Evidence for the decay $\Omega_{c}^{0} \to \pi^+\Omega(2012)^- \to \pi^+ (\bar{K}\Xi)^{-}$

Using a data sample of 980~fb$^{-1}$ collected with the Belle detector operating at the KEKB asymmetric-energy $e^+e^-$ collider, we present evidence for the $\Omega(2012)^-$ in the resonant substructure of $\Omega_{c}^{0} \to \pi^+ (\bar{K}\Xi)^{-}$ ($(\bar{K}\Xi)^{-}$ = $K^-\Xi^0$ + $\bar{K}^0 \Xi^-$) decays. The significance of the $\Omega(2012)^-$ signal is 4.2$\sigma$ after considering the systematic uncertainties. The ratio of the branching fraction of $\Omega_{c}^{0} \to \pi^{+} \Omega(2012)^- \to \pi^+ (\bar{K}\Xi)^{-}$ relative to that of $\Omega_{c}^{0} \to \pi^{+} \Omega^-$ is calculated to be 0.220 $\pm$ 0.059(stat.) $\pm$ 0.035(syst.). The individual ratios of the branching fractions of the two isospin modes are also determined, and found to be ${\cal B}(\Omega_{c}^0 \to \pi^+ \Omega(2012)^-) \times {\cal B}(\Omega(2012)^- \to K^-\Xi^0)/{\cal B}(\Omega_{c}^0 \to \pi^+ K^- \Xi^0)$ = (9.6 $\pm$ 3.2(stat.) $\pm$ 1.8(syst.))\% and ${\cal B}(\Omega_{c}^0 \to \pi^+ \Omega(2012)^-) \times {\cal B}(\Omega(2012)^- \to \bar{K}^0 \Xi^-)/{\cal B}(\Omega_{c}^0 \to \pi^+ \bar{K}^0 \Xi^-)$ = (5.5 $\pm$ 2.8(stat.) $\pm$ 0.7(syst.))\%.

The three-body decay Ω(2012) − → (KΞ(1530)) − → (KπΞ) − has been searched for by Belle [10]. No significant signals were found for the Ω(2012) − → (KΞ(1530)) − → (KπΞ) − decay, and the 90% credibility level (C.L.) upper limit on the ratio of Based on this upper limit for the ratio R (KπΞ) − (KΞ) − , the authors in Refs. [11,12] revisited the Ω(2012) − resonance from the molecular perspective, and concluded that the experimental data was still consistent with their molecular picture with a certain set of naturally allowed parameters. On the other hand, the authors of Ref. [13] conducted a dynamical calculation of pentaquark systems with quark contents sssuū in the framework of the chiral quark model [14] and the quark delocalization color screening model [15,16], and concluded that the Ω(2012) − is not suitable to be interpreted as a (KΞ(1530)) − molecular state.
A theoretical study of the Ω(2012) − resonance in the nonleptonic weak decays Ω 0 c → π +K Ξ(1530)(ηΩ) → π + (KπΞ) − and π + (KΞ) − via final-state interactions of theKΞ(1530) and ηΩ pairs has been reported [17]. The authors found that the Ω 0 c → π + (KπΞ) − decay is not well suited to study the Ω(2012) − because the dominant contribution is from the Ω 0 c → π + (KΞ(1530)) − decay at tree level, and this will not contribute to the production of the Ω(2012) − . On the other hand, they predicted that the Ω(2012) − would be visible in the (KΞ) − invariant mass spectrum of the Ω 0 c → π + (KΞ) − decay. It is clear that observing the Ω(2012) − in different production mechanisms can not only further confirm its existence but also yield important information that can increase the understanding of its internal structure.
This analysis is based on data collected at or near the Υ(1S), Υ(2S), Υ(3S), Υ(4S), and Υ(5S) resonances by the Belle detector [18,19] at the KEKB asymmetricenergy e + e − collider [20,21]. The total data sample corresponds to an integrated luminosity of 980 fb −1 [19]. The Belle detector was a large-solid-angle magnetic spectrometer consisting of a silicon vertex detector, a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrellike arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprising CsI(TI) crystals (ECL) located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux return comprising resistive plate chambers located outside the coil was instrumented to detect K 0 L mesons and to identify muons. A detailed description of the Belle detector can be found in Refs. [18,19].
Monte Carlo (MC) simulated signal events are generated using EvtGen [22] to optimize the signal selection criteria and calculate the reconstruction efficiencies; e + e − → cc events are simulated using PYTHIA [23], where one of the two charm quarks hadronizes into an Ω 0 c baryon. Both Ω 0 c → π + Ω(2012) − and Ω(2012) − → K − Ξ 0 /K 0 S Ξ − decays are isotropic in the rest frame of the parent particle. We also generate the signal MC events of Ω 0 c → π + K − Ξ 0 /π + K 0 S Ξ − decays with a phase-space model to estimate the reconstruction efficiencies of the reference modes.
The simulated events are processed with a detector simulation based on GEANT3 [24]. Inclusive MC samples of Υ(1S, 2S, 3S) decays, Υ(4S) s , and e + e − → qq (q = u, d, s, c) at center-of-mass (C.M.) energies of 10.520, 10.580, and 10.867 GeV corresponding to two times the integrated luminosity of data are used to optimize the signal selection criteria and to check possible peaking backgrounds [25].
The impact parameters of the charged particle tracks, except for those of the decay products of K 0 S , Λ, and Ξ − , measured with respect to the nominal interaction point (IP), are required to be less than 0.2 cm perpendicular to the beam direction, and less than 1 cm parallel to it. For the particle identification (PID) of a wellreconstructed charged track, information from different detector subsystems, including specific ionization in the CDC, time measurement in the TOF, and the response of the ACC, is combined to form a likelihood L i [26] for particle species i, where i = K, π, or p. Kaon candidates are defined as those with L K /(L K +L p ) > 0.8 and L K /(L K + L π ) > 0.8, which is approximately 87% efficient. For protons the requirements are L p /(L p + L K ) > 0.2 and L p /(L p + L π ) > 0.2, while for charged pions L π /(L π +L K ) > 0.2 and L π /(L π +L p ) > 0.2; these requirements are approximately 99% efficient.
An ECL cluster is taken as a photon candidate if it does not match the extrapolation of any charged track. The π 0 candidates are reconstructed from two photons having energy exceeding 30 MeV in the barrel or 50 MeV in the endcaps. The reconstructed invariant mass of the π 0 candidate is required to be within 10.8 MeV/c 2 of the π 0 nominal mass [1], corresponding to approximately twice the resolution (σ). To reduce the large combinatorial backgrounds, the momentum of the π 0 candidate is required to exceed 200 MeV/c [2]. Λ candidates are reconstructed from pπ − pairs with a production vertex significantly separated from the IP, and a reconstructed invariant mass within 3.5 MeV/c 2 of the Λ nominal mass [1] (∼3σ).
The Ξ 0 → Λπ 0 reconstruction is performed as follows. The selected Λ candidate is combined with a π 0 to form a Ξ 0 candidate, and then taking the IP as the point of origin of the Ξ 0 , the sum of the Λ and π 0 momenta is taken as the momentum vector of the Ξ 0 candidate. The intersection of this trajectory with the reconstructed Λ trajectory is then found and this position is taken as the decay location of the Ξ 0 baryon. The π 0 is then refit using this location as its point of origin. Only those combinations with the decay location of the Ξ 0 indicating a positive Ξ 0 path length of greater than 2 cm but less than the distance between the Λ decay vertex and the IP are retained [2]. The Ξ − candidate is reconstructed by combining a Λ candidate with a π − . The vertex formed from the Λ and π − is required to be at least 0.35 cm from the IP, to have a shorter distance from the IP than the Λ decay vertex, and to signify a positive Ξ − flight distance [2].
The K 0 S candidates are first reconstructed from pairs of oppositely charged tracks, which are treated as pions, with a production vertex significantly separated from the average IP, and then selected using an artificial neural network [27] based on two sets of input variables [28].
The Ξ 0 and Ξ − are kinematically constrained to their nominal masses [1], and then combined with a K − or K 0 S to form an Ω(2012) − candidate. Finally, the reconstructed Ω(2012) − candidate is combined with a π + to form an Ω 0 c candidate. To improve the momentum resolution and suppress the backgrounds, a vertex fit (the IP is not included in this vertex) is performed for the π + (KΞ) − final state, and then χ 2 vertex < 20 is required, corresponding to an efficiency exceeding 90%.
To reduce combinatorial backgrounds, especially from B-meson decays, the scaled momentum To extract the Ω(2012) − signal events from Ω 0 c decay, we perform a 2D unbinned maximum-likelihood fit to M ( For Ω 0 c → π + K − Ξ 0 and Ω 0 c → π + K 0 S Ξ − decays, the M (π + K − Ξ 0 ) and M (π + K 0 S Ξ − ) distributions are shown in Fig. 3, together with the fitted results. The signal shapes of Ω 0 c are described by double-Gaussian functions, where the parameters are fixed to those obtained from the fits to the corresponding simulated signal distributions. The backgrounds are parametrized by first-order polynomial functions. The fitted Ω 0 c → π + K − Ξ 0 and Ω 0 c → π + K 0 S Ξ − signal yields are 279 ± 27 and 317 ± 32, respectively. The branching fraction ratios are calculated according to the formulae Here, , ǫ π + K − Ξ 0 , and ǫ π + K 0 S Ξ − are the corresponding reconstruction efficiencies, which are obtained from the signal MC simulations and are listed in Table I. The systematic uncertainties are discussed below.
From these fitted signal yields and reconstruction efficiencies, and the intermediate state branching The Ω(2012) − was first observed in data taken at the Υ(1S), Υ(2S), and Υ(3S) resonances [2]. In order to make a statistically independent check of its existence, we exclude these data sets from our sample and repeat the fitting procedure used to produce Fig. 4. The total number of signal events of Ω 0 c → π + Ω(2012) − → π + (KΞ) − is 38.9±11.2 in this reduced data sample which corresponds to an integrated luminosity of 949.5 fb −1 , and the statistical significance of the signal is 4.2σ. We prefer to use the entire data set for our investigation of the branching fractions of the Ω 0 c . The ratio of the branching fraction of Ω 0 c → π + Ω(2012) − → π + (KΞ) − relative to that of Ω 0 c → π + Ω − decay is also calculated from the following formula π + Ω − = 691 ± 29 and ǫ π + Ω − = 10.08% are the number of signal events and detection efficiency of Ω 0 c → π + Ω − decay taken from Ref. [30].
There are several sources of systematic uncertainties for the measurements of branching fraction ratios R 1 , R 2 , and R 3 as listed in Table II, including detection-efficiency-related uncertainties, the statistical uncertainty of the MC efficiency, the modeling of MC event generation, the branching fractions of intermediate states, the Ω(2012) − resonance parameters, the uncertainty in the Ξ 0 mass (as evaluated from the difference between the reconstructed value and the world average value), as well as the overall fit uncertainty.
The detection-efficiency-related uncertainties include those for tracking efficiency (0.35% per track), PID efficiency (1.2% per kaon, 1.0% or 1.2% per pion depending on the specific decay mode), K 0 S selection efficiency (1.7%), as well as π 0 reconstruction efficiency (2.25%). For the measurements of R 1 and R 2 , the detection-efficiency-related sources can cancel. For the measurement of R 3 , the common sources of systematic uncertainties such as Λ selection cancel; to determine the total detection-efficiency-related uncertainties, the above individual uncertainties from different reconstructed modes (σ i/π + Ω − ) are added using the following standard error propagation formula is the weight factor for the i-th (i = 1, 2) mode of Ω 0 c → π + Ω(2012) − → π + (KΞ) − decays. Assuming these sources are independent and adding them in quadrature, the final uncertainty related to the reconstruction efficiency in the measurement of R 3 is 2.2%.
The MC statistical uncertainties are all 1.0% or less. We assume that both Ω 0 c → π + Ω(2012) − and Ω(2012) − → K − Ξ 0 /K 0 S Ξ − decays are isotropic in the rest frame of the parent particle, and a phase space model is used to generate signal events. Since the signal efficiency is independent of the decay angular distributions of π + in Ω 0 c C.M. and K − /K 0 S in Ω(2012) − C.M., the model-dependent uncertainty has negligible effect on efficiency. For the measurement of R 3 , the uncertainties from the B(Ξ 0 → Λπ 0 ), B(Ξ − → Λπ − ), B(K 0 S → π + π − ), and B(π 0 → γγ) are 0.012%, 0.035%, 0.072%, and 0.035% [1], respectively, which are small and neglected. The uncertainties related to the mass and width of Ω(2012) − resonance are considered as diffierent sources, and are estimated by changing the values of resonance mass and width by ±1σ and refitting [2]. The largest differences compared to the nominal fit results are added in quadrature as systematic uncertainty. The uncertainty in the Ξ 0 mass is estimated by comparing the signal yields of Ω 0 c → π + Ω(2012) − → π + K − Ξ 0 /π + (KΞ) − for the case where the reconstructed Ξ 0 mass is fixed at the found peak value versus the case where the mass is fixed at the nominal mass [1].
The systematic uncertainties associated with the fit range, background shape, and mass resolution are considered as follows. To consider the uncertainty due to mass resolution, we enlarge the mass resolution of signal by 10% and take the difference in the number of signal events as the systematic uncertainty. The order of the background polynomial is replaced by a higherorder Chebyshev function and the fit range is changed. The largest deviation compared to the nominal fit results is taken as the systematic uncertainty. For each mode, all the above uncertainties are summed in quadrature to obtain the total systematic uncertainty due to the fit. Finally, the fit uncertainties of signal and reference modes are added in quadrature as total fit uncertainties in the measurements of branching fraction ratios.
Assuming all the sources are independent and adding them in quadrature, the total systematic uncertainties are obtained. All the systematical uncertainties are summarized in Table II.