Search for $\Omega(2012)\to K\Xi(1530) \to K\pi\Xi$ at Belle

Using data samples of $e^+e^-$ collisions collected at the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ resonances with the Belle detector, we search for the three-body decay of the $\Omega(2012)$ baryon to $K\pi\Xi$. This decay is predicted to dominate for models describing the $\Omega(2012)$ as a $K\Xi(1530)$ molecule. No significant $\Omega(2012)$ signals are observed in the studied channels, and 90\% credibility level upper limits on the ratios of the branching fractions relative to $K \Xi$ decay modes are obtained.


II. THE DATA SAMPLE AND BELLE DETECTOR
The Belle data used in this analysis correspond to 5.7 fb −1 of integrated luminosity at the Υ(1S) resonance, 24.9 fb −1 at the Υ(2S) resonance, and 2.9 fb −1 at the Υ(3S) resonance.The Belle detector [14,15] is a large solid-angle magnetic spectrometer consisting of a silicon vertex detector (SVD), 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 providing a 1.5 T magnetic field.An iron flux-return yoke instrumented with resistive plate chambers (KLM) located outside the coil is used to detect K 0 L mesons and to identify muons.Large signal Monte Carlo (MC) samples (1 million events for each studied process) are generated using the Evtgen [16] code to simulate the expected signal event topology and estimate the signal detection efficiency.The processes Υ(1S, 2S, 3S) → Ω(2012)+anything → KΞ(1530) + anything → KπΞ + anything are simulated; the mass and width of Ω(2012) are fixed at 2.0124 GeV/c 2 and 6.4 MeV [1], respectively.To assess possible backgrounds arising from the continuum (e + e − → q q with q = u, d, s, c), we generate such events at center-of-mass energies of Υ(1S), Υ(2S), and Υ(3S) resonances using the Lund fragmentation model in PYTHIA [17].Inclusive Υ(1S) and Υ(2S) MC samples, corresponding to four times the luminosity of the data, are produced using PYTHIA and are used to identify possible peaking backgrounds from Υ(1S) and Υ(2S) decays.

A. Event selection
The combined information from the CDC, TOF, and ACC is used to identify charged kaons and pions based on the kaon likelihood ratio, R K = L K /(L K + L π ), where L K and L π are the likelihood values for the kaon and pion hypotheses, respectively.Tracks with R K = L K /(L K + L π ) < 0.4 are identified as pions with an efficiency of 96%, while 8% of kaons are misidentified as pions; tracks with R K > 0.6 are identified as kaons with an efficiency of 95%, while 6% of pions are misidentified as kaons.
An ECL cluster is treated as a photon candidate if it does not match the extrapolation of any charged track reconstructed by the tracking systems (CDC and SVD) into the calorimeter.The π 0 candidates are reconstructed from two photons having energy exceeding 50 MeV in the barrel or 100 MeV in the endcaps.To avoid contamination from neutral hadrons, we reject neutral showers if the ratio of the energy deposited in the central array of 3×3 ECL cells to that deposited in the surrounding array of 5×5 cells is less than 0.8.The π 0 → γγ candidates are also required to have an energy balance parameter is the energy of the first (second) photon in the laboratory frame.To further reduce the combinatorial background, the momentum of the π 0 candidate is required to exceed 200 MeV/c.We define the π 0 signal region as where m π 0 is the π 0 nominal mass [2].For each selected π 0 candidate, a mass-constrained fit is performed to improve its momentum resolution.
The K 0 S candidates are reconstructed via the K 0 S → π + π − decay, and the identification is enhanced by selecting on the outputs of a neural network [18].The network uses the following input variables [19]: the K 0 S momentum in the lab frame, the distance along the z axis between the two track helices at their closest approach, the K 0 S flight length in the r − φ plane, the angle between the K 0 S momentum and the vector joining the interaction point (IP) to the K 0 S decay vertex, the angle between the pion momentum and the lab frame direction in the K 0 S rest frame, the distances of closest approach in the r − φ plane between the IP and the two pion helices, the number of hits in the CDC for each pion track, and the presence or absence of hits in the SVD for each pion track.
Candidate Λ decays are reconstructed from pπ − pairs with a production vertex significantly separated from the IP.For the Ξ − (→ Λπ − ) and Ξ 0 (→ Λπ 0 ) candidates, the vertex fits are performed and the positive Ξ − and Ξ 0 flight distances are required.The selected Ξ − (→ Λπ − ) and Ξ 0 (→ Λπ 0 ) candidates are the same as those in Ref. [1].The Ξ − and Ξ 0 are kinematically constrained to their nominal masses [2], and then combined with a π ± or π 0 to form a Ξ(1530) − or Ξ(1530) 0 candidate.Finally, the selected Ξ(1530) candidate is combined with a K − or K 0 S to form the Ω(2012) candidate.In this last step, a vertex fit is performed for the KπΞ final state to improve the momentum resolutions and suppress the backgrounds, requiring χ 2 vertex < 20, corresponding to an estimated selection efficiency exceeding 95%.Reconstruction spans the Ω(2012 , and Ξ 0 π 0 K − three-body decay modes of Ω(2012).

B. The distributions from signal MC samples
After all event selection requirements, Figure 1 shows the distributions of the ΞπK invariant mass versus the Ξπ invariant mass from signal MC samples.Due to phase space limitations, events at high Ξπ and/or low ΞπK mass are kinematically forbidden.We define the optimized Ξ(1530) signal region as 1.49 GeV/c 2 < M(Ξπ) < 1.53 GeV/c 2 (discussed below), between the blue dashed lines in Fig. 1.
The invariant mass distributions from MC signal simulations of Ξ( 1530 S are shown in Fig. 2. The signal shape of the Ω(2012) is described by a Breit-Wigner (BW) function convolved with a Gaussian function, where the BW mass and width are fixed to 2.0124 GeV/c 2 and 6.4 MeV [1], respectively, and the mass-resolution Gaussian width is determined in the fit.

C. Ξ(1530) signals in Υ(1S, 2S, 3S) data
After imposing our selection criteria, the invariant mass spectra of Ξ(1530) 0 → Ξ − π + , Ξ 0 π 0 , and Ξ(1530) − → Ξ − π 0 , Ξ 0 π − candidates are shown in Figs.3(a-d).Clear We fit all the invariant mass distributions, modelling the Ξ(1530) peaks with the convolution of a BW and a Gaussian function and the background as a second-order polynomial.In the fits, the BW parameters are unconstrained, while the Gaussian widths are fixed according to MC simulations.The fit values are consistent with the world averages within their respective errors [2].For Ξ(1530) 0 → Ξ 0 π 0 , the mass and width of Ξ(1530) 0 are fixed to the Particle Data Group (PDG) values [2] since the signal is not clear due to large combinatorial backgrounds.The results of the fits are listed in Table I.Considering phase space limitations and our finite mass resolution, we require 1.49 GeV/c 2 < M(Ξπ) < 1.53 GeV/c 2 to select Ξ(1530) signals as efficiently as possible, as indicated by the red arrows in Fig. 3.We optimize this requirement by maximizing the figure of merit N sig / N sig + N bkg value with the mode Ω(2012) − → Ξ(1530) 0 (→ Ξ − π + )K − , where N sig is number of fitted signal events in the signal MC sample assuming B(Υ(1S, 2S, 3S) → Ω(2012) − + anything) × B(Ω(2012) − → Ξ(1530) 0 K − ) = 10 −6 and N bkg is the number of estimated background events in the Ω(2012) − signal region using inclusive MC samples.The candidate signal region for the Ξ(1530) coincides with the predicted mass interval from Ref. [10].
After application of the above selection criteria, Fig. 4 shows the invariant mass distributions of Ξ(1530) 0 (→ Ξ − π + /Ξ 0 π 0 )K − and Ξ(1530) − (→ Ξ − π 0 /Ξ 0 π − )K 0 S .From these distributions, no obvious Ω(2012) − signal is observed.The shapes of the Ω(2012) signals in the fits are described by BW functions convolved with Gaussian resolution functions; the background shapes are described by a threshold function.The parameters of the BW functions are fixed to the mass and width of the Ω(2012) [1], and the mass resolutions are fixed to those from fits to signal MC samples (1.5, 2.6, 1.7, and 2.8 MeV for the Ω(2012 , and Ξ(1530) 0 (→ Ξ 0 π 0 )K − decay modes, respectively).The threshold function has the form (M(ΞK) , where the parameters α, c 1 , and c 2 are free; the threshold parameter x is fixed at 1.97 GeV/c 2 from the MC simulations.The yields of Ω(2012) signal events from the unbinned extended maximum-likelihood fits are obtained; they are listed in Table II, together with the reconstruction efficiency, signal significance, and the upper limit at 90% credibility level [20] (C.L.) on the signal yield for each Ω(2012) decay mode.In addition, no peaking backgrounds are found from the inclusive MC samples.
An unbinned extended maximum-likelihood simultaneous fit to all three-body decay modes is now performed.In the simultaneous fit, the ratios of the expected observed Ω(2012) signals between each decay channel are fixed according to Eq. ( 7).The functions used to describe the signal and background shapes are parameterized as before.The fit result is shown in Fig. 5 from the combined Υ(1S, 2S, 3S) data samples, corresponding to a total fit yield of 22.4 ± 14.0.The statistical significance of the Ω(2012) signal is 1.6σ.Finally, we determine where In the calculations, each branching fraction is determined individually.Systematic uncertainties are detailed below.

G. Systematic uncertainties
We now discuss the systematic uncertainties inherent in our measurements of the ratios , and R ΞπK ΞK .These include detection efficiency (tracking efficiency, kaon and pion particle ID, Λ, K 0 S , and π 0 reconstruction), the statistical error in the MC efficiency, the branching fractions of possible intermediate states, the Ω(2012) resonance parameters, any possible bias in reconstructed mass (as evaluated from the difference between the reconstructed Ξ 0 mass and the world average value), as well as the overall fit uncertainty.
Based on a study of D * + → D 0 (→ K 0 S π + π − )π + , the uncertainty in tracking efficiency is taken to be 0.35% per track.The uncertainties in particle identification are studied via a lowbackground sample of D * decay for charged kaons and pions.The studies show uncertainties of 1.3% for each charged kaon and 1.1% for each charged pion.The uncertainty in Λ selection is 3% [21].Differences in K 0 S selection efficiency determined from data and MC simulation give a relation of 1−ε data /ε MC = (1.4±0.3)%[22]; 1.7% is taken as a conservative systematic uncertainty.For π 0 reconstruction, the efficiency correction and systematic uncertainty are estimated from a sample of τ − → π − π 0 ν.We find a 2.25% systematic uncertainty on π 0 reconstruction efficiency.In the measurements of , and R Ξ 0 π 0 K − Ξ 0 K − , the common sources of systematic uncertainties such as Ξ selection cancel; the individual errors are summed in quadrature to obtain the total detection efficiency uncertainty.For the measurement of R ΞπK ΞK , to determine the total detection efficiency, the systematic errors for each final state and the errors from tracking, particle identification, Λ, K 0 S , and π 0 reconstruction are first summed in quadrature to obtain σ i .Then, the total systematic uncertainty for detection efficiency (σ DE ) is determined using standard error propagation as follows: Here, W i is the weight factor of the branching fraction in the i-th (i = 0, 1, 2, 3) mode of the Ω(2012) → ΞπK decay; W j (j = 0, 1) is the relative weight for the j-th mode of Ω(2012) → ΞK decay.The statistical uncertainty in the determination of the efficiency from MC simulations is less than 1.0%.In the calculation of R ΞπK ΞK , only the branching fractions of intermediate states B(K 0 S → π + π − ) and B(π 0 → γγ) are included; the corresponding uncertainties are 0.072% and 0.035% [2], respectively, which are sufficiently small to be neglected.The uncertainty in the Ω(2012) resonance parameters is estimated by toggling the values of resonance mass and width by ±1σ and refitting.The largest differences compared to the nominal fit results are taken as the systematic uncertainties associated with the Ω(2012) resonance parameters.The uncertainty in the Ξ 0 mass is estimated by comparing the numbers of the signal yields of the Ω(2012) for the case where the mass of the reconstructed Ξ 0 is fixed at the found peak value versus the case where the mass is fixed to the nominal mass [2].According to the Ξ(1530)K invariant mass distributions in inclusive MC samples, we find that the threshold mass value falls within the [1.96, 1.98] GeV/c 2 interval.The systematic error in the background parameterization is estimated by comparing the yields when the threshold mass is changed by ±10 MeV/c 2 relative to the nominal fit (for which the threshold is fixed at 1.97 GeV/c 2 ).
All the uncertainties are summarized in Table IV, and, assuming all errors are independent, summed in quadrature to give the total systematic uncertainty.In the absence of any significant observed signals, upper limits at 90% C.L. on the , and R ΞπK ΞK modes are determined by solving the equation where t is the assumed ratio of branching fractions, and F likelihood (t) is the corresponding maximized likelihood of the data.To take into account systematic uncertainties, the likelihood is convolved with a Gaussian function whose width equals the corresponding total systematic uncertainty.Finally, we obtain

2 KFIG. 5 :
FIG.5:The final simultaneous fit result to all three-body Ω(2012) decay modes from the combined Υ(1S, 2S, 3S) data samples.The solid curve is the best fit, and the dashed line represents the backgrounds.

TABLE I :
Mass resolution from MC simulations, and the mass and width for inclusive Ξ(1530) signals from fits to the Belle data.

TABLE IV :
Relative systematic errors (%) on the measurements of R