Evidence for the singly Cabibbo-suppressed decay Ωc0→Ξ−π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0\to {\Xi}^{-}{\pi}^{+} $$\end{document} and search for Ωc0→Ξ−K+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$\end{document} and Ω−K+ decays at Belle

Using a data sample of 980 fb−1 collected with the Belle detector at the KEKB asymmetric-energy e+e− collider, we study for the first time the singly Cabibbo-suppressed decays Ωc0→Ξ−π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0\to {\Xi}^{-}{\pi}^{+} $$\end{document} and Ω−K+ and the doubly Cabibbo-suppressed decay Ωc0→Ξ−K+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$\end{document}. Evidence for an Ωc0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0 $$\end{document} signal in the Ωc0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0 $$\end{document}→ Ξ−π+ mode is reported with a significance of 4.5σ including systematic uncertainties. The ratio of branching fractions to the normalization mode Ωc0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0 $$\end{document}→ Ω−π+ is measured to beBΩc0→Ξ−π+/BΩc0→Ω−π+=0.253±0.052stat.±0.030syst..\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{B}\left({\Omega}_c^0\to {\Xi}^{-}{\pi}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)=0.253\pm 0.052\left(\textrm{stat}.\right)\pm 0.030\left(\textrm{syst}.\right). $$\end{document} No significant signals of Ωc0→Ξ−K+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$\end{document} and Ω−K+ modes are found. The upper limits at 90% confidence level on ratios of branching fractions are determined to beBΩc0→Ξ−K+/BΩc0→Ω−π+<0.070\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{B}\left({\Omega}_c^0\to {\Xi}^{-}{K}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)<0.070 $$\end{document} andBΩc0→Ω−K+/BΩc0→Ω−π+<0.29.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{K}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)<0.29. $$\end{document}

The Ω 0 c , which has J P = 1 2 + , is the heaviest singly-charmed hadron that decays weakly. The quark content of the Ω 0 c is c{ss}, where the ss pair is in a symmetric state. The theoretical studies of hadronic weak decays of the Ω c baryon have a long history over several decades [8]. Various methods have been developed to describe the nonfactorizable contributions which play an important role in the hadronic decays. There are many theoretical models that have predicted the mass and branching fractions of the Ω 0 c [9][10][11][12][13][14][15][16][17]. However, the range of these predictions is rather wide. For the singly Cabibbo-suppressed (SCS) and doubly Cabibbo-suppressed (DCS) decays of Ω 0 c → Ξ − π + and Ω 0 c → Ξ − K + , the branching fractions have been calculated using the light-front quark model (LFQM) [16], pole model [17], and current algebra (CA) [17], and these are listed in table 1. The studies of Ω 0 c → Ξ − π + and Ω 0 c → Ξ − K + are crucial to test the theoretical

Data sample and the Belle detector
This measurement is based on data recorded 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 asymmetric-energy e + e − collider [20,21]. The data sample corresponds to a total integrated luminosity of 980 fb −1 [19]. The Belle detector is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector, a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return yoke instrumented with resistive plate chambers located outside the coil is used to detect K 0 L mesons and identify muons. A detailed description of the Belle detector can be found in refs. [18,19].
Monte Carlo (MC) signal samples are generated using evtgen [22] to optimize the signal selection criteria and calculate the signal reconstruction efficiency; e + e − → cc events are simulated using pythia [23] model, and Ω 0 c → Ξ − π + /Ξ − K + /Ω − K + decays are generated with a phase space model. The EvtGen generator widely used in Belle experiment can produce a simulated event stream realistic enough to be essentially indistinguishable from real data [24]. Events containing the reference mode, Ω 0 c → Ω − π + , are produced with its known angular distribution [25]. The effect of final-state radiation is taken into account in the simulation using the photos [26] package. The simulated events are processed with a detector simulation based on geant3 [27].

JHEP01(2023)055 3 Selection criteria
Except for the charged tracks from the relatively long-lived Λ, Ξ − , and Ω − decays, all charged tracks are required to originate from the vicinity of the interaction point (IP). The impact parameters perpendicular to (dr) and along the beam direction (|dz|) with respect to the IP are required to be less than 0.2 cm and 1 cm, respectively. For the particle identification (PID) of a 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 [28] for particle species i. Tracks with R K = L K /(L K + L π ) < 0.4 are identified as pions with an efficiency of 95.5%, while 8.0% of kaons are misidentified as pions; tracks with R K > 0.6 are identified as kaons with an efficiency of 89.4%, while 4.2% of pions are misidentified as kaons. The PID (misidentified) efficiency is evaluated using the signal MC data sample, where the PID of the tracks are known. It is defined as the number of tracks selected under a PID hypothesis divided by the number of tracks before any PID requirements with the same (opposite) PID hypothesis.
The Λ candidates are reconstructed via pπ − pairs. The distance of the Λ decay vertex with respect to the IP is greater than 0.35 cm with an efficiency of 99.5%. For Ξ − → Λπ − , the vertex formed from the Λ and π − is required to be at least 0.35 cm from the IP with an efficiency of 94.1%, and to be a shorter distance from the IP than the Λ decay vertex [29,30]. These efficiencies are obtained by comparing the numbers of MC signal events with and without applying these selection requirements. For Ω − → ΛK − , the flight directions of Λ and Ω − candidates, which are reconstructed from their production and decay vertices after performing vertex and mass constraint fits to the full decay chain, are required to be within five degrees of their momentum directions in both 3D space and the plane perpendicular to the z-axis in the laboratory frame [7], where the z-axis is opposite to the e + beam direction. The values of χ 2 from vertex fits are required to be less than 20 optimized by maximizing the figure-of-merit FoM = N sig / N sig + N bkg , where N sig is the number of expected Ω 0 c signal events using MC simulations assuming B(Ω 0 04 × 10 −1 and 1.06 × 10 −2 , respectively, from table 1, and N bkg is the number of estimated background events in the Ω 0 c signal region using normalized generic MC samples. The Ξ − π + , Ξ − K + , Ω − K + , and Ω − π + candidates are combined to form an Ω 0 c candidate and its daughter tracks fitted to a common vertex. For the reference mode of Ω 0 c → Ω − π + , selection criteria for signal candidates are the same as those applied in ref. [7] except for the x p requirement (see below).
To reduce combinatorial backgrounds, especially from B meson decays, the scaled momentum x p = p * /p * max is required to be greater than 0.65. Here, p * is the momentum of Ω 0 c in the e + e − center-of-mass (C.M.) frame, and p *

JHEP01(2023)055
For Ω 0 c → Ξ − π + , using the values above, the ratio of branching fractions to the normalization mode of Ω 0 c → Ω − π + is measured to be For Ω 0 c → Ξ − K + and Ω 0 c → Ω − K + , since the signal significances are less than 3σ, we compute 90% confidence level (C.L.) upper limits x UL on the signal yields and branching fraction ratios by solving the equation x UL 0 L(x)dx/ +∞ 0 L(x)dx = 0.90, where x is the assumed signal yield or branching fraction ratio, and L(x) is the corresponding maximized likelihood of the fit to the assumption.

Systematic uncertainties
Systematic uncertainties on the branching fraction ratios are summarized in table 3. The sources of uncertainty are reconstruction efficiency, branching fractions of intermediate states, the statistical uncertainty in the determination of efficiency, the generator model, Ω 0 c resonance parameters, the uncertainty associated with the fitting procedure, the statistical uncertainty of signal yield in the reference mode of Ω 0 c → Ω − π + . The reconstruction-efficiency-related uncertainties include those from tracking efficiency and the PID efficiency. The uncertainties from tracking efficiency and part of the PID uncertainties are canceled in the ratio to the normalization mode Ω 0 c → Ω − π + . The uncertainties in PID are studied via low-background sample of D * + → D 0 (→ K − π + )π + for charged kaons and pions. The studies show uncertainties of 1.1% for each charged kaon and 0.9% for each charged pion. The systematic uncertainties from the same particles are added linearly, considering a total correlation, while the ones from different particles are summed in quadrature, as there is no correlation.
As the Ω − branching fraction uncertainty is cancelled in the ratio to the normalization mode, only uncertainties of B(Ξ − → Λπ − ) (0.035%) and B(Ω − → ΛK − ) (1.0%) [1] are included for the Ω 0 c → Ξ − π + and Ω 0 c → Ξ − K + modes. Using simulated signal events of all the decay modes, the statistical uncertainty in the reconstruction efficiency can be calculated as ∆ ε = ε(1 − ε)/N , where ε is the reconstruction efficiency after all the event selections, and N is the total number of generated events. The fractional uncertainty ∆ ε /ε is less than 1.0% in all modes. Simulated Ω 0 c decays are generated by the phase space model. To estimate the uncertainties from MC modeling of the signals, signal MC samples are also generated with an angular distribution of 1 − cos 2 θ or 1 + cos 2 θ at MC-generation level, where θ is the angle between the Ξ − or Ω − momentum vector and boost direction of the Ω 0 c from the laboratory frame in the Ω 0 c rest frame. The largest differences on the efficiencies between the phase space and 1 ± cos 2 θ are 7.6%, 11.2%, and 5.0% for Ω 0 c → Ξ − π + , Ξ − K + , and Ω − K + , and these are included in uncertainties due to the generator model.
In fitting to the M (Ξ − π + ) and M (Ω − π + ) distributions, we enlarge the mass resolution by 0.2 MeV/c 2 as indicated by the differences in the mass resolutions between signal MC and data in Ω 0 c → Ξ − π + and Ω − π + modes and take the difference of the signal yield as the systematic uncertainty of the mass resolution. And for M (Ξ − K + ) and M (Ω − K + )  Table 3. Relative uncertainties on branching fraction ratio measurements (%). The σ syst eff , σ syst MC , σ syst GM , σ syst B , σ syst resonance , and σ syst fit denote uncertainties from reconstruction efficiency, the statistical uncertainty in the determination of efficiency, generator model, branching fractions of intermediate states, Ω 0 c resonance parameters, and fitting procedure, respectively. The σ stat signal and σ stat ref represent the statistical uncertainties in the signal yields from the signal mode and reference mode Ω 0 c → Ω − π + . The σ syst sum , σ stat sum , and σ sum are total systematic uncertainty, total statistical uncertainty, and total uncertainty, respectively. distributions, we enlarge the mass resolution by 10% since the MC simulation is known to reproduce the resolution of mass peaks within 10% over a large number of different systems. In fitting to the M (Ξ − π + ) distribution, we change the Ω 0 c mass to the nominal value [1] and take the difference of the signal yield as the systematic uncertainty of mass central value. In fitting to the M (Ξ − K + ) and M (Ω − K + ) distributions, we change the Ω 0 c mass by ±1σ. The total systematic uncertainty due to Ω 0 c resonance parameters is obtained by summing the uncertainties of resolution and mass in quadrature for Ω 0 c → Ξ − π + . We estimate the systematic uncertainties associated with the fitting procedure by changing the order of the background polynomial, the range of the fit, and the number of bins, and take the deviations of signal yields from the nominal fitted results as systematic uncertainties. The total uncertainty is obtained by summing the uncertainties from Ω 0 c → Ξ − π + and the reference mode of Ω 0 c → Ω − π + in quadrature. The statistical uncertainty of the fitted signal yield for the reference mode (N Ω − π + = 606 ± 29) is 4.8%. The statistical uncertainty of the fitted signal yield for the signal mode (N Ξ − π + = 208 ± 41) is 19.7%. We add them in quadrature to obtain the total statistical uncertainties.

JHEP01(2023)055
Finally, assuming all the sources are independent and adding them in quadrature, the total uncertainties on the branching fraction ratio measurements are calculated and these are listed in table 3.
To estimate the signal significance of the Ω 0 c → Ξ − π + decay after considering the systematic uncertainties, alternative fits to the Ξ − π + mass spectrum are performed by: (a) using a first-order or third-order polynomial for background shape; (b) enlarging the Ω 0 c mass resolution by 0.2 MeV/c 2 ; and (c) changing the Ω 0 c mass to the nominal value [1]. The Ω 0 c signal significance is larger than 4.5σ in all cases. The ratio of branching fractions to the normalization mode of Ω 0 c → Ω − π + is measured to be In the calculations of upper limits, the systematic uncertainties are taken into account in two steps. First, when we study the additive systematic uncertainties from resonance