Evidence of a structure in $\bar{K}^{0} \Lambda_{c}^{+}$ consistent with a charged $\Xi_c(2930)^{+}$, and updated measurement of $\bar{B}^{0} \to \bar{K}^{0} \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-}$ at Belle

We report evidence for the charged charmed-strange baryon $\Xi_{c}(2930)^+$ with a signal significance of 3.9$\sigma$ with systematic errors included. The charged $\Xi_{c}(2930)^+$ is found in its decay to $K_{S}^{0} \Lambda_{c}^+$ in the substructure of $\bar{B}^{0} \to K^{0}_{S} \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-}$ decays. The measured mass and width are $[2942.3 \pm 4.4 (\rm stat.) \pm 1.5(\rm syst.)]$~MeV/$c^{2}$ and $[14.8 \pm 8.8(\rm stat.) \pm 2.5(\rm syst.)]$~MeV, respectively, and the product branching fraction is $\cal{B}(\bar{B}^{0} \to \Xi_c(2930)^{+} \bar{\Lambda}_{c}^{-}) \cal{B}(\Xi_c(2930)^{+}\to \bar{K}^{0} \Lambda_{c}^{+})=[2.37 \pm 0.51 (\rm stat.)\pm 0.31(\rm syst.)]\times 10^{-4}$. We also measure $\cal{B}(\bar{B}^{0} \to \bar{K}^{0} \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-}) = [3.99 \pm 0.76(\rm stat.) \pm 0.51(\rm syst.)] \times 10^{-4}$ with greater precision than previous experiments, and present the results of a search for the charmonium-like state $Y(4660)$ and its spin partner, $Y_{\eta}$, in the $\Lambda_{c}^{+}\bar{\Lambda}_{c}^{-}$ invariant mass spectrum. No clear signals of the $Y(4660)$ or $Y_{\eta}$ are observed and the 90\% credibility level (C.L.) upper limits on their production rates are determined. These measurements are obtained from a sample of $(772\pm11)\times 10^{6} B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance by the Belle detector at the KEKB asymmetric energy electron-positron collider.

We report evidence for the charged charmed-strange baryon Ξc(2930) with a signal significance of 3.9σ. The charged Ξc(2930) is found in its decay to K 0 S Λc in the substructure of These measurements are obtained from a sample of (772 ± 11) × 10 6 BB pairs collected at the Υ(4S) resonance by the Belle detector at the KEKB asymmetric energy electron-positron collider.
PACS numbers: 13.25.Hw,14.20.Lq,14.40.Rt The study of the excited states of charmed and bottom baryons is important as they offer an excellent laboratory for testing the heavy-quark symmetry of the c and b quarks and the chiral symmetry of the light quarks. At present, the particle data group (PDG) lists ten charmed-strange baryons [1]. Among these, Ξ c (2930) and Ξ c (3123) are relatively less established and evidence for them is poor [1]. For most of these excited Ξ c states the spins and parities have not been determined by experiments due to limited statistics.
Theoretically, the mass spectrum of excited charmed baryons has been computed in many models, including quark potential models [2][3][4][5][6], the relativistic flux tube model [7,8], the coupled channel model [9], the Quantum Chromodynamics (QCD) sum rule [10][11][12][13][14], Regge phenomenology [15], the constituent quark model [16,17], and lattice QCD [18,19]. The strong decays of excited Ξ c baryons have also been studied in many models [20][21][22][23][24][25][26]. In these models, some possible J P assignments of these excited Ξ c have been performed. While many new excited charmed baryons have been discovered in experiments in recent years, and there has been much theoretical work devoted to study the nature of charmed baryon internal structure and quark organization, further effort (and cooperation) from both experimentalists and theorists is needed to make progress in this area.
Very recently, Belle reported the first observation of the Ξ c (2930) 0 charmed-strange baryon with a significance greater than 5σ by study of the substructure in B − → K − Λ + cΛ − c decays [27].
The Belle detector is a large solid angle magnetic spectrometer that consists of a silicon vertex detector, a 50layer 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 located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return yoke located outside the coil is instrumented to detect K 0 L mesons and to identify muons. A detailed description of the Belle detector can be found in Ref. [39]. Simulated signal events with B meson decays are generated using EvtGen [41], while the inclusive decays are generated via PYTHIA [42]. These events are processed by a detector simulation based on GEANT3 [43]. Inclusive Monte Carlo (MC) samples of Υ(4S) → BB (B = B + or B 0 ) and e + e − → qq (q = u, d, s, c) events at √ s = 10.58 GeV, corresponding to more than 5 times the integrated luminosity of the data, are used to check the backgrounds.
In our analysis of B 0 → K 0 Λ + cΛ − c , the K 0 is reconstructed via its decay K 0 S → π + π − , and Λ + c candidates are reconstructed in the Λ + c → pK − π + , pK 0 S , and Λπ + (→ pπ − π + ) decay channels. A Λ + c andΛ − c , together with a K 0 S , are combined to reconstruct a B candidate, with at least one required to have been reconstructed via the pK − π + orpK + π − decay process. For well reconstructed charged tracks, except for those from Λ → pπ − and K 0 S → π + π − decays, the impact parameters perpendicular to and along the beam direction with respect to the nominal interaction point are required to be less than 0.5 cm and 4 cm, respectively, and the transverse momentum in the laboratory frame is required to be larger than 0.1 GeV/c. The information from different detector subsystems including specific ionization in the CDC, time measurements in the TOF and response of the ACC is combined to form the likelihood L i of the track for particle species i, where i = π, K or p [44]. Except for the charged tracks from Λ → pπ − and K 0 S → π + π − decays, tracks with a likelihood ratio R π K = L K /(L K + L π ) > 0.6 are identified as kaons, while tracks with R π K < 0.4 are treated as pions. The kaon (pion) identification efficiency is about 94% (97%), while 5% (3%) of the kaons (pions) are misidentified as pions (kaons) with the selection criteria above. For proton identification, a track with R π p/p = L p/p /(L p/p + L π ) > 0.6 and R K p/p = L p/p /(L p/p + L K ) > 0.6 is identified as a proton/anti-proton with an efficiency of about 98%; fewer than 1% of the pions/kaons are misidentified as protons/anti-protons.
The K 0 S candidates are reconstructed from pairs of oppositely-charged tracks, treated as pions, and identified by a multivariate analysis with a neural network [45] based on two sets of input variables [46]. Candidate Λ baryons are reconstructed in the decay Λ → pπ − and selected if the pπ − invariant mass is within 5 MeV/c 2 (5σ) of the Λ nominal mass [1].
A vertex fit to the B candidates is performed and the one with the minimum χ 2 vertex /n.d.f. from the vertex fit is selected as the signal B candidate if there is more than one B candidate in an event, where n.d.f. is the number of degrees of freedom of the vertex fit. The χ 2 vertex /n.d.f. < 15 is required, providing a selection efficiency above 96%. As the continuum background level is very low, further continuum suppression is not necessary.
The B candidates are identified using the beam-energy constrained mass M bc and the mass difference ∆M B . The beam-energy constrained mass is defined as According to the signal MC simulation, the mass resolution of Λ c candidates is almost independent of the Λ c decay mode. The Λ c signal region is defined as |M Λc − m Λc | < 12 MeV/c 2 (∼ 2.5σ) for all Λ c decay modes illustrated by the central green box in the Fig. 1 (left panel), where m Λc is the nominal mass of the Λ c baryon [1]. To estimate the non-Λ c backgrounds, we define the Λ + c andΛ − c mass sidebands as half of the total number of events in the four red sideband regions minus one quarter of the total number of events in the four blue sideband regions as shown in Fig. 1 (left panel). After applying all selection criteria above, the Dalitz  As the statistical signal significance of each Y state is less than 3σ, assuming that the number of signal events follows a Poisson distribution with a uniform prior probability density function, 90% C.L. Bayesian upper limits on B(B 0 → K 0 Y )B(Y → Λ + cΛ − c ) are determined to be 3.2 × 10 −4 and 4.9 × 10 −4 for Y = Y η and Y (4660), respectively, by solving the equation is the assumed product branching fraction; L(B) is the corresponding maximized likelihood of the data; n Y is the number of Y signal events; and ε Y all = ε Y i × Γ i /Γ(pK − π + ) (ε Y i being the detection efficiency from MC simulation for mode i). To take the systematic uncertainty into account, the above likelihood is convolved with a Gaussian function whose width equals the total systematic uncertainty discussed below.  Fig. 5. The shaded histogram is from the normalized Λ + c andΛ − c mass sidebands, which is consistent with the contributions from normalized e + e − → qq and Υ(4S) → BB generic MC samples. Therefore, the estimate from the normalized Λ + c andΛ − c mass sidebands is taken to represent the total background, neglecting the small possible contribution of background with real Λ + c andΛ − c . A clear Ξ c (2930) ± signal is found. No structure is seen in the Λ + c andΛ − c mass sidebands. An unbinned simultaneous extended maximum likelihood fit is performed to the K 0 S Λ c invariant mass spectra for the total selected signal candidates and the Λ + c and Λ − c mass sidebands. The following components are included in the fit: an S-wave Breit-Wigner (BW) function convolved with a Gaussian function with the phase space factor and efficiency curve included (the mass resolution of the Gaussian function being fixed to 5.36 MeV/c 2 from the signal MC simulation) is taken as the Ξ c (2930) ± signal shape; a broader structure obtained by MC simulation is used to represent the reflection of the Ξ c (2930) ± ; direct three-body B 0 → K 0 S Λ + cΛ − c decays are modeled by the MC-simulated shape distributed uniformly in phase space; a second-order polynomial is used to represent the Λ + c andΛ − c mass-sideband distribution, which is normalized to represent the total background in the signal events in the fit. In the above fit, the signal yields of the Ξ c (2930) ± and the corresponding reflection are constrained to be the same.
The fit results are shown in Fig. 5, where the solid blue line is the best fit, and the solid violet line is the total non-Ξ c (2930) ± backgrounds including the fitted phase space, the reflection of the Ξ c (2930) ± , and the fitted sideband shape. The yields of the Ξ c (2930) ± signal and the phase-space contribution are N Ξc(2930) = 21. The signal significance remains at 3.9σ when convolving the likelihood profile with a Gaussian function of width that equals the total systematic uncertainty from detection efficiency, fitting procedure, and intermediate states' branching fractions. Alternative fits to the K 0 S Λ c mass spectra are performed (a) using a first-order or thirdorder polynomial as the background shape; (b) changing the Ξ c (2930) ± mass resolution by ±10%; and (c) using an energy-dependent BW function as the Ξ c (2930) ± signal shape. The Ξ c (2930) ± signal significance is larger than 3.5σ in all cases. The M K 0 S Λc distribution of the selected data candidates, with fit results superimposed. Dots with error bars are the data, the solid blue line is the best fit, the solid violet line is the total non-Ξc(2930) ± backgrounds, the dotted green line is the fitted phase space and sideband shape, the dotted red line is the fitted sideband shape, the shaded cyan histogram is from the normalized Λ + c andΛ − c mass sidebands .
being the number of accumulated Υ(4S) events and B(Υ(4S) → B 0B0 ) = 0.486 ± 0.006 [1]; for B(Λ + c → pK − π + ), we use the world-average value, (6.35 ± 0.33)% [1]. The efficiency ε Ξc(2930) + all , combined for all three Λ c decay modes, is obtained by ε is the detection efficiency for the i-the mode obtained by fitting M K 0 S Λc spectrum from signal MC with a Ξ c (2930) ± intermediate state, and Γ i is the partial decay width of Λ + c → pK − π + , pK 0 S , and Λπ − , for which we use the world-average values [1]. Here, B(K 0 S → π + π − ) or B(Λ → pπ − ) is included in Γ i for the final states with a K 0 S or a Λ. The systematic uncertainties in the branching fraction measurements are listed below. The uncertainties related to detection efficiency (DER) include those for tracking efficiency (0.35%/track), particle identification efficiency (1.0%/kaon, 0.9%/pion, 3.7%/proton and 3.4%/antiproton), as well as Λ (3.0%) and K 0 S (2.3%) selection efficiencies. Assuming all the above systematic uncertainty sources are independent, the DER uncertainties are summed in quadrature for each decay mode, yielding 5.8-8.6%, depending on the mode. For the four branching fraction measurements, the final DER uncertainties are summed in quadrature over the three Λ c decay modes using weight factors equal to the product of the total efficiency and the Λ c partial decay width. Systematic uncertainties associated with the fitting procedure are estimated by changing the order of the background polynomial, the range of the fit, and the values of the masses and widths of the Y η and Y (4660) by ±1σ, and by enlarging the mass resolution by 10% with the deviations from nominal in the fitted results taken as systematic uncertainties. Uncertainties for B(Λ + c → pK − π + ) and Γ i /Γ(pK − π + ) are taken from Ref. [1]. The final uncertainties on the Λ c partial decay widths are summed in quadrature over the three modes weighted by the detection efficiency. The world average of B(Υ(4S) → B 0B0 ) is (48.6 ± 0.6)% [1], which corresponds to a systematic uncertainty of 1.23%. The systematic uncertainty on N Υ(4S) is 1.37%. The total systematic uncertainties are obtained by adding the uncertainties from all sources in quadrature, and are listed in Table I.
The sources of systematic uncertainties of Ξ c (2930) ± mass and width measurements are calculated by the following method. Half of the correction due to the input and output difference on the Ξ c (2930) ± mass determined from MC simulation is conservatively taken as a system- Here, atic uncertainty. By enlarging the mass resolution by 10%, the difference in the measured Ξ c (2930) width is 0.9 MeV, and this is taken as a systematic uncertainty. By changing the background shape, the differences of 0.5 MeV/c 2 and 1.3 MeV in the measured Ξ c (2930) ± mass and width, respectively, are taken as systematic uncertainties.
The signal-parametrization systematic uncertainty is estimated by replacing the constant total width with a mass-dependent width (2930) ), where Γ 0 t is the width of the resonance, Φ(M K 0 S Λc ) = P/M K 0 S Λc is the phase space factor for an S-wave two-body system (P is the K 0 S momentum in the K 0 S Λ c CMS) and M Ξc(2930) is the K 0 S Λ c invariant mass fixed at the Ξ c (2930) ± nominal fitted mass. The differences in the measured Ξ c (2930) ± mass and width are 0.5 MeV/c 2 and 6.9 MeV, respectively, which are taken as the systematic uncertainties. Assuming all the sources are independent, we add them in quadrature to obtain the total systematic uncertainties on the Ξ c (2930) ± mass and width of 1.6 MeV/c 2 and 7.1 MeV, respectively.
In summary, using (772 ± 11) × 10 6 BB pairs, we perform an updated analysis of B 0 → K 0 Λ + cΛ − c decays. There is evidence at the 3.9σ level of the charmed baryon state Ξ c (2930) ± in the K 0 S Λ c mass spectrum. The We do not perform an angular correlation analysis to determine the spin parity of the Ξ c (2930) ± due to the limited statistics. We are not able to identify the nature of Ξ c (2930) ± with the spin parity not determined since there are many theoretical possibilities. We expect this study to be repeated with a much larger data sample to be collected by the Belle II experiment. There are no significant signals seen in the Λ + cΛ − c mass spectrum. We place 90% C.L. upper limits for the Y (4660) and its theoretically predicted spin partner Y η of B(B 0 → K 0 Y (4660))B(Y (4660) → Λ +