Measurement of the branching fraction of $J/\psi \rightarrow \omega \eta' \pi^{+}\pi^{-}$ and search for $J/\psi \rightarrow \omega X(1835), \, X(1835) \rightarrow \eta' \pi^{+}\pi^{-}$ decay

Using a sample of $1.31 \times 10^{9}$ $J/\psi$ events collected by the BESIII detector at BEPCII during 2009 and 2012, we study the $J/\psi \rightarrow \omega \eta' \pi^{+}\pi^{-}$ hadronic process. For the first time, we measure the branching ratio $B(J/\psi \rightarrow \omega \eta' \pi^{+}\pi^{-}) = (1.12 \pm 0.02 \pm 0.13) \times 10^{-3}$. We search for the $X(1835)$ state in the $\eta' \pi^{+}\pi^{-}$ invariant mass spectra. No evidence is found and we estimate the upper limit on the branching fraction at 90% confidence level to be $B(J/\psi \rightarrow \omega X(1835), \, X(1835) \rightarrow \eta' \pi^{+}\pi^{-})<6.2 \times 10^{-5}$.

One of the main topics of the BESIII physics program is the search for unconventional hadronic states.Among the light hadrons, the X(1835) state has caught the attention both from an experimental and a theoretical point of view.It was observed first in the η ′ π + π − invariant mass spectra at BES in the J/ψ → γη ′ π + π − radiative decay [1], and confirmed later with much higher statistics by BESIII [2].Its mass and width were measured to be M = 1836.5 ± 3.0 +5. 6 −2.1 MeV/c 2 and Γ = 190 ± 9 +38 −36 MeV, with the product of branching fractions B(J/ψ → γX(1835)) • B(X(1835) → η ′ π + π − ) = (2.87 ± 0.09 +0.49−0.52 ) × 10 −4 [2].The X(1835) state was also seen in the process J/ψ → γK 0 S K 0 S η [3]; its mass and width were found to be in agreement with those measured in Ref. [2], and he quantum numbers J P C were determined to be 0 −+ from a partial wave analysis.
Just a few years before the observation of the X(1835) state, an anomalous enhancement close to the pp mass threshold, called X(1860), has been observed by BES in the J/ψ → γpp decay [4], and confirmed by BESIII [5] and CLEO [6], while no evidence has been seen in other channels, such as J/ψ → ωpp [7,8] or J/ψ → φpp [9].A partial wave analysis of the pp mass-threshold enhancement was performed [10], and the J P C quantum number were determined to be the same as for the X(1835).The discovery of these new states has stimulated many theoretical speculations on their nature, such as a pp bound state [11][12][13], a pseudo-scalar glueball [14][15][16], a radial excitation of the η ′ meson [17], etc. Thanks to the world's largest e + e − → J/ψ data set collected by BESIII, it has been possible to study in detail the significant abrupt change in the line shape of the X(1835) → η ′ π + π − in correspondence of the pp mass threshold [18], which could be originated from the opening of the pp additional decay channel (threshold effect) or by the interference between two different resonances.However, none of the hypotheses could be excluded and no final conclusion has been made.In order to extract additional information about the states around 1.85 GeV/c 2 with the present BESIII statistics, additional decay modes must be investigated.
In this paper, we report on the search for X(1835) in the J/ψ → ωη ′ π + π − process.The comparison of the production rates between J/ψ → ωX(1835) and J/ψ → γX(1835) could also help to get information on the qq or gluon component of X(1835) [13,14], i.e. if X(1835) contains substantial qq components, like the η ′ meson, it should be observed in J/ψ → ωX(1835).Using the branching fraction of J/ψ → ω(φ)η ′ , the branching fraction of J/ψ → ω(φ)X( 1835) is estimated to be in the order of 10 −5 [14].On the other hand, a very small branching fraction is expected for larger gluon component.Another estimation was done in Ref. [13], where B(J/ψ → ωX(1835)) is expected to be two orders of magnitude less than that of J/ψ → γX(1835) decay.
This analysis is based on 1.31×10 9 J/ψ events collected by BESIII during 2009 and 2012.The BESIII detector [19] is a magnetic spectrometer operating at BEPCII, a double-ring e + e − collider with center-of-mass energies ranging from 2.0 to 4.6 GeV.The geometrical acceptance covered is 93% of a 4π solid angle.From the inner to the outer side, it consists of a helium-based main drift chamber (MDC), a time-of-flight system (TOF) and a CsI(Tl) electromagnetic calorimeter (EMC), all enclosed in a superconducting solenoidal magnet providing a magnetic field of 1 T (0.9 T in 2012).The solenoid is surrounded by an octagonal flux-return yoke with resistive plate chambers interleaved with steel.
A GEANT4-based Monte Carlo (MC) simulation package [20] is used to optimize selection criteria, estimate background processes, and determine detection efficiency.The production of the J/ψ resonance is simulated with KKMC event generator [21,22], while the decays are generated with EvtGen [23,24].Simulated inclusive J/ψ events of approximatively the equivalent luminosity of data are used to study background processes.The known decays of J/ψ are modeled with branching fractions being set to the world average values from Particle Data Group (PDG) [25], while the remaining decays are generated with LUNDCHARM [26].We simulate 700,000 MC events using phase space model for the processes J/ψ → ωη ′ π + π − and J/ψ → ωX(1835), X(1835) → η ′ π + π − , which are used to optimize the event selection and to determine the selection efficiency.For the J/ψ → ωX(1835) signal simulation we also take into account the J P C = 0 −+ quantum numbers.For each candidate event, we select charged tracks well reconstructed in the MDC detector with the polar angle θ satisfying the condition | cos θ| < 0.93.The tracks are required to pass the interaction point within ±10 cm along the beam direction and within 1 cm in the plane perpendicular to the beams.Photon candidates are reconstructed using clusters of energy deposited in the EMC.The energy deposited in the TOF is also included in EMC measurements in order to improve the reconstruction efficiency and the energy resolution.Good photon candidates are required to have a deposited energy larger than 25 MeV in the barrel region (| cos θ| < 0.8) and 50 MeV in the end caps (0.86 < | cos θ| < 0.92).To eliminate those clusters associated with charged tracks, the angle between the direction of any charged track and the photon candidate must be larger than 5 • .Clusters due to the electronic noise and energy deposit unrelated to the event are suppressed by requiring the shower time to be within 700 ns of the event start time.Events with six charged tracks, net charge equal to zero, and at least four photon candidates that satisfy the above requirements are retained for further studies.In the reconstruction of J/ψ → ωη ′ π + π − , the ω meson is reconstructed in its dominant π + π − π 0 decay mode and η ′ via η ′ → ηπ + π − , while both η and π 0 are reconstructed from γγ pairs after applying the corresponding mass constrained kinematic fit.To improve momentum resolution, for each π 0 ηπ + π − π + π − π + π − combination a four constraints (4C) energy-momentum kinematic fit is performed.We select only events with χ 2 4C < 60.In order to determine the π + π − pairs produced in ω/η ′ decays, we select the combination which minimize the quan- 2 , where m ω and m η ′ are the nominal masses of ω and η ′ [25], respectively, while Then, we require M π + π − π 0 and M ηπ + π − to be within 3σ the fitted widths: 1 shows the η ′ π + π − invariant mass distribution (M η ′ π + π − ) from data sample for those events that satisfy the selection criteria.No clear enhancement is visible.
In Fig. 1, the η ′ π + π − invariant mass spectrum from inclusive MC sample is also reported.Since there are some discrepancies between the two distributions, more pronounced for M η ′ π + π − > 1.9 GeV/c 2 , we cannot use the inclusive MC sample to model the background contribution.As an alternative, a two-dimensional fit to the π + π − π 0 and ηπ + π − distributions will be used to get the number of J/ψ → ωη ′ π + π − signal events.The scatter plot of M ηπ + π − as a function of M π + π − π 0 is reported in Fig. 2. The ω signal is parametrized by a Breit-Wigner (BW) function convolved with a double Gaussian and the η ′ signal by a double Gaussian function, while thirdorder polynomial functions are used for both ω and η ′ backgrounds.All the parameters are treated as free with the exception of the ω width, which is fixed to the world average value [25].
As can been seen from Fig. 1, no significant X(1835) signal is observed in the η ′ π + π − invariant mass spectrum, and hence we extract the upper limit (UL) on the number of X(1835) signal events.As stated before, we cannot use inclusive MC sample to parametrize the background shape.Also a polynomial function may not be appropriate to describe a large background component under a very small signal fraction of a broad resonance.As an alternative in order to extract the backgroundcorrected distribution, the two-dimensional fit to the π + π − π 0 and ηπ + π − invariant mass spectra is performed in eight slices of η ′ π + π − mass spectrum from 1.4 GeV/c 2 to 2.2 GeV/c 2 .The background-subtracted η ′ π + π − invariant mass is shown in Fig. 4. The UL on the number of X(1835) signal events is extracted by means of a χ 2fit.In this fit, all processes other than J/ψ → ωX(1835) are considered as background, and we assume there is no interference between X(1835) and non-X(1835) components.Both the X(1835) signal and background yields are fitted as free parameters, and we associate to the signal yield a Gaussian distribution with mean and width equal to the number of signal events and the corresponding uncertainty resulting from the χ 2 -fit.Then, the UL at 90% confidence level (C.L.) is obtained by finding the point where the cumulative probability of this Gaussian distribution is equal to 0.9.
In the χ 2 -fit, two different signal functions are taken into account: a BW function with X(1835) mass and width fixed to values from Ref. [2], and a Flatté function with fixed parameters from Ref. [18], both weighted by the efficiency, while a third-order polynomial function is used for the background.Systematic effects are evaluated by changing the η ′ π + π − fit range and the bin size, as well as by varying the fit parameters within one standard deviation.Since the η ′ π + π − background-corrected distribution is extracted from a two-dimensional fit to the π + π − π 0 and ηπ + π − invariant mass spectra, we need to evaluate its systematic contribution.On this purpose, three different signal functions are used to parametrize the ω and η ′ signal: (1) a BW convolved with a double Gaussian for ω and a double Gaussian for η ′ , (2) the ω and η ′ MC shapes, and (3) the convolution of the ω and η ′ MC shapes with a double Gaussian.The resulting η ′ π + π − background-corrected distribution are then fitted using a χ 2 -fit, as described before.The fit that gives the largest result is then used to extract the UL on the number of X(1835) signal events at 90% C.L., which amounts to N UL = 582.The corresponding UL on the branching fraction of the J/ψ → ωX(1835), X(1835) → η ′ π + π − decay at 90% C.L. is calculated as where ǫ ′ = 5.26% is the X(1835) selection efficiency in the ω − η ′ signal region, and σ sys is the total systematic uncertainty reported in Table I and discussed below.Several sources of systematic uncertainties are considered: uncertainty due to the total number of J/ψ events [27], intermediate branching fractions [25], data-MC differences in tracking efficiency, photon detection efficiency, selection efficiencies, angular distributions, kine-  matic fit, signal and background functions and fit range.Uncertainties due to the tracking efficiency for charged tracks are determined using control samples of J/ψ → π + π − pp and J/ψ → K 0 S K ± π ∓ .The difference between the tracking efficiency in data and MC simulations is 1% for each charged track.However, since we have six charged pions in the final state, and hence pions with very low momentum, we check for possible tracking efficiency underestimation.We correct our MC simulations according to the data, also taking into account possible difference in the polar angle distributions, and we find a tracking efficiency consistent with 6%.For the neutral candidates, control samples of J/ψ → ρπ 0 and e + e − → γγ are used to study the photon detection efficiency, which amount to 1% for each photon candidate.The systematic contributions related to the selection efficiency used to calculate both branching fraction and upper limit are evaluated by means of additional MC samples, in which also different intermediate states are considered.However, since no obvious structures are observed in the different combinations of two-or threeparticles invariant mass distributions, we simulate a MC sample, without intermediate resonances, taking into account the spin-parity of the initial and final states, and the difference in the efficiency is taken as systematic contribution.Additional contribution can arise from differences between the angular distribution of data and simulation in the J/ψ → ωη ′ π + π − process.We simulate a new MC sample following the same angular dependence as in the data.The difference in the efficiency amount to 1%, which is taken as systematic uncertainty.
A control sample of ψ(3686) → π + π − J/ψ, J/ψ → π + π − π 0 η ′ , η ′ → ηπ + π − is used to determine the systematic uncertainty related to the kinematic fit.We perform a 2-dimensional fit to the J/ψ and η ′ invariant mass spectra in order to extract the number of signal events and calculate the efficiency as a function of χ 2 4C .The difference between data and MC in correspondence of the χ 2 4C cut used in this analysis is taken as systematic uncertainty.
Systematic contributions associated only with the branching fraction are those related to the twodimensional fit of the π + π − π 0 and ηπ + π − invariant masses.In particular, the systematic related to the signal functions are evaluated by means of MC shape distributions for both the ω and η ′ invariant mass spectra.For the background, instead, we change the order of the polynomial function.In both cases, the difference in the number of signal events is taken as systematic uncertainty.We also change the fit range by a step of 5 MeV/c 2 , and the difference in the signal yield is taken as systematic uncertainty.
Table I summarizes all sources of systematic uncertainties, for which the total contribution is obtained as sum of them in quadrature.
Using a sample of 1.31 × 10 9 J/ψ events collected with the BESIII detector, we measure for the first time the branching fraction for the decay J/ψ → ωη ′ π + π − to be (1.12 ± 0.02 ± 0.13) × 10 −3 , where the first uncertainty is statistical and the second systematic.We also search for the X(1835) state in the hadronic J/ψ decay J/ψ → ωX(1835), with X(1835) → η ′ π + π − .No significant signal is observed and the upper limit at 90% C.L. on the branching fraction is determined to be B(J/ψ → ωX(1835), X(1835) → η ′ π + π − ) < 6.2 × 10 −5 .Since the X(1835) state is observed only in radiative J/ψ decays and the branching fraction is measured to be of the order of 10 −4 [2,3,18], authors of Ref. [14] suggest that a smaller branching fraction measured in hadronic J/ψ decays could be an indication of a large gluon component.Authors of Ref. [13] treat X(1835) as a baryonium with sizable gluon content, and estimate a branching ratio of the order of 10 −6 .Unfortunately, our upper limit result is too large to confirm or distinguish among several theoretical interpretations, but it provides the first search for the X(1835) state in J/ψ hadronic decays, which can be further investigated by studying additional hadronic decay modes.

FIG. 3 .
FIG. 3. (color online).One-dimensional projections of two dimensional fit results to the π + π − π 0 (left) and ηπ + π − (right) invariant mass distributions.Blue curves refer to the final fit result, while the other fit components are represented by colored dashed curves: red for ω and η ′ signals, green for ω signal and η ′ background, magenta for ω background and η ′ signal, and black for both ω and η ′ backgrounds.

FIG. 4 .
FIG. 4. (color online).χ 2 -fit result (blue curve) to the background subtracted η ′ π + π − invariant mass spectrum (black dots) extracted as described in the text.Dashed green curve shows the background contribution which is parameterized by means of a third-order polynomial function, while for the signal component we use an efficiency-weighted BW function.

ACKNOWLEDGMENT
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support.This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts Nos.11335008, 11425524, 11625523, 11635010, 11735014; the Chinese Acade my of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts Nos.U1532257, U1532258, U1732263; CAS Key Re-

TABLE I .
Summary of systematic uncertainties.Those items marked with "-" has been taken into account in obtaining the UL on the number of X(1835) signal events.