Measurement of integrated luminosity and center-of-mass energy of data taken by BESIII at root s=2.125 GeV

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Measurement of integrated luminosity and

center-of-mass energy of data taken by BESIII at

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data taken by BESIII at

√

s

=2.125 GeV

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E. Boger23,c _{I. Boyko}23_{R. A. Briere}5 _{H. Cai(éÓ)}51 _{X. Cai(é)}1,a_{O. Cakir}40A _{A. Calcaterra}20A _{G. F. Cao(ùIL)}1

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Ma(êëû)33 _{M. M. Ma(ê²²)}1_{Q. M. Ma(ê¢r)}1 _{T. Ma(êU)}1 _{X. N. Ma(êRw)}30_{X. Y. Ma(êœò)}1,a_{Y. M. Ma(ê}

Œ²)33_{F. E. Maas}14_{M. Maggiora}49A,49C _{Q. A. Malik}48_{Y. J. Mao(kæ
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J. G. Messchendorp25 _{G. Mezzadri}21B _{J. Min(Dï)}1,a_{T. J. Min(DUú)}1 _{R. E. Mitchell}19 _{X. H. Mo(#¡m)}1,a_{Y. J. Mo(#}

Œd)6 _{C. Morales Morales}14 _{N. Yu. Muchnoi}9,e_{H. Muramatsu}43 _{P. Musiol}4 _{Y. Nefedov}23_{F. Nerling}14_{I. B. Nikolaev}9,e Received 1 June 2017

∗ Supported in part by National Key Basic Research Program of China (2015CB856700), National Natural Science Foundation of China (NSFC) (11235011, 11322544, 11335008, 11425524, 11635010, 11675184, 11735014), the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); the Collaborative Innovation Center for Particles and Interactions (CICPI); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1232201, U1332201, U1532257, U1532258), CAS (KJCX2-YW-N29, KJCX2-YW-N45), 100 Talents Program of CAS; National 1000 Talents Program of China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG (Collaborative Research Center CRC 1044, FOR 2359), Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) (530-4CDP03), Ministry of Development of Turkey (DPT2006K-120470), National Natural Science Foundation of China (NSFC) (11505010), The Swedish Resarch Council; U. S. Department of Energy (DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0010504, DE-SC-0012069), U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea (R32-2008-000-10155-0)

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3_{and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy} of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

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(BESIII Collaboration)

1 _{Institute of High Energy Physics, Beijing 100049, China} 2_{Beihang University, Beijing 100191, China}

3 _{Beijing Institute of Petrochemical Technology, Beijing 102617, China} 4 _{Bochum Ruhr-University, D-44780 Bochum, Germany} 5 _{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA}

6 _{Central China Normal University, Wuhan 430079, China}

7 _{China Center of Advanced Science and Technology, Beijing 100190, China}

8 _{COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan} 9_{G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia}

10 _{GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany} 11 _{Guangxi Normal University, Guilin 541004, China}

12 _{Guangxi University, Nanning 530004, China} 13 _{Hangzhou Normal University, Hangzhou 310036, China}

14_{Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany} 15_{Henan Normal University, Xinxiang 453007, China}

16_{Henan University of Science and Technology, Luoyang 471003, China} 17_{Huangshan College, Huangshan 245000, China}

18_{Hunan University, Changsha 410082, China} 19_{Indiana University, Bloomington, Indiana 47405, USA}

20 _{(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia,}

Italy

21 _{(A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy} 22_{Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany}

23_{Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia}

24_{Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany} 25_{KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands}

26_{Lanzhou University, Lanzhou 730000, China} 27_{Liaoning University, Shenyang 110036, China} 28_{Nanjing Normal University, Nanjing 210023, China}

29_{Nanjing University, Nanjing 210093, China} 30 _{Nankai University, Tianjin 300071, China}

31_{Peking University, Beijing 100871, China} 32_{Seoul National University, Seoul, 151-747 Korea}

33 _{Shandong University, Jinan 250100, China} 34_{Shanghai Jiao Tong University, Shanghai 200240, China}

35 _{Shanxi University, Taiyuan 030006, China} 36 _{Sichuan University, Chengdu 610064, China}

37 _{Soochow University, Suzhou 215006, China} 38_{Sun Yat-Sen University, Guangzhou 510275, China}

39 _{Tsinghua University, Beijing 100084, China}

40 _{(A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey;}

(C)Uludag University, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey

41 _{University of Chinese Academy of Sciences, Beijing 100049, China} 42_{University of Hawaii, Honolulu, Hawaii 96822, USA} 43_{University of Minnesota, Minneapolis, Minnesota 55455, USA}

44_{University of Rochester, Rochester, New York 14627, USA} 45_{University of Science and Technology Liaoning, Anshan 114051, China}

46_{University of Science and Technology of China, Hefei 230026, China} 47 _{University of South China, Hengyang 421001, China}

48_{University of the Punjab, Lahore-54590, Pakistan}

49_{(A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN,}

I-10125, Turin, Italy

50_{Uppsala University, Box 516, SE-75120 Uppsala, Sweden} 51_{Wuhan University, Wuhan 430072, China} 52_{Zhejiang University, Hangzhou 310027, China} 53 _{Zhengzhou University, Zhengzhou 450001, China}

a_{Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, China} b_{Also at Bogazici University, 34342 Istanbul, Turkey}

c_{Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia} d_{Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia}

e _{Also at the Novosibirsk State University, Novosibirsk, 630090, Russia} f _{Also at the NRC “Kurchatov Institute”, PNPI, 188300, Gatchina, Russia}

g _{Also at University of Texas at Dallas, Richardson, Texas 75083, USA} h _{Also at Istanbul Arel University, 34295 Istanbul, Turkey}

i_{Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany}

Abstract: To study the nature of the state Y (2175), a dedicated data set of e+_e− _{collision data was collected at}

the center-of-mass energy of 2.125 GeV with the BESIII detector at the BEPCII collider. By analyzing large-angle Bhabha scattering events, the integrated luminosity of this data set is determined to be 108.49±0.02±0.85 pb−1_,

where the first uncertainty is statistical and the second one is systematic. In addition, the center-of-mass energy of the data set is determined with radiative dimuon events to be 2126.55±0.03±0.85 MeV, where the first uncertainty is statistical and the second one is systematic.

Keywords: Bhabha scattering, luminosity, radiative dimuon events, center-of-mass energy PACS: 13.66.De, 13.66.Jn DOI:10.1088/1674-1137/41/11/113001

1

Introduction

The state Y (2175), denoted as φ(2170) in Ref. [1], was first observed by the BaBar experiment [2,

3] in the initial-state-radiation (ISR) process e+_e− _→

γISRφ(1020)f0(980), and was subsequently confirmed by BESII [4], Belle [5] and BESIII [6]. The observation of the Y (2175) stimulated many theoretical explanations of its nature, including a s¯s-gluon hybrid [7], an excited φ

To study the Y (2175), a dedicated data set was collected with the BESIII detector [11] at the BEPCII collider in

2015 at the center-of-mass energy (√s) of 2.125 GeV,

which is in the vicinity of the peaking cross sections for

e+_e−_{→ φππ and e}+_e−_{→ φf0(980) decays reported by}

BaBar [2, 3] and Belle [5].

In this paper, we present a determination of the in-tegrated luminosity of this data set using large-angle

Bhabha scattering events e+_e−_→(γ)e+_e−_{. A cross check}

is performed by analyzing di-photon events e+_e−_{→ γγ.}

In addition, using the approach described in Ref. [12], we determine the center-of-mass energy using radiative

dimuon events e+_e−_→(γ)µ+_µ−_{, where γ represents}

pos-sible ISR or FSR (final state radiation) photons.

2

The BESIII detector

BESIII [11] is a general purpose detector, which is

lo-cated at the BEPCII facility, a double-ring e+_e−_collider

with a peak luminosity of 1033 _cm−2_s−1 _{at a}

center-of-mass energy of 3.773 GeV. The BESIII detector covers 93% of the solid angle around the collision point and con-sists of four main components: 1) A small-cell, helium-based main drift chamber (MDC) with 43 layers pro-viding an average single-hit resolution of 135 µm, and charged-particle momentum resolution in a 1 T magnetic field of 0.5% at 1 GeV/c; 2) A Time-Of-Flight system (TOF) for particle identification composed of a barrel and two end-caps. The barrel has two layers, each con-sisting of 88 pieces of 5 cm thick, 2.4 m long plastic scintillator. Each end-cap consists of 96 fan-shaped, 5 cm thick, plastic scintillators. The barrel (end-cap) time resolution of 80 ps (110 ps) provides a 2σ K/π separa-tion for momenta up to about 1.0 GeV/c; 3) An electro-magnetic calorimeter (EMC) consisting of 6240 CsI(Tl) crystals in a cylindrical structure, arranged in one barrel and two end-caps. The energy resolution for 1.0 GeV photons is 2.5% (5%) in the barrel (end-caps), while the position resolution is 6 mm (9 mm) in the barrel (end-caps); 4) A muon counter (MUC) made of nine layers of resistive plate chambers in the barrel and eight layers in each end-cap, which are incorporated in the iron re-turn yoke of the superconducting magnet. The position resolution is about 2 cm. A GEANT4 [13, 14]-based de-tector simulation package has been developed to model the detector response.

3

Monte Carlo simulation

In order to determine the detection efficiency and estimate background contributions, one million Monte

Carlo (MC) events were simulated at√s=2.125 GeV for

each of the four processes: e+_e−_→(γ)e+_e−_{, e}+_e−_→γγ,

e+_e−_{→ (γ)µ}+_µ− _{and e}+_e−_{→ q¯q. The first three}

pro-cesses were generated with the Babayaga 3.5 [15]

gen-erator, while e+_e−_{→ q¯q → hadrons was generated with}

EvtGen [16, 17] according to the ‘LundAreaLaw’ [18, 19].

4

Measurement of the luminosity

4.1 Event selection

To select e+_e−_{→ (γ)e}+_e− _{events, exactly two good}

tracks with opposite charge were required. Each good charged track was required to pass the interaction point within ±10 cm in the beam direction (|Vz| < 10.0 cm) and within 1.0 cm in the plane perpendicular to the

beam (Vr < 1.0 cm). Their polar angles θ were

re-quired to satisfy |cosθ| < 0.8 to ensure the tracks were

in the barrel part of the detector. The energy

de-posited in the EMC of each track was required to be

greater than 0.65×Ebeam, where Ebeam= 2.125/2 GeV

is the beam energy. To select tracks that were

back-to-back in the MDC, |∆θ| ≡ |θ1+θ2−180◦| < 10◦ and

|∆φ| ≡ ||φ1−φ2|−180◦| < 5.0◦ were required, where θ1/2

and φ1/2 are the polar and azimuthal angles of the two

tracks, respectively. Comparisons between data and MC simulation are shown in Fig. 1.

After applying the above requirements, 33,228,098 events were selected as Bhabha scattering candidates. The background contribution is estimated to be at the

level of 10−5 _{using MC samples of e}+_e−_{→ γγ, e}+_e−_→

(γ)µ+_µ− _{and e}+_e−_{→ q¯q processes, and is ignored in}

the calculation of the integrated luminosity. The back-grounds from beam-gas interactions are also ignored due to the powerful rejection rate of the trigger system and the distinguishable features of Bhabha events.

4.2 Integrated luminosity

The integrated luminosity is calculated with

L= Nobs

σ×ε×εtrig

, (1)

where Nobsis the number of observed signal events, σ is

the cross section of the specified process, ε is the

detec-tion efficiency and εtrig is the trigger efficiency.

For the Bhabha scattering process, the cross section

at√s=2.125 GeV is calculated with the Babayaga

gen-erator to be 1621.43±3.47 nb. Using the large sample of MC simulated events, the detection efficiency is

deter-mined to be (18.89±0.04)%. The trigger efficiency εtrigis

100% with an accuracy of better than 0.1% [20]. The in-tegrated luminosity is determined to be 108.49±0.02±0.75

pb−1_{, where the first uncertainty is statistical and the}

second one is systematic, which will be discussed in Sec-tion 4.3.

4.3 Systematic uncertainty

Sources of systematic uncertainty include the require-ments on track angles (θ, ∆θ, ∆φ) and the deposited

+ e θ cos -1 -0.5 0 0.5 1 Events/0.02 10 2 10 3 10 4 10 5 10 6 10 7 10 (a) -e θ cos -1 -0.5 0 0.5 1 Events/0.02 10 2 10 3 10 4 10 5 10 6 10 7 10 _(b) (GeV) + e E 0 0.5 1 Events/(0.01 GeV) 2 10 3 10 4 10 5 10 6 10 (c) (GeV) -e E 0 0.5 1 Events/(0.01 GeV) 2 10 3 10 4 10 5 10 6 10 (d) | (degree) θ ∆ | 0 10 20 30 40 Events/(0.04 degree) ₁₀3 4 10 5 10 6 10 7 10 (e) (degree) φ ∆ -20 -10 0 10 20 Events/(0.04 degree) 3 10 4 10 5 10 6 10 7 10 _(f)

Fig. 1. Distributions of cosθ of (a) e+ _{and (b) e}−_{, deposited energy in the EMC of (c) e}+

and (d) e−_{, (e) |∆θ| and (f) ∆φ (measured in the laboratory frame of reference). The}

dots with error bars are for data, while the solid line indicates signal MC simulation.

energy in the EMC, the tracking efficiency, beam energy, MC statistics, trigger efficiency, and the MC generator.

To estimate the systematic uncertainties associated with the related angular requirements, the same selec-tion criteria with alternative quantities were performed, individually, and the resultant (largest) difference with respect to the nominal result taken as the systematic uncertainty: |cosθ| < 0.8 was changed to |cosθ| < 0.75, resulting in a relative difference to the nominal result

of 0.06%; |∆θ| < 10.0◦ _{was changed to 8.0}◦ _{or 15.0}◦_,

and the systematic uncertainty estimated to be 0.02%;

|∆φ|<5.0◦_{was changed to 4.0}◦_{or 10.0}◦_{, and the}

associ-ated systematic uncertainty is 0.04%.

The uncertainty associated with the requirement on the deposited energy in the EMC is determined by comparing the detection efficiency between data and MC simulation. The data and MC samples were se-lected using the selection criteria listed in Section 4.1 except for the deposited energy requirement on the

elec-tron/positron. The efficiency is determined by the ratio between the numbers of events with and without the de-posited energy requirement. The difference in the detec-tion efficiency between data and signal MC simuladetec-tion is 0.19% and 0.13% for electrons and positrons, respec-tively. The sum, 0.32%, is taken as the systematic un-certainty.

For the uncertainty associated with the tracking effi-ciency, it has been well studied in Ref. [21] by selecting a control sample of Bhabha events with the EMC infor-mation only. It was found that the difference between data and MC simulation is 0.41%, which is taken as the systematic uncertainty.

To estimate the systematic uncertainty associated with the beam energy, the luminosity is recalculated with the updated cross section and detection efficiency at the alternative center-of-mass energy of the measured value in Section 5. The difference from the nominal luminosity, 0.18%, is taken as the systematic uncertainty.

The uncertainty from MC statistics is 0.21% and from trigger efficiency is 0.1% [20]. The uncertainty due to the Babayaga generator is given as 0.5% [15].

All individual systematic uncertainties are summa-rized in Table 1. Assuming the individual uncertainties to be independent, the total systematic uncertainty is calculated by adding them quadratically and found to be 0.78%.

Table 1. Summary of the systematic uncertainties.

source relative uncertainty(%)

|cosθ|<0.8 0.06

|∆θ|<10.0◦ _0.02

|∆φ|<5.0◦ _0.04

deposited energy requirement 0.32 tracking efficiency 0.41 beam energy 0.18 MC statistics 0.21 trigger efficiency 0.10 generator 0.50 total 0.78 4.4 Cross check

As a cross check, an alternative luminosity

measure-ment using e+_e−_{→ γγ events was performed. To select}

e+_e−_{→γγ events, candidate events must have two}

ener-getic clusters in the EMC. For each cluster, the polar an-gle was required to satisfy |cosθ|<0.8 and the deposited

energy E must be in region 0.7×Ebeam<E <1.15×Ebeam.

To select clusters that are back-to-back, |∆φ|<2.5◦

(de-fined in Section 4.1) was required. In addition, there

should be no good charged tracks satisfying |Vz| < 10.0

cm and Vr<1.0 cm. With the selected e+_e−_{→γγ events,}

the integrated luminosity is determined to be 107.91±0.05

pb−1 _{(statistical only), which is in good agreement with}

the result obtained using large-angle Bhabha scattering events.

5

Measurement of the center-of-mass

en-ergy

5.1 Event selection

To select e+_e−_→(γ)µ+_µ− _{candidates, we require}

ex-actly two good tracks with opposite charge satisfying

|Vz| < 10.0 cm, Vr< 1.0 cm and |cosθ| < 0.8. To remove

Bhabha events, the ratio of the deposited energy in the EMC and the momentum of a charged track, E/pc, was required to be less than 0.4. The two tracks should be back-to-back, with the ∆θ and ∆φ (defined in Section

4.1_{) satisfying |∆θ| < 10.0}◦ _{and |∆φ| < 5.0}◦_{. To further}

suppress background from cosmic rays, |∆T |=|t1−t2|<

1.5 ns was required, where t1/2is the time of flight of the

two charged tracks recorded by the TOF. Figure 2 shows

the comparisons between data and MC simulation, where the solid line is signal MC and the shaded histogram

rep-resents the simulation of background e+_e−_→q¯q.

With the above requirements, 1,472,195 events were selected in data with an estimated background level of about 1.8%. The small bumps visible in Figs. 2 (g) and

(h) at about 0.93 GeV/c mainly come from the e+_e−_→

K+_K− _{process. The peak at about 1.07 GeV/c mainly}

consists of events from the processes e+_e−_{→ π}+_π− _and

e+_e−_→π+_π−_γ.

5.2 Center-of-mass energy

Using the e+_e−_→(γ)µ+_µ−_{events, the center-of-mass}

energy of the data set is determined with the method described in Ref. [12].

The center-of-mass energy can be determined with

MCM=Mdata(µ+_µ−_{)−∆M, (2)}

where Mdata(µ+_µ−_{) is the reconstructed µ}+_µ− _invariant

mass of the selected e+_e−_{→ (γ)µ}+_µ− _{events, and ∆M}

is the correction for effects of ISR and FSR, which can

be estimated using the µ+_µ−_{invariant mass of MC}

sam-ples with ISR/FSR turned on (MMC, on(µ+_µ−_{)) and off}

(MMC, off(µ+_µ−_)):

∆M =MMC, on(µ+_µ−

)−MMC, off(µ+_µ−_{). (3)}

By fitting the MMC, on(µ+_µ−_{) and MMC, off(µ}+_µ−₎

distributions of MC samples, the average of ∆M is

de-termined to be −1.13 MeV/c2_{, where MMC, on=2124.60±}

0.04 MeV/c2_{, MMC, off= 2125.73±0.01 MeV/c}2_{, and the}

errors are statistical only. The function fitted to MMC, on is a Gaussian plus a Crystal Ball function [22] with a

common mean, and the function fitted to MMC, off is a

double Gaussian function with a common mean. The fit results are shown in Fig. 3. To calculate ∆M (and

MCM) as a function of run number, MMC, offand MMC, on

for each run are fitted with the above same functions.

For each run, Mdata(µ+_µ−_{) was fitted in the range}

[2.0, 2.2] GeV/c2_{. The signal is described by a Gaussian}

plus a Crystal Ball function with a common mean, while the background is ignored (about 1.1% in the fit range). As an example, the fit result for run 42030 is shown in Fig. 4.

MCM was calculated with Eq. (2) and Eq. (3) for

each run. The average of MCMfor the full data set is

de-termined to be 2126.55±0.03 MeV/c2_{by fitting the MCM}

of different runs with a constant. The MCM distribution

as a function of run number and the overall fit result are shown in Fig. 5, where 21 runs are excluded in the fit due to large statistical errors (less than 100 entries

in the fit range). The MCM values for individual runs

are shown in Fig. 6 as a histogram, which can be fitted very well with a Gaussian function with the parameters

µ_{=2126.55±0.03 MeV/c}2

+ µ θ cos -1 -0.5 0 0.5 1 Events/0.02 0 5000 10000 15000 20000 25000 (a) -µ θ cos -1 -0.5 0 0.5 1 Events/0.02 0 5000 10000 15000 20000 25000 _(b) | (degree) θ ∆ | 0 10 20 30 40 Events/(0.04 degree) 3 10 4 10 5 10 (c) (degree) φ ∆ -20 -10 0 10 20 Events/(0.04 degree) 102 3 10 4 10 5 10 (d) (c) + µ E/p 0 0.1 0.2 0.3 0.4 0.5 Events/(0.005 c) 10 2 10 3 10 4 10 5 10 (e) (c) -µ E/p 0 0.1 0.2 0.3 0.4 0.5 Events/(0.005 c) 10 2 10 3 10 4 10 5 10 (f) (GeV/c) + µ p 0.4 0.6 0.8 1 1.2 Events/(0.01 GeV/c) ₁ 10 2 10 3 10 4 10 5 10 (g) (GeV/c) -µ p 0.4 0.6 0.8 1 1.2 Events/(0.01 GeV/c) 10₁ 2 10 3 10 4 10 5 10 (h) T (ns) ∆ -4 -2 0 2 4 Events/(0.01 ns) 1 10 2 10 3 10 4 10 5 10 (i)

Fig. 2. Distributions of cosθ of (a) µ+ _{and (b) µ}−_{, (c) |∆θ|, and (d) ∆φ (measured in the laboratory frame of}

reference), E/p distributions of (e) µ+ _{and (f) µ}−_{, momentum distributions of (g) µ}+ _{and (h) µ}−_{, and (i) ∆T}

distribution. The dots with error bars represent the data, the solid line indicates signal MC simulation, and the shaded histogram represents the MC simulation of e+_e−_→q¯q.

) 2 ) (GeV/c -µ + µ M( 2 2.05 2.1 2.15 2.2 ) 2 Events/(1 MeV/c 0 5000 10000 15000 20000 _(a) ) 2 ) (GeV/c -µ + µ M( 2.05 2.1 2.15 2.2 ) 2 Events/(1 MeV/c 0 5000 10000 15000 20000 (b)

Fig. 3. Fit to M (µ+_µ−_{) of MC sample (a) with}

and (b) without ISR/FSR.

5.3 Systematic uncertainty

As shown in Section 5.2, MMC, off = 2125.73±0.01

MeV/c2_{is 0.73 MeV/c}2_{higher than the input value (2125}

MeV/c2_{). This difference is taken as the systematic}

un-certainty.

The uncertainty of the momentum measurement

of two muon tracks has been studied using e+_e− _→

γISR_{J/ψ,J/ψ → µ}+_µ− _{in Ref. [12], and is estimated to}

be 0.011%.

)

) (GeV/c

-µ

µ

M(

)

Events/(1 MeV/c

µ−_{) for run 42030. Dots}

with error bars are data, while the solid line is the fit result.

To estimate the uncertainty from the fit to the

in-variant mass of µ+_µ−_{, the signal shape and fit range}

were varied and MCM re-calculated. The difference to

the nominal result is taken as the systematic uncertainty. The systematic uncertainty from signal shape is

esti-mated to be 0.08 MeV/c2 _{by replacing the Crystal Ball}

function in the signal shape with the GaussExp function [23]. The systematic uncertainty from fit range is

es-timated to be 0.13 MeV/c2 _{by varying the fit range to}

[2.00, 2.14] GeV/c2_{and [2.10, 2.20] GeV/c}2_{, respectively.}

Run 42000 42500 43000 ) 2 (GeV/c CM M 2.12 2.122 2.124 2.126 2.128 2.13 2.132 2.134

Fig. 5. Distribution of MCM for individual runs.

The solid line is the average fit.

)

(GeV/c

M

)

Entries/(0.1 MeV/c

Fig. 6. Histogram of MCMfor individual runs.

The solid line is a Gaussian function.

To estimate the uncertainty from the fit to the MCM distribution, fits in different ranges of the run number were carried out. The resultant maximum difference with

respect to the nominal value, 0.34 MeV/c2_{, is taken as}

the uncertainty.

Assuming all of the above uncertainties are indepen-dent, the total systematic uncertainty is calculated to be

0.85 MeV/c2 _{by adding the individual items in}

quadra-ture.

6

Summary

The integrated luminosity of the data taken at 2.125 GeV in 2015 with the BESIII detector is measured to

be 108.49 ± 0.02 ± 0.85 pb−1 _{using large-angle Bhabha}

events. A cross check with e+_e−_{→ γγ events was}

only), which is in good agreement with the nominal

re-sult within the uncertainties. With e+_e− _{→ (γ)µ}+_µ−

events, the center-of-mass energy of the data set is mea-sured to be 2126.55 ± 0.03 ± 0.85 MeV. The results in this measurement are important input for physics

stud-ies, e.g., studies of decays of the Y (2175).

The BESIII collaboration would like to thank the staff of BEPCII and the IHEP computing center for their ded-icated support.

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