9 1.0 0.8 0.5 8.8 1.0 2.0 10.9 4.258 4.0 4.0 2.0 1.0 1.5 0.5 9.1 1.0 2.0 11.2 4.358 4.0 4.0 2.9 1.0 0.8 0.5 9.8 1.0 2.0 11.9 4.416 4.0 4.0 2.4 1.0 2.6 0.5 9.6 1.0 2.0 11.9 4.600 4.0 4.0 1.5 1.0 2.7 0.5 10.2 1.0 2.0 12.3 Table 5

Summaryofthemeasuredrcsatdifferentc.m.energiesandthestatistical-weighted averageoverallsamples.Thefirstuncertaintyisstatistical,andthesecondis sys-tematic. Ecm(GeV) rcs Averaged rcs 4.008 5.22±2.20±0.55 1.75±0.22±0.19 4.226 2.52±0.51±0.25 4.258 1.35±0.39±0.15 4.358 1.90±0.79±0.21 4.416 1.59±0.46±0.18 4.600 1.63±0.56±0.19

h. Simulationmodel. Thedifferencesbetweentheefficiencies

ob-tained with and without re-weighting the PHSP MC sample

are takenastheuncertainties associated withthesimulation model.

i. Luminosity. Thetime-integratedluminosity

[18]

ofeach sam-pleismeasuredwithaprecisionof1%withBhabhaevents. j. Branchingfractions. The uncertaintyinthebranchingfraction

fortheprocess

φ

K+K−istakenfromthePDG

[14]

. Assumingallofthesystematicuncertaintiesshownin

Tables 3

and 4are independent,thetotal systematicuncertainties are ob-tainedbyaddingtheindividualuncertaintiesinquadrature. 7.Ratio

σ

(

e+e

→ φφ

ω

)/

σ

(

e+e

→ φφφ)

The right plot of Fig. 5 shows the measured ratios rcs

σ

(

e+e

→ φφ

ω

)

/

σ

(

e+e

→ φφφ)

at different c.m. energy, and the statistical-weighted average. Except for the measurement at 4.008 GeV, the ratios are consistent with each other within one statisticalstandard deviation. In the calculation of rcs, many

un-certaintieson thecrosssectionscancel,such asthe uncertainties inthetracking,PID,

B(φ →

K+K

)

andluminosity.Onlythe un-certainties from the background shape, line shape and MC sim-ulation model are considered in the determination of rcs. From

themeasurements atsixenergypoints in

Table 5

,we obtainthe statistical-weightedaveragercs

=

1

.

75

±

0

.

22

±

0

.

19,wherethefirst

uncertaintyisstatisticalandthesecondsystematic.Thesystematic uncertainties of rcs atdifferent c.m. energies are assumedto be

independentinthiscalculation.

8. Summaryanddiscussion

Withthedatasamplescollectedbetween4.008 and4.600 GeV withtheBESIIIdetector,theprocessese+e

→ φφ

ω

ande+e

φφφ

are observed forthe first time. The Born cross sectionsare determined atsixc.m. energiesandthe averageratio

σ

(

e+e

φφ

ω

)/

σ

(

e+e

→ φφφ)

overthesixc.m. energiesiscalculated to be 1

.

75

±

0

.

22

±

0

.

19, which is in the range of the estimation with

Fig. 1

.Ourmeasurementsofthesetwoprocessesprovide ex-perimentalconstraintsonthetheoreticalcalculationsofthethree vectorsproductioninthee+e−annihilation.

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 National Key Basic Research Program of

China under Contract No. 2015CB856700; National Natural

Sci-enceFoundation ofChina (NSFC) underContractsNos.11235011,

11335008, 11425524, 11625523, 11635010, 11175189; the

Chi-neseAcademyofSciences(CAS)Large-ScaleScientificFacility Pro-gram; the CAS Center for Excellencein Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS

under Contracts Nos. U1332201, U1532257, U1532258; CAS

un-der Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45,

QYZDJ-SSW-SLH003; 100Talents Programof CAS;National1000 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;IstitutoNazionale diFisica Nucleare,Italy; JointLarge-Scale Scientific Facility Funds of the NSFC and CAS; Koninklijke

Ned-erlandse Akademie van Wetenschappen (KNAW) under Contract

No. 530-4CDP03; Ministry ofDevelopment ofTurkey under

Con-tractNo. DPT2006K-120470; NationalNatural Science Foundation of China (NSFC) under Contract No. 11505010; National Science andTechnologyfund;TheSwedishResearchCouncil; U.S. Depart-mentofEnergyunderContractsNos.DE-FG02-05ER41374,

DE-SC-0010118, DE-SC-0010504, DE-SC-0012069; University of

Gronin-gen(RuG) andtheHelmholtzzentrum fuerSchwerionenforschung

GmbH(GSI),Darmstadt;WCUProgramofNationalResearch Foun-dationofKoreaunderContractNo.R32-2008-000-10155-0.

(9)

References

[1]J.Z.Bai,etal.,BESCollaboration,Phys.Rev.Lett.84(2000)594; J.Z.Bai,etal.,BESCollaboration,Phys.Rev.Lett.88(2002)101802; M.Ablikim,etal.,BESCollaboration,Phys.Lett.B677(2009)239.

[2]B.Aubert,etal.,BaBarCollaboration,Phys.Rev.D77(2008)119902; B.Aubert,etal.,BaBarCollaboration,Phys.Rev.D77(2008)092002.

[3]M.Ablikim,etal.,BESIIICollaboration,Phys.Lett.B753(2016)629; M.Ablikim,etal.,BESIIICollaboration,Phys.Rev.D91(2015)11.

[4]S.Jadach,B.F.L.Ward,Z.Was,Phys.Rev.D63(2001)113009.

[5] T.Sjostrand,L.Lonnblad,S.Mrenna,P.Skands,arXiv:hep-ph/0108264,LUTP 01-21,2002,http://home.thep.lu.se/~torbjorn/pythiaaux/past.html.

[6]K.Abe,etal.,BelleCollaboration,Phys.Rev.D70(2004)071102; B.Aubert,etal.,BABARCollaboration,Phys.Rev.D72(2005)031101.

[7]G.T.Bodwin,E.Braaten,G.P.Lepage,Phys.Rev.D51(1995)1125.

[8]Y.-J.Zhang,Y.-j.Gao,K.-T.Chao,Phys.Rev.Lett.96(2006)092001; B.Gong,J.-X.Wang,Phys.Rev.D77(2008)054028.

[9]E.Braaten, J. Lee, Phys. Rev.D67 (2003) 054007, Phys. Rev. D72 (2005) 099901(E);

K.-Y.Liu,Z.-G.He,K.-T.Chao,Phys.Lett.B557(2003)45; K.Hagiwara,E.Kou,C.-F.Qiao,Phys.Lett.B570(2003)39.

[10]M.Ablikim,etal.,BESIIICollaboration,Chin.Phys.C40(2016)063001.

[11]F.A.Harris,Nucl.Phys.B,Proc.Suppl.162(2006)345.

[12]M.Ablikim,etal.,BESIIICollaboration,Nucl.Instrum.MethodsPhys.Res.,Sect. A,Accel.Spectrom.Detect.Assoc.Equip.614(2010)345.

[13]S.Agostinelli,etal.,GEANT4Collaboration,Nucl.Instrum.MethodsPhys.Res., Sect.A,Accel.Spectrom.Detect.Assoc.Equip.506(2003)250.

[14]C.Patrignani,etal.,ParticleDataGroup,Chin.Phys.C40(2016)100001.

[15]E.A.Kuraev,V.S.Fadin,Sov.J.Nucl.Phys.41(1985)466,Yad.Fiz.41(1985) 733.

[16]M.Ablikim,etal.,BESIIICollaboration,Phys.Rev.Lett.112(2014)022001.

[17]S.Actis,etal.,Eur.Phys.J.C66(2010)585.

Figure

Fig. 1. Feynman graphs for (a) e + e − → γ ∗ gg → 3 ( s ¯ s ) . (b) e + e − → 3 γ ∗ → 3 ( s ¯ s ) .
Fig. 2. (a) Scatter plot of M φ 1 ( K + K − ) versus M φ 2 ( K + K − ) . The central box is the signal region while the boxes around are the two-dimensional sidebands
Fig. 3. Fits to the corrected R M (φφ) distribution for data samples at E cm = (a) 4.008, (b) 4.226, (c) 4.258, (d) 4.358, (e) 4.416 and (f) 4.600 GeV
Fig. 4. Comparison of the cos θ distributions in data (points) and PHSP MC simulation (triangles), for e + e − → φφ ω (top plots) and e + e − → φφφ (bottom plots) signals, combining all data samples

References

Related documents

In the present study, when the participant teachers direct the students’ at- tention to metalinguistic knowledge as well as metacognitive reading strategies, I regard it as a

For example, the online resource from which the teacher excerpted texts used early in the course (Clio, 2020) contains separate sections for contrasting sources representing

En genrepedagogisk undervisningsprocess om narrativ genre observerad i årskurs 1 fokuserar också logiska förbindelser och övergripande genrestruktur, men orienterar sig i högre

Även i arbetet med att lagra kunskap har vi dock kunnat visa inslag av kommunikativt handlande, genom hur läraren och eleverna i öppen dialog sökte en gemensam

Concepts developed during this project in order to facilitate some of these needs and contribute to motivating children to read more include a library service for helping

Restricted to cir- cularly symmetric Gaussian distributed processes, we have obtained (i) a formula for LSPs for the optimal spectral es- timation kernel in the ambiguity

The overall aim was to study periodontitis prevalence and severity in two Swedish adult populations, and to describe the changes over time. Further aims were to examine the effect

Där arbetssätten och lärarnas syfte med skönlitteraturen sviktar begränsas elevernas språkutveckling och de får inte möjligheter till alla dessa kontexter som de måste hamna i