Observation of di-structures in $e^+e^-\rightarrow{J}/\psi{\rm X}$ at center-of-mass energies around 3.773 GeV

We report a measurement of the observed cross sections of the inclusive $J/\psi$ production in $e^+e^-\rightarrow {J}/\psi{\rm X}$ based on 3.21 fb$^{-1}$ of data accumulated at energies from 3.645 to 3.891 GeV with the BESIII detector operated at the BEPCII collider. The energy-dependent lineshape obtained from the measured cross sections cannot be well described by two Breit-Wigner (BW) amplitudes of the expected decays $\psi(3686)\rightarrow {J}/\psi{\rm X}$ and $\psi(3770)\rightarrow {J}/\psi{\rm X}$. Instead it can be better described with three BW amplitudes of the decays $\psi(3686)\rightarrow {J}/\psi{\rm X}$, $R(3760)\rightarrow {J}/\psi{\rm X}$ and $R(3790)\rightarrow {J}/\psi{\rm X}$ with two distinct structures referred to as $R(3760)$ and $R(3790)$. Under this assumption, we extracted their masses, total widths, and the product of the leptonic width and decay branching fractions to be $M_{R(3760)}= {3761.7\pm 2.2 \pm 1.2}$ MeV/$c^2$, $\Gamma^{\rm tot}_{R(3760)}= {6.7\pm 11.1 \pm 1.1}$ MeV, $\Gamma^{ee}_{R(3760)}\mathcal B[R(3760)\rightarrow {J}/\psi {\rm X}]=(4.0\pm 4.3\pm 1.2)$ eV, $M_{R(3790)} = {3784.7\pm 5.7 \pm 1.6}$ MeV/$c^2$, $\Gamma^{\rm tot}_{R(3790)} = {31.6 \pm 11.9 \pm 3.2}$ MeV, $\Gamma^{ee}_{R(3790)}\mathcal B[R(3790)\rightarrow {J}/\psi {\rm X}]=(18.1\pm 10.3\pm 4.7)$ eV, where the first uncertainties are statistical and second systematic.

We report a measurement of the observed cross sections of the inclusive J/ψ production in e + e − → J/ψX based on 3.21 fb −1 of data accumulated at energies from 3.645 to 3.891 GeV with the BESIII detector operated at the BEPCII collider. The energy-dependent lineshape obtained from the measured cross sections cannot be well described by two Breit-Wigner (BW) amplitudes of the expected decays ψ(3686) → J/ψX and ψ(3770) → J/ψX. Instead it can be better described with three BW amplitudes of the decays ψ(3686) → J/ψX, R(3760) → J/ψX and R(3790) → J/ψX with two distinct structures referred to as R(3760) and R(3790). Under this assumption, we extracted their masses, total widths, and the product of the leptonic width and decay branching fractions to be M R(3760) = 3761.7 ± 2.2 ± 1.2 MeV/c 2 , Γ tot R(3760) = 6.7 ± 11.1 ± 1. The mesons with mass above the threshold of open charm (OC) pairs had been considered for more than 25 years to decay entirely to OC final states via the strong interaction. Only a few experimental studies of non-OC (NOC) decays of these mesons had been carried out before the summer of 2002 [1,2]. In July 2003, the BES Collaboration claimed for the first time that they had observed 7 ± 3 events of the NOC final state of J/ψπ + π − [3] in the e + e − collision data taken with the BES-II detector operated at the BEPC collider at center-of-mass energies nearby 3.773 GeV. This observation started worldwide a new era with the aim to study rigorously NOC decays of the mesons lying above open-charm thresholds. After more than two years of intensive discussion in the particle physics community about whether J/ψπ + π − is really a decay product of the mesons lying above the lowest open-charm threshold (3.73 GeV), it has been accepted that this golden final state is a product of the ψ(3770) NOC decays. However, it has not been excluded that this golden final state may be a decay product of some other possible structures [4] which was speculated to exist in this energy region. The discovery of the first NOC final state of J/ψπ + π − from the meson(s) decays overturns the conventional knowledge that almost 100% of the mesons decay into OC final states through the strong interaction. It stimulated a strong interest in studying NOC decays of other mesons lying above the OC thresholds and it inspired more experimental efforts to study NOC decays of the mesons. In particular, the study of the J/ψπ + π − final state or a similar final state such as M cc X LH (M cc is a hidden charm meson such as J/ψ, ψ(3686), χ cJ (J = 0, 1, 2) and h c ..., while X LH refers to any allowed light hadron(s)) lead to the discovery of several new states [5,6], such as the historically labeled X, Y , and Z states.
According to the potential model [7], the ψ(3770) resonance is the only cc state which can be directly produced in e + e − annihilation in the energy region between 3.73 and 3.87 GeV. The ψ(3770) resonance is expected to decay to DD meson pairs with a branching fraction of more than 99%, and to decay to e + e − and γχ cJ (J = 0, 1, 2) with a total branching fraction of less than 1% [7]. However, the BES Collaboration found large fractions of the ψ(3770) decaying to non-DD using different data samples which are (14.5±1.7±5.8)% [8], (16.4 ± 7.3 ± 4.2)% [9], (13.4 ± 5.0 ± 3.6)% [10], and (15.1 ± 5.6 ± 1.8)% [11]. These large branching fractions for ψ(3770) decaying to non-DD indicate that the ψ(3770) may be not a pure cc state or due to the presence of some unknown structure(s) lying at energies nearby ψ(3770) [12]. To search for the new structure(s), as suggested in Ref. [12], we studied the processes e + e − → J/ψX in the energy region between 3.645 and 3.891 GeV, since an analysis of cross sections for e + e − → f , whereby f refers to any final state, at energies above the f threshold can directly reveal new states [12,13].
The BESIII detector and its response are described elsewhere [18]. Here, we discuss only those aspects that are specifically related to this study. The production of the ψ(3686) and ψ(3770) resonances are simulated with the Monte Carlo (MC) event generator KKMC [19]. The decays of these resonances to J/ψππ, J/ψη, J/ψπ 0 , and γχ cJ (J = 0, 1, 2) are generated with EVTGEN [20] according to the relative branching fractions of these final states [22]. To study possible backgrounds, MC samples of inclusive ψ(3686) and ψ(3770) decays, e + e − → (γ)J/ψ, e + e − → (γ)ψ(3686), e + e − → qq (q = u, d, s), and other final states which may be misidentified as J/ψX are also generated, where γ in parentheses denotes the inclusion of photons from the Initial State Radiation (ISR).
The observed cross section at a c.m. energy, E cm , is determined with where N obs and N b are, respectively, the number of J/ψX signal events obtained from the data and the number of background events estimated by MC simulations, L is the integrated luminosity of the data, ǫ is the efficiency for the selection of e + e − → J/ψX events, and B(J/ψ → ℓ + ℓ − ) is the branching fraction for J/ψ decays to the lepton pair ℓ + ℓ − . To optimize the number of signal events, we do not fully reconstruct X.
The J/ψ is reconstructed via the e + e − and µ + µ − final states. Each event is required to have exactly two charged tracks and more than one photon, or to have three or four charged tracks in the final state. For each charged track, the polar angle θ in the multilayer drift chamber (MDC) must satisfy | cos θ| < 0.93. For all charged tracks, the distance of closest approach to the average e + e − interaction point is required to be less than 1.0 cm in the plane perpendicular to the beam and less than 10.0 cm along the beam direction. The electron and the muon can be well separated with the ratio E/p, where E is the energy deposited in the electromagnetic calorimeter (EMC) and p is the momentum of the charged track, which is measured using the information in the MDC. For e ± candidates, the ratio E/p is required to be larger than 0.7, while for µ ± , it is required be be in the range from 0.05 to 0.35. To reject radiative Bhabha scattering events, the polar angles of the leptons are required to satisfy | cos θ| < 0.81, and the angle between the two leptons to be less than 179 • . The momenta of the leptons are required to be larger than 1 GeV and less than 0.47 × E cm . To select π ± and to reject backgrounds such as π + π − K + K − from cc and non-cc state decays and two-photon exchange processes of e + e − → ℓ + ℓ − K + K − , the confidence level of the pion hypothesis, calculated based on dE/dx and time-of-flight measurements, is required to be greater than that of the corresponding kaon hypothesis. For the selection of photons, the deposited energy of a neutral cluster in the EMC is required to be greater than 25 MeV in barrel and 50 MeV in end-caps. Time information from the EMC is used to suppress electronic noise and energy deposits unrelated to the event. To exclude fake photons originating from charged tracks, the angle between the photon candidate and the nearest charged track is required to be greater than 10 • .
The numbers of candidates for J/ψ are determined by fitting the ℓ + ℓ − invariant mass spectra of the events satisfying the previously-described selection criteria. This is illustrated in Fig. 1 which shows the ℓ + ℓ − invariant mass spectra from the data sets obtained at two c.m. energies. Clear peaking structures can be observed that stem from J/ψ decays. We fit these mass spectra with a function describing both the signal and background shapes. The signal shape is described by the MC-simulated signal shape, while the smooth background is modeled by a line. The fits yield the numbers of the candidates for e + e − → J/ψX. Similarly, we obtain the numbers of the candidates for e + e − → J/ψX selected from all of the data sets taken at the other energies.
These selected candidate events still contain some background events, originating from several sources, which includes: (6) continuum light hadron production, (7) e + e − → (γ)J/ψ events. Detailed MC studies of these backgrounds show that only one major background source of e + e − → (γ)J/ψ → (γ)ℓ + ℓ − could be misidentified as e + e − → J/ψX, which is due to picking up fake photons or unphysical charged track(s). From these MC studies we find that the fraction of these background events misidentified as signal events is η mis = (0.181 ± 0.024)%. With the J/ψ resonance parameters [22] as inputs and considering the energy spread, we extract the cross section σ ISRV e + e − →(γ)J/ψ for e + e − → (γ)J/ψ, which include both the ISR and vacuum polarization effects, and we determine N b = Lσ ISRV e + e − →(γ)J/ψ η mis . The efficiencies for the selection of e + e − → J/ψX decays are determined with MC simulated events for these decays in-cluding the ISR and final-state radiative effects, where the final states include J/ψπ + π − , J/ψπ 0 π 0 , J/ψη, J/ψπ 0 , γχ cJ (J=0,1,2) in which χ cJ → γJ/ψ followed by J/ψ → e + e − and J/ψ → µ + µ − , whose decay branching fractions are given by Particle Data Group [22]. With the MC samples generated at 69 c.m. energies ranging from 3.645 to 3.895 GeV, we determine the corresponding efficiencies. We observe an energy-dependent efficiency curve increasing smoothly from 58.8% at 3.645 GeV to 60.8% at 3.891 GeV. With the numbers of candidates for e + e − → J/ψX selected from the 69 data sets, N b , η mis , L, ǫ J/ψX , and B(J/ψ → ℓ + ℓ − ), we determine the observed cross sections at these energies, which are shown in Tab. I For estimating the systematic uncertainty of the crosssection measurements, we considered 12 sources, most of which are determined by comparing the corresponding quantities obtained from both data and MC simulated events. In the following, we summarize the various contributions and our estimate of the respective systematic error in parenthesis: (1) the uncertainty in the efficiency determination due to the angle θ ℓ + ℓ − cut for the leptons (negligible), (2) due to the cos θ cut for the charged tracks (0.4%), (3) due to the E/p cut (0.3%), (4) due to the lepton momentum p l ± cut (0.2%), (5) due to the constraints applied on the number of charged tracks cut or photons (0.4%), (6) the uncertainty of the tracking efficiency (0.3%) for pions, while this uncertainty for the leptons cancels with the corresponding uncertainty in the luminosity measurements, (7) the uncertainty induced by fitting the invariantmass spectrum (0.8%), (8) the uncertainty in the modeling of the MC (0.9%) including the branching-fraction uncertainties of ψ(3686) → J/ψπ + π − and ψ(3686) → J/ψπ 0 π 0 ; (9) the uncertainty related to the identification of π ± (1.0%), (10) the uncertainty in the branching fraction for the decay J/ψ → l + l − (0.4%) [22], (11) the uncertainty in the background subtraction for the decay e + e − → J/ψX (< 0.1%) due to uncertainty of J/ψ resonance parameters, and (12) the systematic uncertainty in the luminosity measurements (1.0%). Adding the individual systematic uncertainties in quadrature, assuming them to be independent, yields a total systematic uncertainty of 2.0%. Figure 2 shows the observed cross sections as circles with error bars, where the errors are statistical taking into account statistical fluctuations of the signal, the number of MC events, and the statistical uncertainties of the luminosity measurements. The dominant peak located at ∼3.686 GeV is due to ψ(3686) decays. The shape of the cross section at energies above 3.73 GeV is anomalous, indicating that there could be structure(s) lying at energies from 3.73 to 3.87 GeV as those observed by the BES Collaboration [4].
We analyze the cross section by performing least-χ 2 fits to the cross section. The expected cross section can be modeled (2) where s = E 2 cm , x is the energy fraction of the radiative photon [23], s ′ = s(1 − x), G(s, w) [9] represents a Gaussian function [24] describing the c.m. energy distribution of BEPCII, w is an integration variable, √ s ± = √ s ± 5∆ sprd , in which ∆ sprd is the energy spread, σ dress (s ′ ) is the dressed cross section including vacuum polarization effects for the J/ψX production, M J/ψ is the mass of J/ψ, and F (x, s) is a sampling function [23].
We perform the least-χ 2 fits with two hypotheses of and A R2 (s ′ ) are, respectively, the decay amplitudes of ψ(3686), S (S could be either ψ(3770) or a new structure), R 1 , and R 2 , while φ 1 and φ 2 are the corresponding phases of these amplitudes. The generic decay amplitude of the resonance or structure are described by a Breit- where the subscript j indicates one of these resonances, M j , Γ ee j , Γ tot j , and B j represent the mass, leptonic width, total width, and branching fraction of the j resonance or structure decaying into J/ψX final states, respectively.
In the fit the observed cross-section values are assumed to be influenced only by the uncertainties of statistical origin [2]. The uncertainties on the parameters returned by the fit are referred to as statistical uncertainties in the subsequent discussion. The remaining cross-section uncertainties (assumed to be fully correlated between different energies) are taken into account using the "offset method" [21]. The cross-section values are changed for all energies simultaneously by the size of the uncertainty and the resulting change in the fit parameter is taken as a systematic uncertainty.
The solid line in Fig. 2 shows the best fit result under assumption of the two decay amplitudes contributing to the cross sections, while the dashed line shows the contribution from ψ(3686) → J/ψX decays. To highlight the difference between the measured cross sections and their fitted values, three enlarged figures are inserted. The sub-figure (a) shows the cross section with the fit, while the sub-figure (b) shows the cross section with the fit, where the ψ(3686) contributions are subtracted. The solid line in the sub-figure (b) corresponds to the best fit result of the cross section taking into account the ψ(3770) decay and interference effects between the ψ(3686) and ψ(3770) decay amplitudes. In this fit, the total and leptonic widths of both the ψ(3686) resonance and S structure as well as the mass of S are fixed to the values of these for ψ(3686) and ψ(3770) given by the Particle Data Group [22], while the branching fractions for the decays of ψ(3686) → J/ψX and ψ(3770) → J/ψX as well as the phase φ 1 are left as free parameters. The fit has two solutions for one free phase. The two solutions have an identical fit goodness of χ 2 = 120.4 for 64 degrees of freedom. Table II shows results from the fits, where the first uncertainties are statistical, and second systematic. The systematic uncertainties have three sources for B(ψ(3686) → J/ψX), B(ψ(3770) → J/ψX) and φ 1 , which are respectively: (1) 2.33%, 1.96% and 0.01% for them due to uncertainty of the observed cross section, (2) 0.16%, 9.80% and 6.01% due to uncertainties of the fixed parameters, and (3) 0.62%, 27.45% and 0.86% due to uncertainties of E cm . Adding these uncertainties in quadrature yields the total systematic uncertainty. The branching fraction for the decay ψ(3770) → J/ψX from one solution is consistent within error with the sum of published branching fractions [22], (0.47 ± 0.06)% [22], of ψ(3770) → J/ψπ + π − , J/ψπ 0 π 0 , and J/ψη, γχ J with J = 0, 1, 2, while the branching fraction from the other solution is larger than the total branching fraction by a factor of about four.
If we leave the mass and total width of S free in the fit, the fit returns  In the inserted sub-figure (c) in Fig. 2, the observed cross section values around 3.758 GeV significantly deviate from the fitted values of the cross section, which could be due to a new structure produced around this energy. To interstage whether these are due to the new structure, we add one more BW amplitude in the fit leaving four parameters free. contributions are subtracted. Table III summarizes  The systematic uncertainties in the magnitude of the fitted parameters are assumed to originate from four sources: (1) the uncertainty of the observed cross section, (2) the uncertainties of the total and leptonic widths of ψ(3686), (3) the uncertainties of the c.m. energies, and (4) the uncertainties of the branching fractions of R(3760) and R(3790) decays. To estimate these uncertainties, we change the values of the fixed parameters by ±1σ, and refit the observed cross section, and subsequently take the difference between the refitted parameters and the ones of the nominal fit result as the corresponding systematic shift. A similar procedure has been applied to estimate the systematic error related to uncertainties of the c.m. energies. In this case, we vary the c.m. energies with a Gaussian uncertainty of 0.25 MeV in the resonance energy region, refit the data, and take the difference of the updated fit parameters with respect to the result of the nominal fit as a measure of the systematic shift. Taking these shifts as independent systematic uncertainties, we add them in quadrature to obtain the total systematic uncertainty for each parameter, which is indicated by the second uncertainty of each parameter in Table III.   TABLE III. The fitted results, where M , Γ tot and Γ ee are the mass, total, and leptonic widths of resonance(s) Ri, B(Ri → f ) (f = J/ψX) is the branching fraction for the Ri decay into f , and φi is the phase of the amplitude, in which i = 1, 2, 3 indicate ψ(3686), R(3760) and R(3790), respectively; B(R2 → f ) and B(R3 → f ) are determined using Γ ee R(3760) = 186 ± 201 ± 8 eV and Γ ee R(3790) = 243 ± 160 ± 9 eV [4], where the normalization uncertainties are not included. The fit has four solutions for two free phases. However, we only found two distinguishable solutions. Two of the solutions overlap with the other two, as expected according to mathematical predictions reported in Ref. [25]. The two distinct solutions, summarized in Table III, gave a fit quality of χ 2 =78.6 with 58 degrees of freedom. Thus, both solutions are equally acceptable. We choose Solution I as the nominal results of the analysis. The fit yields a branching fraction B(ψ(3686) → J/ψX) = (62.7 ± 0.2 ± 1.5)%, where the first uncertainty is statistical, and the second systematic. This result is consistent within error with the world average of B(ψ(3686) → J/ψX) = (61.6 ± 0.6)% [22].
Comparing the hypothesis of ψ(3686)+S(3790) with all parameters of S(3790) structure free in the fit, including an additional structure R(3760) with all parameters free, reduce the χ 2 of the fit by 16.8, which corresponds to a statistical significance for the observation of the R(3760) of 3.1σ. The masses and total widths of these two structures, R(3760) and R(3790), which are measured in this work are consistent within 1.3σ uncertainties with those measured in analysis of e + e − → hadrons by the BES Collaboration [4].
In summary, we have measured for the first time the observed cross sections for e + e − → J/ψX at c.m. energies ranging from 3.645 to 3.891 GeV. We fitted to the cross sec-