Study of open-charm decay and radiative transitions of the X(3872)

The processes $X(3872)\to D^{*0}\bar{D^{0}}+c.c.,~\gamma J/\psi,~\gamma \psi(2S),$ and $\gamma D^{+}D^{-}$ are searched for in a $9.0~\rm fb^{-1}$ data sample collected at center-of-mass energies between $4.178$ and $4.278$ GeV with the BESIII detector. We observe $X(3872)\to D^{*0}\bar{D^{0}}+c.c.$ and find evidence for $X(3872)\to\gamma J/\psi$ with statistical significances of $7.4\sigma$ and $3.5\sigma$, respectively. No evident signals for $X(3872)\to\gamma\psi(2S)$ and $\gamma D^{+}D^{-}$ are found, and upper limits on the relative branching ratio $R_{\gamma \psi} \equiv\frac{\mathcal{B}(X(3872)\to\gamma\psi(2S))}{\mathcal{B}(X(3872)\to\gamma J/\psi)}$ are set at $90\%$ confidence level. Measurements are also reported of the branching ratios for $X(3872)\to D^{*0}\bar{D^{0}}+c.c., ~\gamma\psi(2S),~\gamma J/\psi$, $\gamma D^{+}D^{-}$, as well as the non-$D^{*0}\bar{D^{0}}$ three-body decays $\pi^0D^{0}\bar{D^{0}}$ and $\gamma D^{0}\bar{D^{0}}$, relative to $X(3872)\to\pi^+\pi^- J/\psi$.

In this paper, we report the study of X(3872) → D * 0D0 , γJ/ψ, γψ ′ , and γD + D − using e + e − annihilation data collected with the BESIII detector at center-of-mass (CM) energies ranging from 4.178 to 4.278 GeV. The total integrated luminosity is 9.0 fb −1 . Charge-conjugate modes are implied throughout. A detailed description of the BESIII detector and the upgrade of the time-of-flight system can be found in Refs. [19,20].
Simulated samples of events produced with the GEANT4based [21] Monte Carlo (MC) package, which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiency and to estimate the backgrounds. The simulation includes the beam energy spread and initial-state radiation (ISR) in the e + e − annihilations modeled with the generator KKMC [22]. The signal process e + e − → γX(3872) is generated assuming it is a pure electric dipole (E1) transition, and the subsequent X(3872) decays are generated uniformly in the phase space except X(3872) → γJ/ψ (γψ ′ ) which is generated assuming a pure E1 transition too. The X(3872) resonance is described with a Flatté formula with parameter values taken from Ref. [23]. An inclusive MC sample, which is 40 times the size of the data sample produced at √ s = 4.178 GeV, is used to analyze possible backgrounds. The inclusive MC sample consists of open-charm production, ISR production of vector charmonium(-like) states, and continuum processes incorporated in KKMC [22]. The known decay modes are modeled with EVTGEN [24] using branching fractions taken from the Particle Data Group (PDG) [25], and the remaining unknown decays from charmonium states with LUNDCHARM [26]. Final-state radiation from charged final-state particles are incorporated with the PHOTOS package [27].
Photon and charged-track selections are based on the following criteria.
Showers identified as good photon candidates must satisfy fiducial and shower-quality requirements. The minimum EMC energy is 25 MeV for barrel showers, which are within a polar-angle (θ) range of | cos θ| < 0.80, and 50 MeV for end-cap showers (0.86 < | cos θ| < 0.92). To eliminate showers produced by charged particles, a photon must be separated by at least 10 degrees from any charged track in the EMC. The time information from the EMC is also used to suppress electronic noise and energy deposits unrelated to the event. For each charged track, the polar angle in the MDC must satisfy | cos θ| < 0.93, and the point of closest approach to the e + e − interaction point must be within ±10 cm in the beam direction and within ±1 cm in the plane perpendicular to the beam direction.
When selecting X(3872) → γJ/ψ decays, we use lepton pairs (ℓ + ℓ − , ℓ = e, µ) to reconstruct the J/ψ, while for the X(3872) → γψ ′ selection, we exploit the decays ψ ′ → π + π − J/ψ (J/ψ → ℓ + ℓ − ) and ψ ′ → µ + µ − . The energy deposited in the EMC and the reconstructed momentum in the MDC are used to discriminate the three involved final state particles: pions, muons and electrons. Tracks with momentum less than 1.0 GeV/c are taken as pions while the others are taken as leptons. Lepton candidates with energy deposits in the EMC lower than 0.4 GeV are identified as muons, while those with deposited energy larger than 0.8 GeV are considered to be electrons. The invariant mass of the lepton pair is required to be ∈ [m J/ψ(ψ ′ ) − 0.02, m J/ψ(ψ ′ ) + 0.02] GeV/c 2 for the J/ψ or ψ ′ selection. We use throughout this paper the notation m particle to represent the mass of the specific particle listed in the PDG [25]. In the case of X(3872) decays to charmed mesons, the D * 0 → γD 0 and π 0 D 0 decays are used to reconstruct the D * 0 . The D 0 is reconstructed via its K − π + , K − π + π 0 , and K − π + π + π − decay modes, while the D + is reconstructed via its K − π + π + and K − π + π + π 0 modes. The particle identification (PID) of kaons and pions is based on the dE/dx and TOF information. The probability of the identified particle assumption is required to be larger than the other PID hypotheses.
A vertex fit is performed to ensure that the charged tracks come from a common point. To improve the track momentum and photon energy resolution, and to suppress backgrounds, a kinematic fit is applied to the event with the hypothesis e + e − → γX(3872) that constrains the sum of four-momentum of the final-state particles to those of the initial colliding beams, with the additional constraints on the masses of the π 0 , D 0 , and D ± candidates. When there are ambiguities due to multi-photon candidates in the same event, we choose the combination with the smallest χ 2 from the kinematic fit. The momenta returned by this kinematic fit are used in the subsequent analysis. The χ 2 of the kinematic fit is required to be less than 40 for X(3872) → γJ/ψ, and less than 60 for the other modes. In addition, the χ 2 of the kinematic fit of the hypothesis under study should be smaller than those for hypotheses with extra or fewer photons. For channels with two radiative photons, we denote the photon with larger energy after the kinematic fit as γ H and the other γ L . In these decays, π 0 and η vetoes are imposed on the invariant mass of the photon pair, M (γ L γ H ) to suppress further the possible π 0 and η background, i.e., For the decay X(3872) → γJ/ψ, studies performed on the inclusive MC sample indicate that the dominant backgrounds are Bhabha and di-muon events for J/ψ → e + e − and µ + µ − , respectively. To suppress Bhabha events in the J/ψ → e + e − selection, the cosine of the polar angle of the selected photons, cos θ, is required to be within To determine the number of signal events, a simultaneous fit is performed on the mass spectra of γ H J/ψ with J/ψ → µ + µ − and e + e − . Throughout this paper, we use an unbinned maximum-likelihood fit as the nominal fit method. Assuming that the X(3872) signal is entirely produced via Y (4260) decays whose parameters are taken from Ref. [25], we compute the averaged reconstruction efficiency for the sum of the data samples. The ratio of signal yields for µ + µ − and e + e − modes is constrained to the product of the corresponding BFs and weighted reconstruction efficiencies. In the fit, the signal distributions are described with shapes obtained from the MC simulation, and the backgrounds are described with a second-order Chebyshev polynomial. The distributions of M (γ H J/ψ) as well as the fit results are shown in Fig. 1(a). The statistical significance for X(3872) → γJ/ψ is always greater than 3.5σ, evaluated with a range of alternative background shapes. The significance is calculated by comparing the likelihoods with and without the signal components included, and taking the change in the number of degrees of freedom (ndf) into account. The fit yields 38.8 ± 11.9 and 18.4 ± 5.6 X(3872) → γJ/ψ events, for J/ψ → µ + µ − and e + e − , respectively, corresponding to (20.1 ± 6.2) × 10 2 BF-and efficiency-corrected X(3872) → γJ/ψ events. The goodness of the fit is χ 2 /ndf = 46.9/68 (p = 0.98).
To determine the number of X(3872) → γψ ′ decays, similar fits are performed to the corrected mass M (γπ + π − J/ψ) and M (γψ ′ ) as described above. The distribution of M (γψ ′ ) as well as the fitting results are shown in Fig. 1(b). The fit yields −0.9 ± 4.1 and −0.4 ± 1.6 X(3872) → γψ ′ events with ψ ′ → π + π − J/ψ and µ + µ − , respectively, corresponding to (−1.1 ± 5.2) × 10 2 BF-and efficiency-corrected X(3872) events, and the goodness of the fit is χ 2 /ndf = 45.0/58 (p = 0.89). The UL of the number of produced events (N UL ) is estimated to be 10.0 × 10 2 at the 90% C.L., by finding the solution of where L(N ) is the likelihood distribution in various number of BF-and efficiency-corrected X(3872) events (N ). By sampling the likelihood distributions of N prod (γψ ′ ) and N prod (γJ/ψ), the UL of the R γψ is determined to be 0.59 at the 90% C.L. where the common systematic uncertainties cancel out.
We also perform fits where the signal contribution is fixed to the expectation calculated from previous measurements. We fix the cross-section of e + e − → γX(3872), X(3872) → π + π − J/ψ production to the value reported in Ref. [17] and take the relative ratio B(X(3872)→γψ ′ ) B(X(3872)→π + π − J/ψ) from a global fit [29], or fix X(3872) → γJ/ψ to our own result and take R γψ from an LHCb measurement [14], and from a Belle measurement [16]. The results, also shown in Fig. 1(b), have a goodness-of-fit of χ 2 /ndf = 46.9/59 (p = 0.87), 66.8/59 (p = 0.23), and 46.0/59 (p = 0.89) for the BESIII, LHCb and Belle hypotheses, respectively. Our result for R γψ is 2.8σ lower than that reported by the LHCb collaboration, corresponding to a p-value of 0.0048 calculated with p = We consider the possibility of non-resonant three-body production to the final states γD 0D0 and π 0 D 0D0 , in addition to the well-established decay X(3872) → D * 0D0 . The mass spectra M (γD 0D0 ) and M (π 0 D 0D0 ) are shown in Fig. 2 for the case when M (γπ 0 D) lies in (a) or out of (b) the D * 0 mass region, and when M (π 0 D 0D0 ) lies in this mass range (c). We fit the two mass spectra individually, and determine the signal yields to be N in γD 0D0 = 17.5 ± 6.3, N out γD 0D0 = 4.3 ± 2.2, and N in π 0 D 0D0 = 35.4 ± 7.6, where the superscript indicates the mass range under consideration, and the subscript the final state. Note that there are overlaps between the three-and two-body decays on the M (γ(π 0 )D 0D0 ) distribution, thus the results from the fits are not the true yields in each category. We use these fit results, and an efficiency matrix determined from MC simulation that accounts for migrations of true events between the mass ranges, to determine the number of produced events in each category. The efficiency-corrected yields for nonresonant three-body X(3872) → γD 0D0 production and the decay X(3872) → D * 0D0 (D * 0 → γD 0 ) events are found to be 1.3 ± 0.7 and 20.5 ± 7.4, respectively, and the corresponding yields for X(3872) → π 0 D 0D0 and X(3872) → D * 0D0 (D * → π 0 D 0 ) decays are −0.5 ± 2.3 and 36.1 ± 7.7, respectively. The yields for the three-body decays are not significant and so we set ULs at the 90% C.L. of 8.7 events for X(3872) → γD 0D0 and 2.3 events for X(3872) → π 0 D 0D0 , corresponding to 3.2 × 10 2 and 1.2 × 10 2 BF-and efficiency-corrected events, respectively. Here systematic uncertainties, which are discussed later, are taken into account.
In the next stage of the analysis of the X(3872) → D * 0D0 decays, the combination of γD 0 or π 0 D 0 with an invariant mass closest to the D * 0 nominal mass is taken as the D * 0 candidate. For the channel D * 0 → γD 0 , the mass window for selecting the Fig. 2(d,e) following these requirements, where contributions from non-resonant three-body processes are neglected.
To measure the X(3872) → D * 0D0 signal, a simultaneous fit is performed to the corrected invariant-mass distributions. The ratio of the signal yields for D * 0 → γD 0 and π 0 D 0 is constrained to the product of corresponding BFs and averaged reconstruction efficiencies. The signals are represented by MC simulated shapes, and the backgrounds by ARGUS functions [28], with thresholds fixed at m D * 0 + mD0. The fit results are shown in Fig. 2(d,e). The number of signal events are 20.2 ± 3.6 and 25.5 ± 4.6 from the D * 0 → γD and π 0 D modes, respectively, corresponding to (30.0 ± 5.4) × 10 3 efficiency-and BF-corrected X(3872) → D * 0D0 events. The goodness-of-fit is χ 2 /ndf = 13.0/16 (p = 0.67) after rebinning the data to satify the criterion that there are at least seven events in one bin. Varying the fit range and describing the background with alternative shapes always results in a signal fit that has a statistical significance greater than 7.4σ.
The invariant mass of the γD + D − system following the X(3872) → γD + D − selection is shown in Fig. 2

(f).
No evident X(3872) signal is found. This conclusion is quantified by performing an unbinned maximum-likelihood fit to the invariant-mass distribution, in which the signal component is described by a MC-simulated shape and the background is represented by a second-order polynomial. The goodness-of-fit is χ 2 /ndf = 6.2/5 (p = 0.29). The fit yields (0.0 +0.5 −0.0 ) X(3872) events. The UL on the number of the produced X(3872) → γD + D − is 2.8 × 10 3 events at the 90% C.L., with systematic uncertainties included in the calculation.
The sources of the systematic uncertainties considered in the analysis are listed in Table I. The uncertainties associated with the knowledge of the tracking efficiency (1% per track), photon detection (1% per photon), PID (1% per track), luminosity (1%), π 0 reconstruction (1% per π 0 ) are assigned following the results of earlier BESIII studies [30][31][32]. The uncertainties listed for the modes involving D 0 and D + mesons are calculated considering the correlations between the different decay channels used to reconstruct these states. The uncertainties on the BFs of the D meson, J/ψ, and ψ ′ decays are taken from Ref. [25].
The uncertainty associated with the mass window used to select J/ψ mesons, which arises from a difference in resolution between data and MC, is 1.6% [17], and that for selecting D mesons is 0.7% per D meson [33]. There are various mass windows in our analysis to veto backgrounds.
These background processes, e.g., e + e − → ηJ/ψ, e + e − → π + π − ψ ′ (ψ ′ → π + π − J/ψ), e + e − → γχ c1,2 (χ c1,2 → γJ/ψ), have been studied in other analyses, and the MC simulation found to exhibit a similar mass resolution to the data. For this reason, and because these backgrounds enter our sample at a very low level, no systematic uncertainty is assigned for residual discrepancies. The systematic uncertainty associated with the efficiency of the kinematic fit is estimated using the method discussed in Ref. [34].
To assign the systematic uncertainty associated with the MC events generation, we take the change in reconstruction efficiency when varying the assumption of an E1 transition in e + e − → γX(3872) and X(3872) → γJ/ψ(ψ ′ ) decays to pure phase space. We change the energy-dependent cross-section lineshape of the Y (4260) [25] in the generator to the measured e + e − → γX(3872) [18] lineshape and the difference on the Born cross section is taken as the systematic uncertainty due to the ISR correction. To estimate the uncertainty arising from the limited knowledge of the background shapes, we vary the shapes to different order of polynomials in the fit, and change the fit range at the same time. To incorporate the systematic uncertainty in to the UL, the most conservative result in the various fits is taken as the final result. The effects on the modeling of the signal shapes from discrepancies between the mass resolution in data and MC simulation are negligible.
A summary of the systematic uncertainties is presented in Table I, and the total systematic uncertainty is obtained by adding the individual components in quadrature. TABLE I. Summary of the systematic uncertainties in the crosssection measurements (in %). Symbols "-" the cases where the uncertainties are already incorporated in UL estimations.