Study of $e^+e^- \to \gamma \omega J/\psi$ and Observation of $X(3872) \to \omega J/\psi$

We study the $e^+e^-\to\gamma\omega J/\psi$ process using $11.6 ~\rm fb^{-1}$ $e^+ e^-$ annihilation data taken at center-of-mass energies from $\sqrt{s}=4.008~\rm GeV$ to $4.600~\rm GeV$ with the BESIII detector at the BEPCII storage ring. The $X(3872)$ resonance is observed for the first time in the $\omega J/\psi$ system with a significance of more than $5\sigma$. The relative decay ratio of $X(3872)\to\omega J/\psi$ and $\pi^+\pi^- J/\psi$ is measured to be $\mathcal{R}=1.6^{+0.4}_{-0.3}\pm0.2$, where the first error is statistical and the second systematic (the same hereafter). The $\sqrt{s}$-dependent cross section of $e^+e^-\to\gamma X(3872)$ is also measured and investigated, and it can be described by a single Breit-Wigner resonance, referred to as the $Y(4200)$, with a mass of $4200.6^{+7.9}_{-13.3}\pm3.0~{\rm MeV}/c^2$ and a width of $115^{+38}_{-26}\pm12~{\rm MeV}$. In addition, to describe the $\omega J/\psi$ mass distribution above $3.9~\rm GeV/c^2$, we need at least one additional Breit-Wigner resonance, labeled as $X(3915)$, in the fit. The mass and width of the $X(3915)$ are measured to be $3926.4\pm2.2\pm1.2~\rm MeV/c^2$ and $3.8\pm7.5\pm2.6~\rm MeV$, or $3932.6\pm8.7\pm4.7~\rm MeV/c^2$ and $59.7\pm15.5\pm3.7~\rm MeV$, respectively, depending on the fit models. The resonant parameters of the $X(3915)$ agree with those of the $Y(3940)$ in $B\to K\omega J/\psi$ and of the $X(3915)$ in $\gamma\gamma\to\omega J/\psi$ by the Belle and BABAR experiments within errors.

We study the e + e − → γωJ/ψ process using 11.6 fb −1 e + e − annihilation data taken at center-of-mass energies from √ s = 4.008 GeV to 4.600 GeV with the BESIII detector at the BEPCII storage ring. The X(3872) resonance is observed for the first time in the ωJ/ψ system with a significance of more than 5σ.
The relative decay ratio of X(3872) → ωJ/ψ and π + π − J/ψ is measured to be R = 1.6 +0.4 −0.3 ± 0.2, where the first uncertainty is statistical and the second systematic (the same hereafter). The √ s-dependent cross section of e + e − → γX(3872) is also measured and investigated, and it can be described by a single Breit-Wigner resonance, referred to as the Y (4200), with a mass of 4200.6 +7.9 −13.3 ± 3.0 MeV/c 2 and a width of 115 +38 −26 ± 12 MeV. In addition, to describe the ωJ/ψ mass distribution above 3.9 GeV/c 2 , we need at least one additional Breit-Wigner resonance, labeled as X(3915), in the fit. The mass and width of the X(3915) are determined. The resonant parameters of the X(3915) agree with those of the Y (3940) in B → KωJ/ψ and of the X(3915) in γγ → ωJ/ψ observed by the Belle and BABAR experiments within errors. The X(3872) resonance was first observed by the Belle experiment [1], and confirmed by the CDF [2], D0 [3], BABAR [4], LHCb [5], and BESIII Collaborations [6]. Its unusual properties do not accommodate with a charmonium state, and thus, the X(3872) resonance is widely explained as an unconventional meson candidate [7]. Since the X(3872) mass is near theD 0 D * 0 mass threshold, it is often interpreted as a hadronic molecule by theoretical models [8]. The hadronic molecule model predicts that the decay of X(3872) → ωJ/ψ is sensitive to its internal structure, and a precise measurement of the decay rate would help to determine the ratio of various components that contribute to the X(3872) wave function. While the decay X(3872) → π + π − J/ψ, where π + π − is found to be dominated by a ρ 0 [9], violates the isospin symmetry in the strong interaction, the X(3872) → ωJ/ψ decay process conserves isospin symmetry, and thus such a decay provides an excellent metric for probing its isospin-violation effect. Previously, the Belle and BABAR Collaborations only reported less than 5σ evidences for the X(3872) → ωJ/ψ decay [10]. A solid observation is still lacking and necessary for improved interpretation of this first experimentally observed state potentially composed of four quarks.
The BESIII Collaboration recently reported evidence for the radiative transition Y (4260) → γX(3872) in X(3872) → π + π − J/ψ mode [6]. A charged charmoniumlike state Z c (3900), which is a good candidate for a four-quark state [11], was observed near √ s = 4.26 GeV by BESIII [12] and Belle [13], and later confirmed with CLEO-c's data at √ s = 4.17 GeV [14]. All these observations show potential connections among the X(3872), Y (4260) and Z c (3900) resonances, and strongly hint towards a common underlying nature for them. At the moment, more supportive experimental observation for the transition process Y (4260) → γX(3872) is needed to establish these connections.
The Y (3940) resonance was observed by the Belle Collaboration [15] and confirmed by the BABAR Collaboration [16] in B → KωJ/ψ. Later on, both Belle and BABAR reported observations of the X(3915) resonance in γγ → ωJ/ψ process [17], and it was suggested to be the same resonance as the Y (3940) by the Particle Data Group (PDG) [18]. The underlying nature of the X(3915) is still unclear. It was once considered as a candidate for the χ c0 (2P ) charmonium state. However, such kind of assignment was challenged by a recent Belle observation [19]. Other interpretations, such as a tetraquark [20] or a hadronic molecule [21] are proposed for the X(3915). Morever, a theoretical calculation predicted a 1 ++ tetraquark with mass near 3.95 GeV/c 2 [22]. To make the situation more clear, it is important to provide additional data on the X(3915).
Events with four charged tracks with net zero charge are selected. For each charged track, the polar angle in the mul-tilayer drift chamber 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. Since the π ± from ω decay and ℓ ± from J/ψ decay are kinematically well separated, charged tracks with momenta larger than 1.0 GeV/c in the laboratory frame are assumed to be ℓ ± , and the ones with momenta less than 1.0 GeV/c are assumed to be π ± . The energy deposition of charged tracks in the electromagnetic calorimeter (EMC) is used to separate e and µ. For µ ± candidates, the deposited energy in the EMC are required to be less than 0.35 GeV, while for e ± , it is required to be larger than 1.1 GeV.
Showers identified as good photon candidates must satisfy fiducial and shower-quality requirements. The minimum EMC energy is 25 MeV for barrel showers (| 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 20 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. At least three good photon candidates are required in each event.
To improve the momentum and energy resolutions and to reduce backgrounds, a five-constraint (5C) kinematic fit is applied to an event with the hypothesis e + e − → γπ + π − π 0 ℓ + ℓ − , which constrains the sum of four momentum of the final-state particles to the initial colliding beams, and the mass of two photon combinations to the π 0 world average mass [18]. The χ 2 over number of degree of freedom (ndf) of the kinematic fit is required to be less than 100/5. When there are ambiguities due to multi-combinations or multi-photon candidates in one event, we choose the combination with the smallest χ 2 .
An unbinned maximum-likelihood fit is performed to the M (ωJ/ψ) mass distribution. In the fit, we use as the signal probability-density-function (PDF), the incoherent sum of three Breit-Wigner (BW) resonances (denoted as X(3872), X(3915) and X(3960), respectively), each convolved with a Gaussian resolution function. The X(3872) width is set to 1.2 MeV [18]. The shape and yield of the e + e − → ωχ c0 background component are fixed to the results of the MC simulation. Contribution from other backgrounds is parameterized as a linear shape. The upper panel of Fig. 2 shows the fit results (numerical results are listed in Table I), and the extracted X(3872) mass agrees with its world average value within errors. The obtained X(3872) signal events yield is N sig = 45 ± 9 ± 3. The statistical significance of the X(3872) resonance is estimated to be 5.7σ, by comparing the likelihood difference with or without the X(3872) in the fit, ∆(−2 ln L) = 40.8, and by taking the change of ndf (∆ndf = 3) into account. Possible systematic effects on the X(3872) signal significance, including background shape, ωχ c0 background normalization, X(3872) intrinsic width and mass resolution are investigated, and no sign for a decreased X(3872) significance is observed. The statistical significance of X(3915) and X(3960) are estimated to be 3.1σ and 3.4σ

only.
As an alternative choice, we fit the M (ωJ/ψ) mass distribution only with the X(3872) and X(3915) resonances as signal PDF. The e + e − → ωχ c0 background is handled in the same way as before. The contribution from other backgrounds is parameterized as a linear function and has been fixed to the result from fitting to the data of the J/ψand ω-mass sidebands. The bottom panel of Fig. 2 shows the fit results (c.f. Table I), and the number of fitted X(3872) signal events is N sig = 40 ± 8 ± 3. The statistical significance of X(3872) is estimated to be 5.2σ, and found to be larger than 5.1σ after considering systematic effects from ωχ c0 and linear background normalization, X(3872) intrinsic width and mass resolution. The statistical significance of X(3915) is estimated to be 6.9σ. We test the significance between these two fit scenarios, and find they only differ by 2.5σ.
The production cross section of e + e − → γX(3872) times the branching fraction B[X(3872) → ωJ/ψ] at each CM en-  (3872)] times the branching fraction of X(3872) → ωJ/ψ (left) and π + π − J/ψ (right), and a simultaneous fit to data with a single BW resonance. Dots with error bars are data, the open triangles are an early measurement reported in Ref. [6], and the red curves show the fit results.
Using the same analysis method as described in Ref. [6] and the radiative correction factor in this study, σ · B[X(3872) → π + π − J/ψ] is measured as well. Our result agrees with and supersedes the earlier published BESIII measurement [6], as shown in the right panel of Fig. 3. All the numerical results can be found in Supplemental Materials [24].
A simultaneous maximum-likelihood fit is performed to both the σ · B[X(3872) → ωJ/ψ] and the σ · B[X(3872) → π + π − J/ψ] distributions. We use a single BW resonance, denoted as Y (4200), with free mass and width as PDF. A free parameter R = B[X(3872)→ωJ/ψ] B[X(3872)→π + π − J/ψ] is used to describe the relative decay rate of X(3872) → ωJ/ψ and π + π − J/ψ, which is common for every CM energy. The systematic uncertainty for X(3872), X(3915), and X(3960) mass and width measurements come from the uncertainties in the absolute mass scale, background and resolution effects. The e + e − → γ ISR ψ(3686) → γ ISR ηJ/ψ events with the same event selection (except the ω mass window is replaced by the η mass window) are used as a control sample to calibrate the mass scale. The measured ψ(3686) mass is 3685.4±0.4 MeV/c 2 , and the difference to the ψ(3686) world average mass is 0.8 MeV/c 2 . Backgrounds are varied from a linear shape to a second-order polynomial or by ±1σ for the linear component, and varied by ±1σ for the ωχ c0 component in the fit. The differences in the mass and width measurements  with respect to the nominal results are taken as a systematic uncertainty. The systematic uncertainty of resolution is estimated by varying the Gaussian parameters of the resolution response function by ±1σ in the signal PDF. In both fit scenarios (with and without the X(3960)), the X(3872) mass difference 0.5 MeV/c 2 is taken as a systematic uncertainty due to the fit model. All these contributions are summarized in Table II, and the total uncertainty is calculated by adding the independent contributions in quadrature. The systematic uncertainty for the e + e − → γX(3872) cross section measurement mainly comes from uncertainties in the luminosity measurements, detection efficiency, signal extraction, radiative correction and branching fractions. The integrated luminosities of each data set are measured with large-angle Bhabha scattering events, with an uncertainty of 1.0% [32]. The tracking efficiency is estimated to be 1% per track from a study of the control sample J/ψ → ppπ + π − . The uncertainty due to the photon reconstruction is studied using the J/ψ → π + π − π 0 events, and is found to be 1% for the radiative photon [33]. An additional systematic uncertainty of 1% is assigned to the efficiency of π 0 reconstruction by studying ψ(3686) → π 0 π 0 J/ψ and e + e − → ωπ 0 events. In our event selection, a 5C kinematic fit is used, and the systematic uncertainty related to the kinematic fit is estimated to be 0.8% by using a helix correction method as discussed in Ref. [34].
The number of X(3872) signal events is extracted by fitting the M (ωJ/ψ) distribution, and the difference between the two fit scenarios is 9.5%. The X(3872) intrinsic width is fixed to 1.2 MeV in the signal PDF. Varying the width from 50 keV to 1.2 MeV results in a 5% difference for the X(3872) signal yield. The systematic uncertainty of the ωχ c0 background is estimated by varying the normalization by ±1σ, which will cause a difference of 0.9% in the X(3872) signal yield. The remaining background is parameterized as a linear function. Varying the background shape from linear to a second-order polynomial or the normalization by ±1σ will cause a 3.1% difference for the X(3872) signal yield.
The total systematic uncertainty is calculated to be 12.3% by adding all contributions in quadrature.
The systematic uncertainty for the Y (4200) parameters mainly comes from the uncertainties related to the e + e − CM energy measurement, the parameterization of the fit model, and the cross section measurement. The CM energy of each data set is measured with dimuon events, with ±0.8 MeV uncertainty [35]. Such kind of common uncertainty will shift the Y (4200) line shape globally, and thus, propagate to the Y (4200) mass linearly. In the fit to cross section, the Y (4200) resonance is parameterized as a BW with a constant full width. We also use a BW with a phase-space dependent full width, Γ Φ( √ s) Φ(M) , and the difference is 2.8 MeV/c 2 for the mass, 12 MeV for the width, and 6.5% for Γ ee . The cross section data measured in X(3872) → ωJ/ψ and π + π − J/ψ channels are fitted simultaneously. The common uncertainties of cross section measurements in both channels, including luminosity, tracking, photon detection, radiative correction, kinematic fit, X(3872) intrinsic width, J/ψ mass window, and J/ψ → ℓ + ℓ − branching fraction, will propagate to Γ ee linearly, i.e. 6.9%. The uncommon ones, including π 0 , background, fit model and ω → π + π − π 0 (π 0 → γγ) branching fraction, will affect the R measurement, and the total contribution is 10.9%, by adding them in quadrature.
In summary, we have studied the e + e − → γωJ/ψ process with 11.6 fb −1 data at the BESIII experiment. For the first time, the X(3872) → ωJ/ψ decay was firmly observed with more than 5σ significance, and the X(3872) mass was measured to be 3873.3 ± 1.1 ± 1.0 MeV/c 2 . The relative decay ratio for X(3872) → ωJ/ψ and π + π − J/ψ is measured to be R = 1.6 +0.4 −0.3 ± 0.2, which agrees well with previous measurements within errors [10]. These measurements provide important input for the hadronic molecule interpretation for the X(3872) resonance [8].