Observation of $e^{+}e^{-}\rightarrow\eta\psi(2S)$ at center-of-mass energies from 4.236 to 4.600 GeV

Using a total of $5.25~{\rm fb}^{-1}$ of $e^{+}e^{-}$ collision data with center-of-mass energies from 4.236 to 4.600 GeV, we report the first observation of the process $e^{+}e^{-}\to \eta\psi(2S)$ with a statistical significance of $5\sigma$. The data sets were collected by the BESIII detector operating at the BEPCII storage ring. We measure the yield of events integrated over center-of-mass energies and also present the energy dependence of the measured cross section.

Searching for new decay modes of Y states produced in e + e − annihilation and measuring the line shapes of the production cross sections will shed light on the nature of the Y states.Besides the ππ hadronic transitions, other hadronic transitions (via η, η ′ ) of these Y states to lower mass charmonia such as the J/ψ or ψ(2S) also provide further insight into their internal structure.The CLEO-c [24], Belle [25], and BESIII [26][27][28] experiments measured the cross section of e + e − → ηJ/ψ, and BESIII observed the decays of the Y (4220) and Y (4390) into ηJ/ψ final states.The authors of ref. [29] reproduced the measured e + e − → ηJ/ψ line shape and predicted the production cross section of the analogous process e + e − → η ′ J/ψ at O(α 4 s ) accuracy in the framework of nonrelativistic Quantum Chromodynamics (NRQCD).However, the measured cross sections of e + e − → η ′ J/ψ [30,31] by BESIII are significantly smaller than the theoretical prediction [29].
To provide more information to study the vector charmonium(like) states, the cross section of e + e − → ηψ(2S) can also be compared with those of the processes e + e − → ηJ/ψ and e + e − → η ′ J/ψ.The CLEO-c experiment searched for the process e + e − → ηψ(2S) with data at center-of-mass (c.m.) energy √ s = 4.260 GeV, and reported an upper limit on the Born cross section, σ[e + e − → ηψ(2S)] < 25 pb, at a 90% confidence level (C.L.) [24].This is the only available experimental study of this process.

BESIII detector and Monte Carlo simulation
The cylindrical core of the BESIII detector 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 chamber muon identifier modules interleaved with steel.The acceptance of charged particles and photons is 93% over 4π solid angle.The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for the electrons from Bhabha scattering events.The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region.The time resolution of the TOF barrel part is 68 ps, while that of the end cap part is 110 ps.The end cap TOF system was upgraded in 2015 with multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [37,38].
To optimize the signal event selection criteria, estimate the background contributions and determine the detection efficiency, simulated samples are produced with the geant4based [39] Monte Carlo (MC) package which includes the geometric description of the BESIII detector and the detector response.The signal MC events of e + e − → ηψ(2S) with the corresponding η and ψ(2S) decay modes are generated using HELAMP and evtgen [40,41] at each c.m. energy.The beam energy spread and ISR in the e + e − annihilations are modelled with the generator kkmc [42,43] and the final state radiations (FSR) from charged final-state particles are incorporated with the photos package [44].
The possible background contributions are also studied with kkmc [42,43] at each c.m. energy.The decay modes are modelled with evtgen using branching fractions taken from the PDG [16].

Event selection
Candidate events with four charged tracks with zero net charge and at least two photons are selected.The charged tracks are required to be well reconstructed in the MDC with a polar angle θ satisfying | cos θ| < 0.93, and the distances of the closest approach to the interaction point in x− y plane and z direction have to be less than 1 cm and 10 cm, respectively.Since the π ± and ℓ ± are kinematically well separated, charged particles with momenta less than 0.8 GeV/c in the laboratory frame are assumed to be π ± , whereas the ones with momenta larger than 1.0 GeV/c are assumed to be ℓ ± .To separate electron from muon candidates, the EMC deposited energy is used.The energy deposits of electron candidates and muon candidates are required to be larger than 1.0 GeV and less than 0.4 GeV, respectively.Photon candidates are reconstructed from showers in EMC crystals.The reconstructed energies for the clusters in the barrel (| cos θ| < 0.80) and the end caps (0.86 < | cos θ| < 0.92) of the EMC are required to be higher than 25 and 50 MeV, respectively.To eliminate showers associated with charged particles, the angle between the photon and any charged track in the EMC must be at least 10 degrees.To suppress the electronic noise and energy deposits unrelated to the event, the time of the EMC shower is required to be 0 t 700 ns with respect to the start of the event.To improve the mass resolution and suppress background contributions, a four-constraint (4C) kinematic fit is performed under the hypothesis of e + e − → γγπ + π − ℓ + ℓ − to constrain the sum of four momenta of the final state particles to the initial colliding beams.The chi-square of the kinematic fit, χ 2 4C , is required to be less than 40.If there are more than two photons in an event, the combination of γγπ + π − ℓ + ℓ − with the least χ 2 4C is retained for further study.To identify signal candidates that involve the J/ψ resonance, we select events with a ℓ + ℓ − invariant mass within a window of ±3σ around the J/ψ nominal mass, 3064.6 < M (ℓ + ℓ − ) < 3140.8MeV/c 2 , referred to as the J/ψ mass window.To remove the background from process e + e − → η ′ J/ψ with η ′ → π + π − η, the invariant mass of π + π − γγ is required to be larger than 1 GeV/c 2 .Two-dimensional (2D) distributions for γγ and π + π − J/ψ invariant masses, M (γγ) versus M (π + π − J/ψ), and the corresponding one-dimensional (1D) projections for data, signal MC samples, background contributions at √ s = 4.258 GeV are presented in figures 1(a-e).The distributions for the sum of 14 energy points are shown in figures 1(f-j).Signal candidates are required to be within the η mass region [±3σ around the η nominal mass], defined as 507.1 < M (γγ) < 579.1 MeV/c 2 , and ψ(2S) mass region [±3σ around the ψ(2S) nominal mass], defined as 3680.3< M (π + π − J/ψ) < 3692.5 MeV/c 2 (as indicated by red dashed boxes or the ranges between two arrows in figure 1).Significant clusters can be seen in the mass windows of the η and ψ(2S).The same distributions for the sum of the 14 data samples and MC samples are shown in (f), (g), (h), (i), and (j) correspondingly.

Background analysis
To study background processes, we generated a series of MC samples for final states that include a π + π − pair, two leptons with high momenta, and at least two photons in the final state using the kkmc generator at each energy point.These background processes are listed in table 1.The dominant background contribution is e + e − → γγψ(2S), and it is measured directly in this analysis.The yields for each of the other background processes in the 2D signal region (N bkg,i ) are calculated using external input by: where i represents each background channel, L int is the integrated luminosity, |1 − Π| −2 is the vacuum polarization factor [45], ǫ i and B i are the selection efficiency and the product branching fraction of the intermediate states taken from the PDG [16] for the ith background mode, respectively, and σ B bkg,i is the measured Born cross section of the ith background mode.The production cross sections for these background processes are taken from refs.[22,[46][47][48][49][50][51].(1+ δ) i is the ISR correction factor obtained from a quantum electrodynamics calculation [42,43,52] using the kkmc generator, assuming an input lineshape from refs.[22,[46][47][48][49][50][51].
The number of e + e − → γγψ(2S) events outside the η signal region [N 0 γγψ(2S) ] and the F factor at each c.m. energy are listed in table 2. The total number of background events (n b ) in the 2D signal region is obtained with Finally, the total number of background events in the signal region at different energy points, together with the number of background events from different final states are listed in table 3.

Cross section measurement
It is assumed that the number of observed events (n obs ) in the signal region follows a Poisson distribution, with the numbers of expected background (n b ) and signal (µ) events, respectively, P (n obs ; µ, n b ) = (µ + n b ) n obs e −(µ+n b ) /n obs !. (5.1) There are some energy points where the number of observed events is zero, but the number of background events is non-zero, such as √ s = 4.244 GeV.Using the same method as in ref. [53], the value of µ with the maximum P (n obs ; µ, n b ) is taken as the non-negative (GeV) s number of signal events (n sig ).Thus, n sig = max(0, n obs − n b ) is the best estimation of the number of signal events in the physically-allowed region.
The statistical uncertainty of the number of signal events at a 68.27%C.L. is estimated with the Feldman-Cousins (FC) method [53].Since no significant ηψ(2S) signal events are observed at some energy pints, the upper limits at a 90% C.L. for the number of signal events are obtained with the Poissonian limit estimator (POLE) computer program [54].
The Born cross section of e + e − → ηψ(2S) is calculated with where B 1 and B 2 are the branching fractions of ψ(2S) → π + π − J/ψ and η → γγ [16], respectively; (1 + δ) is the radiative correction factor obtained from the quantum electrodynamics calculation [42,43,52] using the kkmc generator, assuming an input lineshape of the Y (4260) [16] cross section.The Born cross sections (and upper limits at the 90% C.L.), and the numbers used in the calculation are listed in table 4. Figure 2 shows the measured Born cross sections for e + e − → ηψ(2S) as a function of the collision energy.
The P -value is obtained by calculating the probability of the expected number of background events to fluctuate to the number of observed events or more in the signal region assuming a Poisson distribution.The total number of observed events and total expected number of background events are 34 and 10.77 ± 1.85, respectively, in the sum of the 14 data samples at different c.m. energies.Considering the uncertainty of the number of background events, the P -value and the corresponding statistical significance of e + e − → ηψ(2S) signals from the 5.25 fb −1 BESIII data are 4.6 × 10 −7 and 5σ, respectively, which are listed in table 4. the uncertainty in the number of background events to the number of signal events is taken as the uncertainty of the background estimation.
Table 5 summarizes the systematic uncertainties from all the sources.The total systematic uncertainty is obtained by summing the individual uncertainties in quadrature, assuming that all sources are independent.

Summary
In summary, using 5.25 fb −1 data collected at c.m. energies from 4.236 to 4.600 GeV, the process e + e − → ηψ(2S) is observed for the first time with a 5σ statistical significance.The energy-dependent cross section has been measured and the results are listed in table 4. Because of the limited statistics, the signals at some energy points are not significant, thus it is impossible to extract the couplings of the Y states to ηψ(2S) from a fit to the cross sections of e + e − → ηψ(2S).Further experimental studies with higher statistics are needed to draw a clear conclusion on the structure in the e + e − → ηψ(2S) process.BESIII plans to collect additional data samples over a variety of c.m. energies in the future [57].Furthermore, a partial event reconstruction technique with a missing track may improve the detection efficiency of this process.This will allow us to study the structure of the ηψ(2S) and explore the nature of the vector charmonium(like) states.

Figure 1 .
Figure 1.Two-dimensional distributions of M (γγ) versus M(π + π − J/ψ) for (a) data, (b) signal MC simulation, and (c) background MC contributions with the red dashed boxes for the defined η and ψ(2S) signal regions, and the corresponding projections of (d) M (γγ) distribution in the ψ(2S) mass window and (e) M (π + π − J/ψ) distribution in the η mass window with red arrows for the defined signal regions at √ s = 4.258 GeV, where the dots with error bars, the dashed blue lines, and the green histograms represent data, signal MC, and background MC simulations, respectvely.The same distributions for the sum of the 14 data samples and MC samples are shown in (f), (g), (h), (i), and (j) correspondingly.

Figure 2 .
Figure 2. The measured Born cross section as a function of the collision energy.The uncertainties are statistical only.

Table 2 .
The number of e + e − → γγψ(2S) events outside the η signal region [N 0 γγψ(2S) ] and the F factor at each c.m. energy.