Search for the reaction e + e − → χ cJ π + π − and a charmoniumlike structure decaying to χ cJ π (cid:1) between 4.18 and 4.60 GeV

for the process e þ e − → χ cJ π þ π − ( J ¼ 0 , 1, 2) and for a charged charmoniumlike state in the χ cJ π (cid:1) subsystem. The search uses datasets collected with the BESIII detector at the BEPCII storage ring at center-of-mass energies between 4.18 GeV and 4.60 GeV. No significant χ cJ π þ π − signals are observed at any center-of-mass energy, and thus upper limits are provided which also serve as limits for a possible charmoniumlike structure in the invariant χ cJ π (cid:1) mass.

S. F. Zhang, 36 T. J. Zhang, 42,g X. Y. Zhang, 41 Y. Zhang, 58 Y. H. Zhang, 1,48 Y. T. Zhang, 60,48 Yan Zhang, 60,48 Yao Zhang, 1 Yi Zhang, 9,h  We search for the process e þ e − → χ cJ π þ π − (J ¼ 0, 1, 2) and for a charged charmoniumlike state in the χ cJ π AE subsystem. The search uses datasets collected with the BESIII detector at the BEPCII storage ring at center-of-mass energies between 4.18 GeV and 4.60 GeV. No significant χ cJ π þ π − signals are observed at any center-of-mass energy, and thus upper limits are provided which also serve as limits for a possible charmoniumlike structure in the invariant χ cJ π AE mass. DOI

I. INTRODUCTION
In the past decade, the discovery of new and exotic resonances has opened up exciting possibilities for further study of quantum chromodynamics in the charmonium and bottomonium energy regions [1][2][3]. One important resonance is the Yð4260Þ, which was observed by the BABAR collaboration in the initial state radiation (ISR) process e þ e − → γ ISR J=ψπ þ π − [4,5] and was confirmed by several other collaborations, such as CLEO [6], Belle [7,8] and BESIII [9]. Despite lying above several open-charm thresholds (starting at 3.73 GeV=c 2 ), the Yð4260Þ state, with quantum number J PC ¼ 1 −− , unconventionally couples much more strongly to the final state J=ψπ þ π − [10] rather than to open-charm final states. This unexpected behavior has stimulated much interest in the hadron-spectroscopy community.
In 2008, the Belle collaboration, studying the decaȳ B 0 → K − π þ χ c1 , observed two charged charmoniumlike structures in the χ c1 π AE subsystem with a statistical significance of 5σ. These structures were denoted as the Z c ð4050Þ AE and the Z c ð4250Þ AE , with masses of 4051 AE 14 þ20 −41 MeV=c 2 and 4248 þ44þ180 −29−35 MeV=c 2 , respectively, and corresponding widths of 82 þ21þ47 −17−22 and 177 þ54þ316 −39−61 MeV [11]. This observation was not confirmed by BABAR, who set 90% confidence level on the presence of these intermediate states [12]. The first charged charmoniumstructure to be found was the Zð4430Þ AE decaying to ψð2SÞπ AE , observed by Belle [13], whose resonance nature was established by the LHCb collaboration [14]. The presence of an electric charge indicates a possible internal structure of at least four quarks.
In order to gain additional insight into these states, we perform a search for the Z c ð4050Þ AE in e þ e − production using data collected by the BESIII experiment at center-ofmass energies between 4.18 GeV=c 2 and 4.60 GeV=c 2 . The observation of other charged charmoniumlike states, such as the Z c ð3900Þ AE in J=ψπ þ π − [9] and Z c ð4020Þ AE in h c π þ π − [15] in some of these data samples, make the BESIII experiment an ideal environment for the search for exotic particles. In this paper the reaction channels e þ e − → χ cJ π þ π − (J ¼ 0, 1, 2) are investigated, in which the Z c ð4050Þ AE resonance is expected to appear as a structure in the χ cJ π AE invariant-mass spectrum. Due to phase-space restrictions, the production of the second state Z c ð4250Þ AE is only possible at higher energies.

II. EXPERIMENTAL DATA AND MONTE CARLO SAMPLES
The BESIII detector is a magnetic spectrometer [16] located at the Beijing Electron Positron Collider (BEPCII) [17]. 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 for charged particles and photons is 93% over the 4π solid angle. 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 (endcap) region. The time resolution of the TOF barrel part is 68 ps. The time resolution of the end-cap TOF system was upgraded in 2015 with multigap resistive plate chamber technology, providing a time resolution of 60 ps. For data taken before 2015 the time resolution was 110 ps [18,19].
For the determination of reconstruction efficiencies and the estimation of background contributions, several Monte Carlo (MC) simulated data samples were produced with a GEANT4-based [20] MC software package. This includes the geometric description of the BESIII detector and the detector response. The signal channels e þ e − → χ cJ π þ π − , with χ cJ → γJ=ψ (J ¼ 0, 1, 2) and J=ψ → l þ l − , are generated via the KKMC generator [21] for the initial resonance and the event generator EvtGen [22] for subsequent decays, using the phase-space distribution (PHSP). The PHSP model is also assumed for the decay χ cJ → γJ=ψ, and the VLL (vector to lepton lepton) model is used for the J=ψ → l þ l − (l ¼ e, μ) decay. The generation of final state radiation is handled by the PHOTOS package [23]. The simulation includes the beamenergy spread and initial state radiation (ISR) in the e þ e − annihilations modeled with the generator KKMC [21]. The inclusive MC samples consist of the production of opencharm processes, the ISR production of vector charmonium (like) states, and the continuum processes incorporated in KKMC [21]. Known decay modes are modeled with EvtGen using branching fractions taken from the Particle Data Group [24], and the remaining unknown decays from the charmonium states with LUNDCHARM [25,26]. The size of these inclusive MC samples is scaled to five times of the integrated luminosity of their respective measured data point, with the exception at 4.18 GeV which has forty times the integrated luminosity.
The datasets studied in the analysis are shown in Table I Studies on MC simulated samples are performed in order to optimize the event selection criteria. For all generated MC simulated signal samples of e þ e − → χ cJ π þ π − , initial state radiation has been deactivated, except for those samples required for the dedicated investigation of the influence of ISR on the final result. Furthermore, several inclusive MC samples have been analyzed to identify dominant background contributions. The dominant contributions found in the inclusive MC samples have been exclusively simulated. All generated exclusive MC samples contain 500 000 events.

III. EVENT SELECTION
Several selection criteria are applied in order to perform the particle identification (PID) and the event selection.
Photon candidates are constructed from clusters of energy deposits of at least 25 MeV of energy in the barrel part of the EMC (polar angle region of j cos θj < 0.80 with respect to the beam axis) and 50 MeV in the endcap region (0.86 < j cos θj < 0.92). The corresponding EMC time is required to be within a window of 700 ns relative to the event start time, and the candidates are requested to be at least 20°away from the nearest charged track to reject EMC hits caused by split-offs of clusters of charged particles.
Charged-track candidates must pass the interaction point within a cylindrical volume, with a radius of 1 cm and length of 10 cm, around the interaction point. Furthermore, due to the limitation of the MDC acceptance, the region close to the beams is excluded by requiring j cos θ Track j < 0.93. To distinguish pion candidates from the leptons coming from the J=ψ, a combination of the track momenta measured with the MDC (P MDC ) and the energy deposited in the EMC (E EMC ) is used. Pion candidates are tracks with a momentum smaller than 1.0 GeV=c and lepton candidates are tracks with a momentum greater than 1.0 GeV=c. Furthermore, to separate the electrons from muons, tracks with a ratio of E EMC =P MDC < 0.3c are considered to be muon candidates and tracks with E EMC =P MDC > 0.7c are considered as electron candidates.
In order to select e þ e − → χ cJ π þ π − events, four track candidates with a net charge of zero, including two lepton candidates, and at least one photon candidate are required. A vertex fit of the tracks to a common vertex is applied. Then, a kinematic fit with constraints on the initialfour-momentum (4C) and the mass of the J=ψ meson (5C-fit) to m J=ψ;PDG [24] is performed. Candidates that satisfy χ 2 5C < 50 are retained for further analysis. If multiple candidates are found in an event, the one with the lowest χ 2 5C value is selected. However, only one candidate is seen after the event selection in signal MC data and predominantly one in data.

IV. BACKGROUND STUDIES
The following processes have been identified as the principal sources of background events through the study of the inclusive Monte Carlo samples: ; e þ e − → γ ISR ψð2SÞ; ψð2SÞ → π þ π − J=ψ; and e þ e − → Yð4260Þ → γXð3872Þ; Xð3872Þ → J=ψπ þ π − . In all these reactions the J=ψ decays into a lepton pair (e þ e − =μ þ μ − ). Apart from the first process, these contributions have the same final state as the signal reaction channel and are thus not distinguishable by the applied kinematic fit. Additional selection criteria based on other kinematic variables are required to suppress these background channels. Background from Bhabha scattering with associated ISR/FSR photons that convert into an electronpositron pair misidentified as a pion pair is suppressed by the requirement that the pion opening angle in the laboratory system, α π þ π − , satisfies cosðα π þ π − Þ < 0.98. This criterion results in a signal loss below 1% for all studied energy points. The background contributions from ηJ=ψ and η 0 J=ψ are rejected by requiring m rec ≥ 0.57 GeV=c 2 and rejecting candidates with 0.95 ≤ m rec ≤ 0.97 GeV=c 2 , where m rec is the J=ψ recoil mass. Contamination from ωχ cJ events are suppressed by rejecting candidates where the χ cJ recoil mass lies between 0.74 and 0.82 GeV=c 2 .
The main ISR background contribution originates from the process e þ e − → γ ISR ψð2SÞ. This reaction is dangerous because the ISR photon has a wide range of possible energies, depending on the center of mass energy. The final source of contamination that is considered is illustrated in Fig. 1, where events that are most likely coming from γXð3872Þ are confused with π þ π − χ c0 signal candidates. Apparent Yð4260Þ → γXð3872Þ events at the center-ofmass energy of 4.18 GeV coincidentally have a photon energy similar to the one coming from a radiative decay of χ c0 → γJ=ψ.
Exclusive Monte Carlo datasets containing 500 000 events each are simulated and analyzed for each background process and center-of-mass energy. For e þ e − → γ ISR ψð2SÞ, samples are simulated for each studied center-of-mass energy using KKMC to evaluate the cross section. Events coming from e þ e − → γ ISR ψð2SÞ=γXð3872Þ with ψð2SÞ=Xð3872Þ → π þ π − J=ψ decays are suppressed by rejecting the region m π þ π − J=ψ ≤ 3.71 GeV=c 2 and 3.86 GeV=c 2 ≤ m π þ π − J=ψ ≤ 3.88 GeV=c 2 , respectively. Due to the restrictions on the phase space, ωχ c1 and ωχ c2 contribute only for center-of-mass energies above 4.3 GeV and ωχ c0 only above 4.2 GeV, respectively. The reconstruction efficiency is evaluated with simulated MC data of the signal channel. The reconstruction efficiency ranges from 16% to 28% after the application of all selection criteria, depending on the center-of-mass energy (see Tables III-V).

V. CROSS SECTION DETERMINATION
The signal yield is directly determined by counting the events surviving the selection criteria. Since the radiative process χ cJ → γJ=ψ is a two-body decay, the photon energy of each decay mode serves as a distinctive signature for the separation of the three χ cJ channels. Figure 2 shows the photon energy after boosting it into the π þ π − recoil system. This method allows for a clear separation of the three χ cJ channels by setting the (boosted) photon energy windows and leads to the results shown in Tables III to V. There, the first uncertainties are statistical and the second systematic, arising from the sources discussed in Sec. VI. The expected background events for each center-of-mass energy are estimated by adding up each background contribution: where L is the integrated luminosity at a given center-ofmass energy, σ i is the cross section for each background contribution, B i the corresponding branching ratio and ϵ i the efficiency from the exclusive background MC data samples after all selection criteria. The values of σ i are taken from previous BESIII measurements [28][29][30][31][32]. In the cases where no cross section has yet been measured the upper limits are used to provide an estimate. Finally, B i is taken from the Particle Data Group (PDG) [24]. The observed cross section σ obs is calculated via with the selection efficiency ϵ and Bðχ cJ → γJ=ψÞ being the corresponding branching fraction for the selected χ cJ decay channel and BðJ=ψ → l þ l − Þ the sum of the two branching fractions BðJ=ψ → e þ e − Þ and BðJ=ψ → μ þ μ − Þ. The determination of the upper limits is discussed in further detail in Sec. VIII.

VI. SYSTEMATIC-UNCERTAINTY ESTIMATION
Systematic uncertainties are assigned, where appropriate, for each step and input in the analysis. The uncertainty on the measurement of the integrated luminosity is 1% [27]. The uncertainty on the reconstruction efficiency due to the finite size of the MC simulation sample is 0.3-0.4%. The difference between data and MC simulation of the track and photon reconstruction efficiencies and also the correlation between the tracks are taken into account by assigning a 1% uncertainty per track [33] and per photon [34], resulting in an overall uncertainty of 4.1%. The uncertainty associated with final state radiation is stated to be roughly 0.1% [35] and considered to be negligible.
The uncertainty associated with the selection criteria is assigned to be the largest shift in efficiency observed when the applied criteria are moved by 10% in both directions. For the selection on the χ 2 5C of the kinematic fit, this results in an uncertainty of around 1.4%, depending on the centerof-mass energy and applied χ cJ selection. For the η veto the range is much larger and varies between 0.2% and 4.5%.
Similarly, uncertainties associated with other selection criteria also depend on the collision energy. For the background vetoes, the windows are increased and decreased by 10% and again the largest difference, which varies in the range of a few percent, is assigned. In the case of the χ c2 selection, the ψð2SÞ veto contributes larger systematic uncertainties at lower center-of-mass energies, where the invariant π þ π − J=ψ mass of the expected signal lies, coincidentally, in the vicinity of the ψð2SÞ mass. The systematic uncertainty is largest for the χ c0 selection, on account of the larger natural width of this state. Table II summarizes the individual systematic uncertainties. Contributions arising from the variation of a certain input from the nominal value are considered to be negligible if the observed change in result is found to be less than the uncorrelated systematic uncertainty. The total systematic uncertainty is calculated as the sum in quadrature of each component, assuming negligible correlations, and results in values between 4.7% to 11.0%. When calculating upper limits, a Gaussian-shaped uncertainty is added to the efficiency with a width equal to the total systematic uncertainty.

VII. ISR CORRECTION
An ISR correction factor is applied to the measured cross section, as listed in Tables III to V. The number of observed events can be written as  where x ≡ E ISR =E beam and WðxÞ is the radiator function [36,37]. After factoring out the Born cross section σ 0 and the efficiency ϵ 0 at x ¼ 0 this expression becomes The ISR correction factor is defined as so that The efficiency ratio ϵðxÞ=ϵ 0 is determined from a sample of MC simulated signal events, which are generated including ISR. Figure 3 a shows the efficiency ratio as a function of x for the χ c1 signal MC sample at 4.6 GeV. The superimposed fit is an error function, which is found to describe all χ cJ modes and collision energies.
The correction factor κ is strongly correlated to the energy dependence of the signal cross section, which is currently unknown. To obtain conservative upper limits on the signal we estimate the lowest possible κ value. We assume a narrow resonance of width 10 MeV and mass 4.26 GeV=c 2 , which results in the κ energy dependence shown in Fig. 3 b. Changing the position of the resonance results in a corresponding shift of the κ energy dependence, while the shape is nearly unchanged. The minimal value of the correction factor, κ ¼ 0.64, is conservatively used to set the upper limits of the cross section at all collision energies.

VIII. UPPER-LIMIT DETERMINATION
The upper limits on the branching ratios are calculated following a frequentist procedure [38,39], using the definition Here N UL is the upper limit on the signal yield, L is the integrated luminosity, ð1 þ δÞ ≡ κ is the ISR correction factor (see section VII), 1 j1−ΠðsÞj 2 is the vacuum polarization correction factor (with values in the range 1.05-1.06 from Ref. [40]), ϵ the efficiency from corresponding signal Monte Carlo after selection criteria, and B is the combined branching ratio of Bðχ cJ → γJ=ψÞ and BðJ=ψ → l þ l − Þ. The systematic uncertainties are taken into account by assuming a Gaussian-shaped uncertainty on the efficiency with a width equal to the total systematic uncertainty. TABLE III. Measured cross sections and associated information for e þ e − → χ c0 π þ π − at different center-of mass-energies E cms . Shown are the integrated luminosity L, the selection efficiency ϵ, the number of observed events N obs , the number of expected background events N bkg , the observed cross sections σ obs with statistical and systematic uncertainties, the statistical significance and the respective upper limits at 90% confidence level. The measured cross sections and the corresponding upper limits at the 90% confidence level are summarized in Tables III-V and in Fig. 4. The quoted statistical significance is based on the binomial assumption Z Bi , taken from Cousins et al. [38] and does not include any systematic uncertainties. With the exception of the channel e þ e − → π þ π − χ c1 , the measured cross sections show no significant variation with center-of-mass energy. It should be noted that the upper limits for e þ e − → π þ π − χ c0 are less restrictive than those for the other two modes on account of the small branching ratio of χ c0 → γJ=ψ. Since no convincing χ cJ π þ π − signal is seen, the quoted upper limits can also be considered as upper limits on the reaction proceeding through a hypothetical Z c ð4050Þ AE particle.