Observation of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}$ and $\Xi(1530)^{-}\bar\Xi^{+}$

Using 448.1 $\times$ $10^{6}$ $\psi(3686)$ events collected with the BESIII detector at BEPCII, we employ a single-baryon tagging technique to make the first observation of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}$ and $\Xi(1530)^{-}\bar\Xi^{+}$ decays with a statistical significance of more than 10$\sigma$ and 5.0$\sigma$, respectively. The branching fractions are measured to be $\cal{B}$$[\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}] $ = (11.45 $\pm$ 0.40 $\pm$ 0.59) $\times$ $10^{-5}$ and $\cal{B}$$[\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi^{+}]$ = (0.70 $\pm$ 0.11 $\pm$ 0.04) $\times$ $10^{-5}$. The angular distribution parameter for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}$ is determined to be $\alpha$ = 0.40 $\pm$ 0.24 $\pm$ 0.06, which agrees with the theoretical predictions within 1$\sigma$. The first uncertainties are statistical, and the second systematic.

Due to hadron helicity conservation [1,7], the angular distributions for the process e + e − → ψ(3686) → BB are given by where θ B is the angle between one of the baryons and the e + beam direction in the e + e − center-of-mass (CM) system, and the α is the angular distribution parameter, which is widely investigated in theory and experiment [8][9][10]. Many theoretical models, such as those considering quark mass effects [11], and electromagnetic effects [12], predict that the angular distribution parameter obeys α < 1. The BES and BESIII collaborations measured the angular distribution of J/ψ → Σ 0Σ0 , Σ(1385)Σ(1385) and obtained a negative α value, but with poor precision [10,13]. H. Chen et al. [14] noted that the angular distribution parameter for J/ψ and ψ(3686) → BB could be negative when re-scattering effects of BB in heavy quarkonium decays are taken into account. Additional measurements of the α parameter are of interest to confront the various theoretical approaches.
Negative α values were found for the processes J/ψ → Σ 0Σ0 , Σ(1385)Σ(1385), while for other processes α was either measured to be positive, or not measured. The BESIII experiment has a large data sample at the ψ(3686) resonance, which can be used to verify the theoretical models for the process like ψ(3686) → Ξ(1530) −Ξ (1530) + , for which the α value is predicted to be 0.18 and 0.31 [11,12].
Charged tracks are reconstructed in the main drift chamber (MDC) within an angular range of (| cos θ| < 0.93, where θ is the polar angle with respect to the e + beam direction). Information on the specific energy deposition (dE/dx) in the MDC and from the time-of-flight (TOF) counters are combined to form particle identification (PID) confidence levels (CLs) for pion, kaon, and proton hypotheses. Each track is assigned to the particle type with the highest CL. At least two negatively-charged pions and one proton are required. Photons are reconstructed from isolated showers in the electromagnetic calorimeter (EMC). Energy deposited in the nearby TOF counters is included to improve the reconstruction efficiency and energy resolution. Photon energies are required to be greater than 25 MeV in the EMC barrel region (| cos θ| < 0.80) or greater than 50 MeV in the EMC end caps (0.86 < | cos θ| < 0.92). Showers in between these angular regions are poorly reconstructed and are excluded. The EMC shower timing is required to be within the range [0, 700] ns, relative to the event start time, to suppress electronic noise and energy deposits unrelated to the analyzed event. The number of good photon candidates, N γ , must satisfy 2 ≤ N γ ≤ 15.
In order to reconstruct π 0 candidates, a one-constraint (1C) kinematic fit is applied to all γγ combinations, constraining the two-photon invariant mass to the nominal π 0 mass [22]. To suppress non-π 0 backgrounds, only combinations with χ 2 1C < 20 are retained. The Λ candidates are reconstructed from pπ − pairs with an invariant mass within 5 MeV/c 2 of the nominal Λ mass. This interval is determined by optimizing the figure of merit FOM = S √ S+B , where S is the number of signal events and B is the number of background events, based on the MC simulation. A secondary vertex fit [24] is performed on all pπ − combinations; those with χ 2 < 500 are kept for further analysis. To further suppress the background, the decay length of the Λ is required to be positive. In the case of multiple candidates, the one with an unconstrained mass closest to the nominal mass is retained as used in Refs. [13,25,26]. The Ξ candidates are reconstructed by considering all πΛ combinations within 10 MeV/c 2 of the nominal Ξ mass. For Ξ − candidates, a secondary vertexconstrained fit is used, while for both charged and neutral Ξ, only the candidate closest to the nominal mass is retained when there is more than one per event. The decay length of the Ξ − is required to be positive to further suppress the back-grounds. The Ξ(1530) − candidates are reconstructed in the π 0 Ξ − and π − Ξ 0 modes and the candidate closest to the nominal mass is retained when there is more than one per event.
The anti-baryon candidatesΞ + andΞ(1530) + are inferred by the mass recoiling against the selected πΞ system, where E πΞ and p πΞ are the energy and momentum of the selected πΞ system, and E CM is the CM energy. Figure 1 shows the scatter plot of M πΞ versus M recoil πΞ . To determine signal yields, the mass of the πΞ is required to be within 15 MeV/c 2 of the nominal mass of Ξ(1530) − . Our inclusive MC sample reveals that the main background for ψ(3686) → Ξ(1530) −Ξ (1530) + and Ξ(1530) −Ξ+ decays comes from ψ(3686) → π + π − (π 0 π 0 )J/ψ with J/ψ → Ξ −Ξ+ ; it is distributed smoothly in the signal region of M recoil πΞ . Only a few events in the off-peak data sample survive and do not form any obvious peaking structures in the Ξ(1530) signal region of the corresponding M recoil πΞ distribution. Taking into account the normalization of the luminosity and CM energy dependence of the cross section, the contribution from continuum processes is expected to be small and is neglected in the further analysis. There are transition π 0 s with similar momenta in both the baryon and anti-baryon decay chains within the signal events. Incorrect use of these in the Ξ 0 or Ξ(1530) − reconstruction leads to a wrong combination background (WCB).
The signal yields for the two decays ψ(3686) → Ξ(1530) −Ξ (1530) + and Ξ(1530) −Ξ+ are determined by performing an extended maximum likelihood fit to the M recoil πΞ spectrum. In the fit, the signal shapes for the two decays are represented by the simulated MC shape convolved with a Gaussian function to take into account the mass resolution difference between the data and the MC simulation, where the parameters of the Gaussian function are left free but are shared by the two decay modes. The WCB is described by the simulated MC shape, and the corresponding numbers of events are fixed according to the MC simulation. The other remaining backgrounds (Other-Bkg) are found to distribute smoothly in the M recoil πΞ spectrum and are therefore described by a third-order Chebychev function. Figure 2 shows the M recoil πΞ distributions for the Ξ(1530) − andΞ (1530) + tags, respectively, with Ξ and Ξ(1530) peaks evident in each. Including systematic uncertainties, the significance for ψ(3686) → Ξ(1530) −Ξ+ is calculated to be more than 5.0σ for the Ξ(1530) −Ξ mode and its c.c. mode combined. The individual significances are calculated from the change in log likelihood and degrees of freedom with and without the signal in the fit.
The branching fraction is calculated as where X stands for Ξ(1530) −Ξ (1530) + or Ξ(1530) −Ξ+ , N obs is the number of extracted signal events, N ψ(3686) is the total number of ψ(3686) events [16], i runs over the π − Ξ 0 and π 0 Ξ − modes, ǫ i denotes the detection efficiency obtained with the measured α value for both modes, B i denotes the product of branching fractions of Ξ(1530) → πΞ and Ξ → πΛ. Table I Table I. Systematic uncertainties on the branching fractions measurements are mainly due to differences of detection efficiency between data and the MC simulation. The uncertainties associated with the efficiencies of tracking and PID for the pion from the mother particle Ξ(1530) − in the π − Ξ 0 decay mode, are investigated with the control sample J/ψ → ppπ + π − . The uncertainty due to the 1C kinematic fit for the π 0 reconstruction is estimated with the control sample J/ψ → ρπ. The uncertainties related to the Ξ 0 and Ξ − reconstruction efficiency combined with tracking, PID, and the Λ reconstruction efficiencies are estimated using the control sample ψ(3686) → Ξ 0Ξ0 and Ξ −Ξ+ . A detailed description of our methods can be found in Ref. [13,27]. The uncertainties due to the requirements for mass window and decay length of Ξ, Λ are estimated with the control sample J/ψ → Ξ 0Ξ0 and Ξ −Ξ+ . The uncertainty related to the mass window of Ξ(1530) − is estimated by varying the half-width of 15 MeV/c 2 by ±1 MeV/c 2 . The largest difference of the efficiency between data and MC simulation is taken as the systematic uncertainty. The uncertainty due to the signal shape is estimated by changing the nominal signal function to the Breit-Wigner function; the difference of the signal yields is taken as the systematic uncertainty.  The uncertainties due to the assumed polynomial background shape are estimated by alternate fits using a second or a fourthorder Chebychev function. The uncertainty due to the WCB is estimated by comparing the signal yields between the fits with and without the corresponding component included in the fit. The uncertainty related with the detection efficiency due to the modeling of the angular distribution of the baryon pairs, represented by the parameter α, is estimated for the Ξ(1530) −Ξ (1530) + mode by varying the measured α values by 1σ in the MC simulation. For the Ξ(1530) −Ξ+ mode, α is set to zero. The uncertainties due to the branching fractions of the intermediate states, Ξ → πΛ and Λ → pπ are taken to be 0.1% and 0.8% according to the PDG [22]. The uncertainty of the branching fraction of Ξ(1530) → πΞ is taken conservatively according to the branching fraction of Ξ(1530) → γΞ, 4.0% from the PDG [22]. The uncertainties due to the total number of ψ(3686) events (N ψ(3686) ) are determined with inclusive hadronic ψ(3686) decays [16]. The various systematic uncertainties on the branching fraction measurements are summarized in Table II. The total systematic uncertainty is obtained by summing the individual contributions in quadrature.
Systematic issues for the measurement of the α include the determinations of signal yields in cos θ B intervals and the cos θ B fitting procedure. Signal yield systematic uncertainties arise from the fit range, the background shape, signal shape and WCB. These are evaluated with a method similar to the one described above; the resulting differences with respect to the nominal α values are taken systematic uncertainties. The cos θ B fitting uncertainties are estimated by re-fitting the cos θ B distribution with a different binning and fit range. We divide cos θ B into five intervals instead of eight, and the change in α is taken as the systematic uncertainty. We also repeat the fit after altering the cos θ B range to [−0.9, 0.9] or [−0.7, 0.7], with the same bin size as the nominal fit. The largest changes of α with respect to the nominal fit are taken as systematic uncertainties. All the systematic uncertainties for the α measurement are summarized in Table III, where the total systematic uncertainty is the quadratic sum of the contributions. Combined branching fractions and α values are calculated according to the unconstrained averaging introduced in the PDG [22]. Note that the single-baryon recoil mass method leads to some double-counting of the Ξ(1530) −Ξ (1530) + final-state; MC studies indicate this occurs at a rate of about 10%. This is taken into account when combining branching fractions and angular distribution parameters. The systematic uncertainties are weighted to properly account for common and uncommon systematic uncertainties using 1 2 i,j(i =j) , where σ (σ ′ ) is the systematic uncertainty with (without) common sources, and i, j run over the baryon and anti-baryon tags.