Observation of $h_1(1380)$ in the $J/\psi \to \eta^{\prime} K\bar K \pi$ Decay

Using $1.31 \times 10^9$ $J/\psi$ events collected by the BESIII detector at the BEPCII $e^+e^-$ collider, we report the first observation of the $h_1(1380)$ in $J/\psi \to \eta^{\prime} h_1(1380)$ with a significance of more than ten standard deviations. The mass and width of the possible axial-vector strangeonium candidate $h_1(1380)$ are measured to be $M = (1423.2 \pm 2.1 \pm 7.3)\mevcc$ and $\Gamma = (90.3 \pm 9.8 \pm 17.5)\mev$. The product branching fractions, assuming no interference, are determined to be $\mathcal{B}(J/\psi \to \eta^{\prime}h_1(1380)) \times \mathcal{B}(h_1(1380) \to K^{*}(892)^{+} K^{-} +c.c.) = (1.51 \pm 0.09 \pm 0.21) \times 10^{-4}$ in $\eta^{\prime}K^+K^-\pi^0$ mode and $\mathcal{B}(J/\psi \to \eta^{\prime}h_1(1380)) \times \mathcal{B}(h_1(1380) \to K^{*}(892)\bar K +c.c.) = (2.16 \pm 0.12 \pm 0.29) \times 10^{-4}$ in $\eta^{\prime}K_S^0K^{\pm}\pi^{\mp}$ mode. The first uncertainties are statistical and the second are systematic. Isospin symmetry violation is observed in the decays $h_1(1380) \to K^{*}(892)^{+} K^{-} +c.c.$ and $h_1(1380) \to K^{*}(892)^{0}\bar K^{0} +c.c.$. Based on the measured $h_1(1380)$ mass, the mixing angle between the states $h_1(1170)$ and $h_1(1380)$ is determined to be $(35.9\pm2.6)^{\circ}$, consistent with theoretical expectations.

The BESIII detector [15] is a magnetic spectrometer operating at BEPCII, a double-ring e + e − collider with center of mass energies between 2.0 and 4.6 GeV. The cylindrical BESIII detector has an effective geometrical acceptance of 93% of 4π. It is composed of a small cell helium-based main drift chamber (MDC) which provides momentum measurements for charged particles, a timeof-flight system (TOF) based on plastic scintillators that is used to identify charged particles, an electromagnetic calorimeter (EMC) made of CsI(Tl) crystals used to measure the energies of photons and electrons, and a muon system (MUC) made of resistive plate chambers (RPC). The momentum resolution of the charged particles is 0.5% at 1 GeV/c in a 1 Tesla magnetic field. The energy loss (dE/dx) measurement provided by the MDC has a resolution of 6%, and the time resolution of the TOF is 80 ps (110 ps) in the barrel (end caps). The photon energy resolution is 2.5% (5%) at 1 GeV in the barrel (end caps) of the EMC.
A GEANT4 based [16] simulation software BOOST [17] is used to simulate the Monte Carlo (MC) samples. An inclusive J/ψ MC sample is generated to estimate the backgrounds. The production of the J/ψ resonance is simulated by the MC event generator KKMC [18], while the decays are generated by BesEvtGen [19] for known decays modes with branching fractions according to the world average values [1], and by the Lundcharm model [20] for the remaining unknown decays. Exclusive MC samples are generated to determine the detection efficiencies of the signal processes and optimize event selection criteria.
For J/ψ → η ′ K + K − π 0 with η ′ → π + π − η, η → γγ and π 0 → γγ, candidate events are required to have four charged tracks with zero net charge and at least four photons. Each charged track is required to be within the polar angle range | cos θ| < 0.93 and must pass within 10 cm (1 cm) of the interaction point in the beam (radial) direction. Information from TOF and dE/dx measurements is combined to form particle identification (PID) confidence levels for the π, K, and p hypotheses, respectively. Each track is assigned the particle type corresponding to the hypothesis with the highest confidence level. Two oppositely charged kaons and pions are required for each event. Photon candidates are reconstructed from isolated clusters of energy deposits in the EMC and must have an energy of at least 25 MeV for barrel showers (| cos θ| < 0.8), or 50 MeV for end cap showers (0.86 < | cos θ| < 0.92). The energy deposited in nearby TOF counters is also included. EMC cluster timing requirements (0 ≤ t ≤ 14 in units of 50 ns) are used to suppress electronics noise and energy deposits unrelated to the event.
For J/ψ → η ′ K 0 S K ± π ∓ with η ′ → π + π − η, η → γγ and K 0 S → π + π − , candidate events are required to have six charged tracks with zero net charge and at least two photons. Each charged track and photon candidate is reconstructed as described above except for the π + π − pair from K 0 S . The K 0 S candidates are reconstructed from all combinations of pairs of oppositely charged tracks, assuming each of the two tracks is a pion. A secondary vertex fit is performed and the fit χ 2 is required to be less than 100. If more than one K 0 S candidate is reconstructed in an event, the one with the minimum |M (π + π − ) − m K 0 S | is selected for further analysis. The K 0 S candidates are further required to satisfy . The other four charged tracks must be identified as three pions and one kaon according to PID information.
To determine the signal yields, a simultaneous unbinned maximum likelihood fit is performed to the M (K + π 0 ) and M (K − π 0 ) spectra for the K + K − π 0 mode. The signal shapes are taken directly from the corresponding MC simulation. The backgrounds are described with fifth-order Chebychev polynomial functions. In the K + K − π 0 mode, the efficiencies of the charged conjugated channels are found to be consistent within the statistics uncertainies, and the number of signal events containing a K * (892) + or a K * (892) − is constrained to be the same in the fit. The fit yields a total of 5066 ± 79 events, as shown in Fig. 2. In the K 0 S K ± π ∓ mode, a similar simultaneous fit is performed to the M (K 0 S π ± ) and M (K ± π ∓ ) spectra. The fit results are of similar quality compared to those in Figs. 2 (b) and (c) and yield 7749 ± 134 K * (892) ± and 8268 ± 137 K * (892) 0 or K * (892) 0 events. Here, the uncertainties are statistical only.
The branching fractions are calculated with B(J/ψ → η ′ K * K + c.c.) = N obs /(N J/ψ × B × ǫ), where N obs is the total number of signal events; N J/ψ is the number of J/ψ decays [13,14]; ǫ is the selection efficiency obtained from a phase space MC simulation; and B is the product of branching fractions of intermediate states. Considering the negligible differences for the final states with and without the h 1 (1380), the signal efficiencies are obtained using exclusive MC samples without the h 1 (1380). The selection efficiencies are 9.3% and 10.3% (9.8%) for the decay modes η ′ K + K − π 0 and η ′ K 0 Here, the uncertainties are statistical only.
To characterize the observed enhancement and determine the signal yields, a simultaneous unbinned maximum likelihood fit is performed to the M (K * (892)K) distributions in the K + K − π 0 and K 0 S K ± π ∓ modes with a common mass and width for the h 1 (1380) signal. The signal shape is parameterized using a relativistic S-wave Breit-Wigner function with a mass-dependent width multiplied by a phase space factor q, where Γ(m) = Γ 0 ( m0 m )( p p0 ) 2l+1 , l = 0 is the orbital momentum, m is the reconstructed mass of K * (892)K, m 0 and Γ 0 are the nominal resonance mass and width, q is the η ′ momentum in the J/ψ rest frame, p is theK momentum in the rest frame of the K * (892)K system, and p 0 is theK momentum in the resonance rest frame at m = m 0 . The large total decay widths of the K * (892) are taken into account by convolving the momentum of theK with the invariant mass distribution of the K * (892) [21]. The mass resolution, fixed at the MC simulated value of 6.0 MeV/c 2 , is taken into account by convolving the signal shape with a Gaussian function. In the fit, the background shape is fixed to that from inclusive MC and its magnitude is allowed to vary. The possible interference between the signal and background is neglected in the fit.
The fit yields a mass of (1423.2 ± 2.1) MeV/c 2 and a width of (90.3 ± 9.8) MeV, as shown in Fig. 5. The fit qualities (χ 2 /ndf, with ndf = 6) are 1.41 for the K + K − π 0 mode and 1.09 for the K 0 S K ± π ∓ mode. The numbers of the fitted h 1 (1380) signal events are 1054 ± 60 and 1195 ± 68 for the K + K − π 0 and K 0 S K ± π ∓ modes, respectively. The product branching fractions are B(J/ψ → η ′ h 1 (1380)) × B(h 1 (1380) → K * (892) + K − + c.c.) = (1.51 ± 0.09) × 10 −4 in the η ′ K + K − π 0 mode and B(J/ψ → η ′ h 1 (1380)) × B(h 1 (1380) → K * (892)K + c.c.) = (2.16 ± 0.12) × 10 −4 in the η ′ K 0 S K ± π ∓ mode. Here, the uncertainties are statistical only. The statistical significance is calculated by comparing the fit likelihoods with and without the h 1 (1380) signal with the change on the number of degrees of freedom considered. The differences due to the fit uncertainties by changing the fit range, the signal shape, or the background shape are included into the systematic uncertainties. In all cases, the significance is found to be larger than 10σ. According to isospin symmetry, B(h 1 (1380) → K * (892) + K − + c.c.) should be equal to B(h 1 (1380) → K * (892) 0K 0 + c.c.). However, considering the mass differences between the charged and neutral K and K * (892) mesons (∆m K = 3.97 MeV/c 2 , and ∆m K * (892) = 4.15 MeV/c 2 [1]) and the fact that the h 1 (1380) state resides near the K * (892)K threshold,  isospin symmetry breaking effects are expected [22,23]. We also fit the K * (892)K invariant mass distribution allowing interference between the h 1 (1380) signal and the non-resonant background. The phase angle is allowed to be free, and the lowest negative likelihood corresponds to constructive interference. The final fit and the individual contribution of each component are shown in Fig. 6. The fitted mass and width of the h 1 (1380) are M = (1441.7 ± 4.9) MeV/c 2 and Γ = (111.5 ± 12.8) MeV. In this analysis, the fit results without considering interference are taken as the nominal values.
Sources of systematic uncertainties for the h 1 (1380) resonance parameters include the mass calibration, parameterizations of the signal and background shapes, fit range and mass resolution. The uncertainty from the mass calibration is estimated using the difference between the measured η ′ mass and the nominal value [1]. The uncertainty due to the mass resolution is estimated by varying the resolution, which is determined from the MC simulation. For the systematic uncertainty associated with the signal shape, an alternative fit is performed by assuming a P -wave between the η ′ and the h 1 (1380). The uncertainty due to the background shape is determined by changing the inclusive MC shape to a third-order polynomial function. The fit range is varied to determine the associated uncertainty. Finally the individual uncertainties are summarized in Table I. Assuming all sources of systematic uncertainty are independent and adding them in quadrature, the total systematic uncertainty is 7.3 MeV/c 2 for the mass, and 17.5 MeV for the width of the h 1 (1380). Systematic uncertainties in the branching fraction measurements come from the uncertainties in the number of J/ψ events, tracking efficiency, particle identifi- cation, photon detection, K 0 S reconstruction, kinematic fit, mass window requirements, fitting procedure, peaking background estimation, and the branching fractions of intermediate state decays.
In Refs. [13,14], the number of J/ψ events is determined with an uncertainty of 0.6%. The uncertainty of the tracking efficiency is estimated to be 1.0% for each pion and kaon from a study of the control samples J/ψ → K 0 S K ± π ∓ and K 0 S → π + π − [24]. With the control samples, the uncertainty from PID is estimated to be 2.0% for each charged pion and kaon. The uncertainty due to photon detection is 1.0% per photon, as obtained from a study of the high-purity control sample of J/ψ → ρπ [25]. For K 0 S reconstruction, the uncertainty is studied with a control sample of J/ψ → K * (892) ± K ∓ → K 0 S K ± π ∓ . A conservative value of 3.5% is taken as the systematic uncertainty. The uncertainty associated with the kinematic fit comes from the inconsistency between data and MC simulation of the track helix parameters and the error matrices. Following the procedure described in Ref. [26], we take the difference between the efficiencies with and without the helix parameter correction as the systematic uncertainty, which is 2.8% in the η ′ K + K − π 0 mode and 1.6% in the η ′ K 0 S K ± π ∓ mode. The uncertainties arising from the π 0 , η, η ′ and K 0 S selection are estimated by varying the mass window requirements. To estimate the uncertainties from the choice of signal shape, background shape and fit range: for K * (892) signal fit, the signal shape is changed from the MC shape to a Breit-Wigner function convolved with a Gaussian function; the background shape is varied from a polynomial function to the MC shape plus the non-η ′ sideband, and the fit range is also varied; for the h 1 (1380) signal fit, the methods are following the h 1 (1380) resonance parameters study described above. The peaking background from the K * (892) is estimated using the non-η ′ and non-π 0 sidebands. The uncertainties associated with the branching fractions of intermediate states are taken from the PDG [1]. The total systematic uncertainties in the branching fractions are determined to be 14.1% and 12.6% for B(J/ψ → η ′ h 1 (1380)) × B(h 1 (1380) → K * (892) + K − + c.c.) and B(J/ψ → η ′ K * (892) + K − + c.c.), respectively, for the η ′ K + K − π 0 final states, and 13.3%, 11.8% and 12.9% , respectively, for η ′ K 0 S K ± π ∓ final states, as summarized in Table II.
The BESIII collaboration thanks the staff of BEPCII, the IHEP computing center and the supercomputing center of USTC for their strong support. This work