Measurement of integrated luminosities at BESIII for data samples at center-of-mass energies between 4.0 and 4.6 GeV

The integrated luminosities of the data samples collected in the BESIII experiment in 2016--2017 at center-of-mass energies between 4.19 and 4.28 GeV are measured with a precision better than 1% by analyzing large-angle Bhabha scattering events. The integrated luminosities of the old data sets collected in 2010--2014 are updated by considering correction related to the detector performance, offsettting the effect of newly discovered readout errors in the electromagnetic calorimeter that happen haphazardly.


I. INTRODUCTION
In recent years, the newly discovered charmonium-like states have drawn great attention due to their exotic properties [4]. These states are above the open-charm threshold, and their strong coupling to hidden-charm processes suggests that they could be candidates for unconventional charmonium states. Study of the properties of these states, through either verifying or excluding possible interpretations about their exotic nature (such as molecular states, tetraquark states, hybrid states, etc.), or establishing the connection between these states and higher excited charmonium states, has the potential to provide more insight into the quark model and a better understanding of quantum chromodynamics (QCD).
The BESIII experiment [1], which operates at the τ -charm factory BEPCII [2], has collected the world's largest e + e − collision data samples at center-of-mass (CM) energies between 3.81 and 4.60 GeV [3]. In this energy region, the charmonium-like states (also called XYZ states), together with higher excited charmonium states, can be produced copiously, and comprehensive studies of these particles can be performed. Also, the data can be used in other studies beyond the field of charmonium physics, such as R measurement or on various topics in charm physics.
To shed light on the topics mentioned above, it is essential to measure the production cross sections of these states, which in return require the precise knowledge of the time-integrated luminosities of the relevant data samples.
In this paper, we present the results of the luminosity measurements for the XYZ data samples taken by BESIII from December 2016 to May 2017, as well as an update on the previous measurement for the XYZ data samples taken from December 2011 to May 2014 [5]. The update is necessary since a malfunction of the detector that was not modelled in Monte Carlo (MC) simulation, which resulted in an underestimation of the previously measured integrated luminosities, has been recently discovered. The measurement is based on analysis of the Bhabha scattering process e + e − → (γ)e + e − , and the procedure we take is similar to the one in a previous BESIII analysis [5]. The process is chosen for its clean signature and large production cross section, which is known with high theoretical precision. These features allow a precise measurement with small statistical and systematic uncertainties.

II. THE BESIII DETECTOR AND DATA SAMPLES
BESIII is a general purpose detector which operates at the e + e − collider BEPCII [2]. Due to the crossing angle of the beams at the interaction point, the e + e − CM system is slightly boosted with respect to the laboratory frame. A detailed description of the facility is given in Ref. [1]. The cylindrical core of the BESIII detector covers 93% of the full solid angle and consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identification modules interleaved with steel. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end-cap) region. The time resolution in the TOF barrel region is 68 ps, whereas that in the end-cap region is 110 ps. The end-cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [6]. A GEANT4 [7] based detector simulation package has been developed to model the detector response.
From December 2016 to May 2017, eight data sets were taken at CM energies between 4.19 and 4.28 GeV. These data sets were collected in the vicinity of the Y (4230) and Y (4320) resonances, aimed at studying the line shapes of the production cross sections and the decay properties of these charmonium-like states. The CM energy (E CM ) of each data sample has been determined with the process e + e − → µ + µ − [8], and is listed in Table I. For each data set, two million Bhabha events were generated with the BABAYAGA@NLO [9] generator, using the parameters presented in Table II. In the simulation, the scattering polar angle of the final state electrons has been limited to a range from 20 • (θ min ) to 160 • (θ max ), fully covering the detector acceptance. The beam energy is set to the value determined with e + e − → µ + µ − events in the same data set [8], and the energy spread is set to be 1.364 MeV. An energy threshold of 1.0 GeV (E min ) is applied to the final-state electrons and positrons. The acollinearity of the events (i.e. the angle between the electron and the reverse extension line of the positron) and the number of photons from initial/final state radiation are not constrained. Additionally, a selection on the invariant mass of the e + e − pair (M(e + e − )) larger than 3.8 GeV/c 2 has been applied, to reduce the computing time for simulation by avoiding the need to sample over narrow states such as the ψ(2S) and J/ψ resonances.

Parameter
Value

III. EVENT SELECTION
Signal Bhabha candidate events are required to have two oppositely charged good tracks. The good tracks must originate from a cylindrical volume, centered around the interaction point, with a radius of 1 cm perpendicular to the beam axis and a length of ±10 cm along the beam axis. The polar angle of the tracks θ MDC , measured by the MDC and boosted to the e + e − CM frame, is required to be in the fiducial volume of | cos θ MDC | < 0.8. The deposited energy of each track in EMC must be larger than 0.37 × E CM , and the momentum of each track has to be larger than 0.47 × E CM , to reduce background from di-muon pairs or from the decays of light resonances, respectively. The invariant mass of the track pair is required to be larger than 3.85 GeV/c 2 , because only the events with an invariant mass above 3.8 GeV/c 2 are produced in the MC event generator. As demonstrated by a similar previous analysis [5], the remaining background contribution after applying these selection criteria is negligible. Figure 1 shows the comparison between data and MC simulation for the kinematic variables previously discussed. There is a reasonable agreement in the distributions of all the variables.

IV. EMC READOUT CORRECTION AND LUMINOSITY RESULTS
The energy deposition in the EMC is used to identify the final state electron/positron tracks. In a study of high energy EMC showers we found that the EMC electronics occasionally failed to provide valid signals for crystals with high deposited energy. The problem mainly occurs for the channels in the absolute polar angle (cos θ) ranges of (0.6, 0.8) close to the horizontal plane. To illustrate this issue, consider the left plot of Fig. 2, which shows the EMC energy deposition of a typical high energy (around 2 GeV) electron or positron shower, where no problem occurs. The shower extends across 5 × 5 crystals and the deposited energy in crystal numbered (24, 2) is 1592 MeV, one order of magnitude larger than those of the nearby crystals. In contrast, the right plot of Fig. 2 shows an example of a shower missing the readout of the EMC energy deposition from one crystal. Here, the largest energy deposition is expected to be found in the crystal numbered (59, 3) but no valid value is recorded, which leads to an underestimation of the total deposited energy by more than 1 GeV. This effect is not simulated in the MC samples, and must be corrected.
While the reason of this problem is still under investigation, the amount of affected events can be estimated by searching for the MDC tracks with unexpected EMC information. the dielectron deposited energies for events satisfying all the other requirements of our selection criteria, for the MC sample and the experimental data. As one can see in the plots, two abnormal peaks can be found in the data samples, which are not present in the MC sample. These peaks are formed by events where the reconstructed energy deposition by the charged track in the EMC is missing the readout signal from one crystal. To select these events, we apply all the requirements apart from that on the deposited energy in EMC; afterwards, we require that the deposited energy in EMC must be larger than 0.37×E CM for one track and lower than 0.15×E CM for the other. The events in which both tracks are affected by EMC readout errors are rare, and their contribution is considered as negligible. Finally, we require that the ionization energy loss of both tracks in MDC must be close to the expected energy loss of electron tracks of the same energy.
Since no normal physics events should be able to pass the above selection, we assume that all the candidates passing the requirements are Bhabha events that suffered from the EMC readout errors. These events are simply added to the sample of observed Bhabha events whose selection is summarized in Section III.
The integrated luminosity is calculated with the equation where N obs is the number of observed Bhabha events, N cor is the number of events recovered by the correction of the EMC readout error, σ Bhabha is the cross section of the Bhabha process, and ε is the efficiency determined with the signal MC sample. The cross sections are calculated by BABAYAGA@NLO generator using the parameters listed in Table II. All the input numbers and the luminosity results are listed in Table I.

V. SYSTEMATIC UNCERTAINTIES
The following sources of systematic uncertainties are considered: the tracking efficiency, the requirements on the kinematic variables, the limited sizes of the MC samples, the beam energy measurement, the EMC readout correction, and the MC generator.
To estimate the systematic uncertainty of the tracking efficiency, we employed an alternative selection criterion using information from the EMC only. Here, at least two clusters in the EMC The systematic uncertainties related to the requirements on the kinematic variables are evaluated by varying the thresholds on the variables. For the requirement on the EMC energy, the alternative threshold is 0.41 × E CM ; for the polar angle, the alternative range is [−0.75, 0.75]; for the requirement on momentum, the threshold is changed to 0.48 × E CM . For the invariant mass of the e + e − pair, the alternative threshold is 3.80 GeV/c 2 , and the corresponding uncertainty is found to be negligible.
The statistical uncertainties of the MC samples size, each one having two million events with a selection efficiency of around 17%, are estimated to be 0.2% at each energy point.
The uncertainty on the CM energy measurement is ±0.6 MeV [8]; its effect on the luminosity determination is estimated by repeating the analysis on the same data sets, while changing the CM energy value by plus and minus this value. To avoid an additional systematical uncertainty due to the MC data sample size, we obtain the detection efficiency and cross section values through the linear extrapolation from the nearby energy points. The uncertainty is estimated as the difference in integrated luminosity compared to our standard result. The small difference between the measured beam-energy spread [10] and that used in the generation of the MC samples leads to a negligible bias in the analysis.
The systematic uncertainty from the EMC readout correction is estimated by comparing the results with an alternative correcting method, where the events with one or two tracks not satisfying the energy requirements are selected, and the correction is estimated by fitting the two-dimensional dE/dx distribution of the two tracks in these events with a model containing three components: Bhabha events, di-muon events, and a background of uniform distribution. The uncertainty is estimated as the difference in result between the two correction methods.
The uncertainty on the predictions of the BABAYAGA@NLO generator is assigned to be 0.1%, following Ref. [9].
The total uncertainty for each energy point is summarized in Table III. The uncertainties from different sources are assumed to be independent, therefore the total uncertainties are obtained by adding up the uncertainties in quadrature.  An update of the integrated luminosities for the 21 data samples collected in 2010-2014, previously reported in Ref. [5], is needed in order to apply the EMC readout correction, as described in the previous section, and to include additional events coming from the recovery of data files that were not originally available.
The same procedure described for the 2016-2017 data samples has been applied for this update, with the same configurations of the MC generator, the same event selection criteria, and the same EMC readout correction. The BABAYAGA@NLO event generator we use in this analysis has a significantly better precision than the event generator used in the previous analysis [5] (0.1% versus 0.5%), which contributes to the reduction of the total uncertainties. Table IV summarizes the updated integrated luminosities with statistical uncertainties, the correction factors due to the EMC readout error, and the comparison with the results of the previous analysis. The results of the three lowest energy points (samples 3810, 3900, and 4009) are not updated, since there is no file update and, according to the correlation between the amount of the EMC readout correction and the CM energies in other data sets, the EMC readout correction is expected to be negligible at these energy points. We skip the unnecessary update of these data samples to avoid dealing with the computational difficulty of the MC sampling over narrow resonances. For the remainder of the energy points, the updated results are 0.3% − 4.8% larger than the original values. The discrepancies are mainly caused by the EMC readout correction, and for a few data sets such as 4420 1 and 4600 there're also the contributions from recovery of data files. Figure 4 shows the correlation between the sizes of the EMC readout correction and the CM energies. This figure shows that the size of this correction grows exponentially as the CM energy increases, indicating that the problem may grow to be much more severe if BESIII is to operate in higher energy zones. Besides, the fact that the frequencies of EMC readout error fit well to an exponential model may hint at its mechanism. TABLE IV. The updated integrated luminosities of the 2010-2014 XYZ data sets, the correction factor due to the EMC readout error (σ EMC = N cor /N obs ), and comparison with the previous results [5]. The first uncertainties are statistical and the second ones are systematic. 3.51 ± 0.15 586.9 ± 0.1 ± 3.9 566.9 ± 0.1 ± 5.5 +3.52 Systematic uncertainties are assigned following the same procedure as for the 2016-2017 data sets. For each source of uncertainty, we take the maximum uncertainty for all the energy points. These uncertainties from individual sources are then added up in quadrature to obtain the total systematic uncertainty. The result is summarized in Table V. The total systematic uncertainty is determined to be 0.66% for all the energy points except for the lowest three energy points, for which we quote the original uncertainty 0.97% [5]. The logarithm of relative sizes of the EMC readout correction at different CM energies for 2010-2014 (blue) and 2016-2017 (red) XYZ data sets. In this plot, the data points have a seemingly linear relationship, suggesting that the frequencies of the EMC readout errors may grow exponentially as the CM energy further increases. We have measured the integrated luminosities of the XYZ data sets taken at BESIII from 2016 to 2017, and the results are listed in Table I. Additionally, we have updated the luminosity measurement of the XYZ data taken from 2010 to 2014, with corrections arising from an improved understanding of the EMC performance and the recovery of data files, as shown in Table IV. These high precision results are of fundamental importance for the measurements of the production cross sections of the XYZ particles as well as those of conventional charmonium states in this energy range, which will enable a more precise comparison with the predictions of the quark model and an improved understanding of QCD. The results presented in this work have been used in several recent analyses of the BESIII collaboration (e.g. see Refs. [11][12][13]) and will be used by many other analyses in the future. Figure 4 shows that the impact of the EMC readout errors may grow exponentially to above 10% as the CM energy increases to around 5.0 GeV. This means that the dangerous effect warrants more inspection if BESIII is to operate in higher energy zones with BEPCII update project in the future.