The singly charmed baryon is composed of a charm quark and two light quarks. Charmed baryon spectroscopy provides an excellent ground for studying the dynamics of light quarks in the environment of a heavy quark and offers an excellent laboratory for testing heavy-quark or chiral symmetry of the heavy or light quarks, respectively. Although many new excited charmed baryons have been discovered by BaBar, Belle, CLEO and LHCb in the past two decades [1], and many efforts have been made to identify the quantum numbers of these new states and understand their properties, we do not yet have a fully phenomenological model that describes the complicated physics of this sector [2, 3]. Identification and observation of new members in the charmed-baryon family will provide more information to address these open issues.

The \(\Xi _{c}(2930)\) charmed-strange baryon has been reported only in the analysis of \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) by BaBar [4], where they claim a signal in the \(K^-\Lambda _{c}^+\) invariant mass distribution with a mass of \([2931 \pm 3(\mathrm{stat.}) \pm 5(\mathrm{syst.})]\) MeV/\(c^{2}\) and a width of \([36 \pm 7(\mathrm{stat.}) \pm 11 (\mathrm{syst.})]\) MeV. However, neither the results of the fit to their spectrum nor the significance of the signal were given; the Particle Data Group (PDG) lists it as a “one star” state [1]. Despite the weak experimental evidence for the \(\Xi _{c}(2930)\) state, it has been taken into account in many theoretical models, including the chiral quark model [5], the light-cone Quantum Chromodynamics (QCD) sum rule [6], the \(^3P_0\) mode [7], the constituent quark model [8, 9], and the heavy-hadron chiral perturbation theory [10].

Belle has previously studied \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) decays [11] with a data sample of \(386\times 10^{6}~B\bar{B}\) pairs but the distributions of the intermediate \(K\Lambda _c\) systems have not been presented. The full Belle data sample of \((772\pm 11)\times 10^{6} B\bar{B}\) pairs permits an improved study of \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) and a test for the existence of the \(\Xi _{c}(2930)\).

The same B decay mode can be used to study the \(\Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) invariant mass. In this system, Belle has previously observed a charmonium-like state, the Y(4630), in the initial state radiation (ISR) process \(e^+e^-\rightarrow \gamma _\mathrm{ISR} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) [12] with a measured mass of \([4634^{+8}_{-7}(\mathrm{stat.})^{+5}_{-8}(\mathrm{syst.})]\) MeV/\(c^2\) and a width of \([92^{+40}_{-24}(\mathrm{stat.}) ^{+10}_{-21}(\mathrm{syst.})]\) MeV. As this mass is very close to that of the Y(4660) observed by Belle in the ISR process \(e^+e^- \rightarrow \gamma _\mathrm{ISR}\pi ^+\pi ^-\psi '\) [13, 14], many theoretical explanations assume they are the same state [15,16,17]. In Refs. [18, 19], where the Y(4660) is modeled as an \(f_{0}(980)\psi '\) bound state, the authors predict that it should have a spin partner—a \(f_{0}(980)\eta _{c}(2S)\) bound state denoted as the \(Y_{\eta }\)—with a mass and width of \((4613 \pm 4)\) MeV/\(c^2\) and around 30 MeV, respectively, and a large partial width into \(\Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) [17, 19].

In this Letter, we perform an updated measurement of \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) [20] and observe the \(\Xi _{c}(2930)^0\) signal with a significance of 5.1\(\sigma \). This analysis is based on the full data sample collected at the \(\Upsilon (4S)\) resonance by the Belle detector [21, 22] at the KEKB asymmetric energy electron–positron collider [23, 24]. Simulated signal events with B meson decays are generated using EvtGen [25], while the inclusive decays are generated via PYTHIA [26]. These events are processed by a detector simulation based on GEANT3 [27]. Inclusive Monte Carlo (MC) samples of \(\Upsilon (4S)\rightarrow B \bar{B}\) (\(B=B^+\) or \(B^0\)) and \(e^+e^- \rightarrow q \bar{q}\) (\(q=u,~d,~s,~c\)) events at \(\sqrt{s}=10.58\) GeV are used to check the backgrounds, corresponding to more than 5 times the integrated luminosity of the data.

We reconstruct the \(\Lambda _c^+\) via the \(\Lambda _c^+\rightarrow p K^- \pi ^+\), \(pK_{S}^{0}\), \(\Lambda \pi ^{+}\), \(pK_{S}^{0}\pi ^{+}\pi ^{-}\), and \(\Lambda \pi ^{+}\pi ^{+}\pi ^{-}\) decay channels. When a \(\Lambda _c^+\) and \(\bar{\Lambda }_{c}^{-}\) are combined to reconstruct a B candidate, at least one is required to have been reconstructed via the \(p K^+ \pi ^-\) or \(\bar{p} K^- \pi ^+\) decay process. For charged tracks, information from different detector subsystems, including specific ionization in the central drift chamber, time measurements in the time-of-flight scintillation counters and the response of the aerogel threshold Cherenkov counters, is combined to form the likelihood \({\mathcal L}_i\) for species i, where \(i=\pi \), K, or p [28]. Except for the charged tracks from \(\Lambda \rightarrow p \pi ^{-}\) and \(K_{S}^{0} \rightarrow \pi ^{+} \pi ^{-}\) decays, a track with a likelihood ratio \(\mathcal {R}_K^{\pi } = \mathcal {L}_K/(\mathcal {L}_K + \mathcal {L}_\pi )> 0.6\) is identified as a kaon, while a track with \(\mathcal {R}_K^{\pi }<0.4\) is treated as a pion [28]. With this selection, the kaon (pion) identification efficiency is about 94% (98%), while 5% (2%) of the kaons (pions) are misidentified as pions (kaons). A track with \(\mathcal {R}^\pi _{p/\bar{p}} = \mathcal {L}_{p/\bar{p}}/(\mathcal {L}_{p/\bar{p}}+\mathcal {L}_\pi ) > 0.6\) and \(\mathcal {R}^K_{p/\bar{p}} = \mathcal {L}_{p/\bar{p}}/(\mathcal {L}_{p/\bar{p}}+\mathcal {L}_K) > 0.6\) 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 \(K_{S}^{0}\) candidates are reconstructed from pairs of oppositely-charged tracks, treated as pions, and identified by a multivariate analysis with a neural network [29] based on two sets of input variables [30]. Candidate \(\Lambda \) baryons are reconstructed in the decay \(\Lambda \rightarrow p \pi ^-\) and selected if the \(p \pi ^-\) invariant mass is within 5 MeV/\(c^2\) (5\(\sigma \)) of the \(\Lambda \) nominal mass [1].

We perform a vertex fit to signal B candidates. If there is more than one B signal candidate in an event, we select the one with the minimum \(\chi ^{2}_\mathrm{vertex}\) from the vertex fit. We require \(\chi ^{2}_\mathrm{vertex}<50\) with a selection efficiency above 96%. As the continuum background level is very low, continuum suppression is not necessary.

The B candidates are identified using the beam-energy constrained mass \(M_\mathrm{bc}\) and the mass difference \(\Delta M_{B}\). The beam-energy constrained mass is defined as \(M_\mathrm{bc} \equiv \sqrt{E_\mathrm{beam}^{2}/c^2 - (\sum \vec {p}_{i})^2}/c\), where \(E_\mathrm{beam}\) is the beam energy and \(\vec {p}_{i}\) are the three-momenta of the B-meson decay products, all defined in the center-of-mass system (CMS) of the \(e^+e^-\) collision. The mass difference is defined as \(\Delta M_{B} \equiv M_{B} - m_{B}\), where \(M_{B}\) is the invariant mass of the B candidate and \(m_{B}\) is the nominal B-meson mass [1].

Figure 1 shows clear evidence of \(\Lambda _c^+\) and \(\bar{\Lambda }_c^-\) in the distribution of \(M_{\bar{\Lambda }_{c}^{-}}\) versus \(M_{\Lambda _{c}^{+}}\) (left panel) from the selected \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) data candidates in the B signal region of \(|\Delta M_B| < 0.018\,\mathrm{GeV}/c^2\) and \(M_\mathrm{bc} > 5.27\,\mathrm{GeV}/c^2\) (\(\sim 3\sigma \)), illustrated by the green box in the right panel’s distribution of \(\Delta M_B\) versus \(M_\mathrm{bc}\). The \(\Lambda _{c}\) signal region (the central green box in the left panel) is defined as \(|M_{\Lambda _{c}} - m_{\Lambda _{c}} |< 10\) MeV/\(c^{2}\) (\( \sim 2.5\sigma \)), where \(m_{\Lambda _{c}}\) is the nominal mass of the \(\Lambda _{c}\) baryon [1]. As the mass resolution of \(\Lambda _{c}\) candidates is almost independent of the \(\Lambda _{c}\) decay mode, according to the signal MC simulation, the same requirement is placed on all \(\Lambda _{c}\) decay modes. The non-\(\Lambda _c\) background in the \(\Lambda _c\) signal region is estimated 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 of the left panel.

Fig. 1
figure 1

Signal-enhanced distribution of \(M(\bar{\Lambda }_{c}^{-})\) versus \(M(\Lambda _{c}^{+})\) (left panel) and of \(\Delta M_{B}\) versus \(M_\mathrm{bc}\) (right panel) from the selected \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) candidates, summing over all five reconstructed \(\Lambda _{c}\) decay modes. Each panel shows the events falling in the solid green signal region of the other panel. The dashed red and blue boxes in the left panel show the \(\Lambda _c\) sideband regions used for the estimation of the non-\(\Lambda _c\) background (see text)

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To obtain the \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }^{-}_{c}\) signal yields, we perform an unbinned two-dimensional (2D) simultaneous extended maximum likelihood fit to the \(\Delta M_{B}\) versus \(M_\mathrm{bc}\) distributions for the five reconstructed \(\Lambda _{c}\) decay modes. The model used to fit the \(M_\mathrm{bc}\) distribution is a Gaussian function for the signal shape plus an ARGUS function [31] for the background. The model for the \(\Delta M_{B}\) distribution is the sum of a Gaussian function for the signal plus a first-order polynomial for the background. The Gaussian resolutions are fixed to the values from the fits to the individual MC distributions, and the relative signal yields among the five final states is fixed according to the relative branching fraction between the final states and the detection acceptance and efficiency of the intermediate states.

Figure 2 shows the projections of the fit superimposed on the \(\Lambda _c\)-signal-enhanced \(M_\mathrm{bc}\) and \(\Delta M_{B}\) distributions, summing over all five reconstructed \(\Lambda _{c}\) decay modes. We observe \(153 \pm 14\) signal events with a signal significance above 10\(\sigma \), and extract the branching fraction of \(\mathcal{B}(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-})=[4.80 \pm 0.43(\mathrm{stat.})] \times 10^{-4}\).

Fig. 2
figure 2

The \(\Lambda _c\)-signal-enhanced distributions of (a) \(M_\mathrm{bc}\) in the \(\Delta M_{B}\) signal region and (b) \(\Delta M_{B}\) in the \(M_\mathrm{bc}\) signal region for \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }^{-}_{c}\), combining five exclusive final states. The dots with error bars are data, the solid blue curves are the best-fit projections to the distributions and the dashed magenta lines are the fitted backgrounds

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The Dalitz distribution of the reconstructed \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) candidates is shown in Fig. 3. A vertical-band enhancement near \(M(K^-\Lambda _{c}^+)\sim 2.93\) GeV/\(c^2\) is observed; no signal band is apparent in the \(M(\Lambda _c^+ \bar{\Lambda }_c^-)\) horizontal direction nor in the \(M(K^- \bar{\Lambda }_c^-)\) diagonal direction.

Fig. 3
figure 3

Dalitz distribution of reconstructed \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) candidates in the B signal region. The black dots are data; the shaded region is the MC simulated phase-space distribution

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The B-signal-enhanced \(K^{-} \Lambda _{c}^{+}\) mass spectrum is shown in Fig. 4. The shaded histogram is from the normalized \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass sidebands, and the dot-dashed line is the sum of the contributions from normalized \(e^+e^-\rightarrow q\bar{q}\) and \(\Upsilon (4S) \rightarrow B \bar{B}\) generic MC samples. Since they are consistent, we take the \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass sidebands to represent the total background, neglecting the small possible contribution of background with real \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\). A clear \(\Xi _c(2930)\) signal is observed. No structure is seen in the \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass sidebands, nor in the generic MC samples, nor in the wrong-sign-combination distribution of \(K^- \bar{\Lambda }_{c}^{-}\).

An unbinned simultaneous extended maximum likelihood fit is performed to the \(K^-\Lambda _{c}^+\) invariant mass spectra for selected B- and \(\Lambda _c\)-signal events and the \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass sidebands. 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 Gaussian function being fixed to 4.46 MeV/\(c^2\) from the signal MC simulation) is taken as the \(\Xi _c(2930)\) signal shape. Direct three-body B decays are modeled by the shape corresponding to \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) MC-simulated decays distributed uniformly in phase space. A second-order polynomial is used to represent the \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass-sideband distribution, which is normalized to represent the total background in the signal events in the fit.

The fit results are shown in Fig. 4. The fitted mass and width of the \(\Xi _{c}(2930)\) are \(M_{\Xi _{c}(2930)} = [2928.9 \pm 3.0(\mathrm{stat.})]\) MeV/\(c^{2}\) and \(\Gamma _{\Xi _{c}(2930)} = [19.5 \pm 8.4(\mathrm stat.)]\) MeV, where a fit bias of 1.4 MeV/\(c^2\) on the \(\Xi _{c}(2930)\) mass, determined using MC simulation, has been corrected. The yields of the \(\Xi _{c}(2930)\) signal and the phase-space contribution are \(N_{\Xi _{c}} = 61 \pm 16 \) and \(N_\mathrm{phsp} = 79 \pm 19\).

To estimate the \(\Xi _{c}(2930)\) signal significance, we use an ensemble of simulated experiments to estimate the probability that background fluctuations alone would produce signals as significant as that seen in the data. We generate \(K^-\Lambda _{c}^+\) mass spectra according to the shape of the non-\(\Xi _{c}(2930)\) background distribution (the dashed red line in Fig. 4), with each spectrum containing 192 events which corresponds to the total data entries in Fig. 4. We fit each spectrum as we do the real data, searching for the most significant fluctuation, and thus obtain the distribution of \(-2\ln (L_0/L_\mathrm{max})\) for these simulated background samples. We perform a total of 13.2 million simulations and found 3 trials with a \(-2\ln (L_0/L_\mathrm{max})\) value greater than or equal to the value obtained in the data. The resulting p value is \(2.27\times 10^{-7}\), corresponding to a significance of \(5.1\sigma \).

Fig. 4
figure 4

The \(M_{K^-\Lambda _{c}^+}\) 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 dashed red line is the total non-\(\Xi _{c}(2930)\) backgrounds, the dotted green line is the phase space contribution, the shaded cyan histogram is from the normalized \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass sidebands, and the dot-dashed magenta line is the sum of the MC-simulated contributions from the normalized \(e^+e^-\rightarrow q\bar{q}\) and \(\Upsilon (4S) \rightarrow B \bar{B}\) generic-decay backgrounds

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The product branching fraction of \(\mathcal{B}(B^{-} \rightarrow \Xi _{c}(2930) \bar{\Lambda }_{c}^{-})\) \(\mathcal{B}(\Xi _{c}(2930) \rightarrow K^{-} \Lambda _{c}^{+})=[1.73 \pm 0.45(\mathrm stat.)]\times 10^{-4}\) is calculated as \(N_\mathrm{total}^{\Xi _{c}}/[2N_{B^{\pm }}\varepsilon _\mathrm{all}^{\Xi _{c}} \mathcal{B}(\Lambda _{c}^{+} \rightarrow p K^{-} \pi ^{+})^{2}]\), where \(N_\mathrm{total}^{\Xi _{c}}\) is the fitted \(\Xi _{c}(2930)\) signal yield; \(N_{B^\pm }=N_{\Upsilon (4S)}\mathcal{B}(\Upsilon (4S)\rightarrow B^+B^-)\) (\(N_{\Upsilon (4S)}\) is the number of accumulated \(\Upsilon (4S)\) events and \(\mathcal{B}(\Upsilon (4S)\rightarrow B^+B^-)=0.514\pm 0.006\) [1]); \(\mathcal{B}(\Lambda _c^+\rightarrow p K^- \pi ^+)=(6.35\pm 0.33)\%\) is the world-average branching fraction for \(\Lambda _c^+\rightarrow p K^- \pi ^+\) [1]; \(\varepsilon _\mathrm{all}^{\Xi _{c}} = \sum \varepsilon _{i}^{\Xi _{c}} \times \Gamma _{i}/\Gamma (p K^{-} \pi ^{+})\) (i is the \(\Lambda _c\) decay-mode index, \(\varepsilon _{i}^{\Xi _{c}}\) is the detection efficiency from MC simulation and \(\Gamma _{i}\) is the partial decay width of \(\Lambda _{c}^{+} \rightarrow p K^{-} \pi ^{+},~pK_{S}^0,~\Lambda \pi ^{-},~pK_{S}^0 \pi ^{+} \pi ^{-}\), and \(\Lambda \pi ^{-} \pi ^{+} \pi ^{-}\) [1]). Here, \(\mathcal{B}(K_{S}^0 \rightarrow \pi ^+\pi ^-) \) or \(\mathcal{B}(\Lambda \rightarrow p \pi ^{-})\) is included in \(\Gamma _{i}\) for the final states with a \(K_{S}^0\) or a \(\Lambda \).

The \(M_{\Lambda _{c}^{+}\bar{\Lambda }_{c}^{-}}\) spectrum is shown in Fig. 5, in which no clear \(Y_{\eta }\) or Y(4660) signals is evident. An unbinned extended maximum likelihood fit is applied to the \(\Lambda _{c}^{+}\bar{\Lambda }_{c}^{-}\) mass spectrum to extract the signal yields of the \(Y_{\eta }\) and Y(4660) in B decays. In the fit, the signal shape of the \(Y_{\eta }\) or Y(4660) is obtained from MC simulation directly with the input parameters \(M_{Y_{\eta }} = 4616\) MeV/\(c^{2}\) and \(\Gamma _{Y_{\eta }} = 30\) MeV for \(Y_{\eta }\) [17], and \(M_{Y(4660)} = 4643\) MeV/\(c^{2}\) and \(\Gamma _{Y(4660)} = 72\) MeV for Y(4660) [1]; a third-order polynomial is used to describe all other contributions. The fit results are shown in Figs. 5(a) and (b) for the \(Y_{\eta }\) and Y(4660), respectively. From the fits, we have \((10\pm 23)\) \(Y_{\eta }\) signal events with a statistical signal significance of \(0.7\sigma \), and \((-10 \pm 26)\) Y(4660) signal events.

As the statistical signal significance of each Y state is less than \(3\sigma \), 90% C.L. Bayesian upper limits on \(\mathcal{B}(B^{-} \rightarrow K^{-} Y)\mathcal{B}( Y \rightarrow \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-})\) are determined to be \(1.2 \times 10^{-4}\) and \(2.0 \times 10^{-4}\) for \(Y=Y_\eta \) and Y(4660), respectively, by solving the equation \(\int _{0}^{\mathcal{B}^\mathrm{up}}\mathcal {L}(\mathcal{B})d\mathcal{B}/\int _0^{+\infty }\mathcal {L}(\mathcal{B}) d\mathcal{B}= 0.9\), where \(\mathcal{B}= n_{Y}/[2\varepsilon _\mathrm{all}^{Y} N_{B^{\pm }}\mathcal{B}(\Lambda _{c}^{+} \rightarrow p K^{-} \pi ^{+})^{2}]\) is the assumed product branching fraction; \(\mathcal {L}(\mathcal{B})\) is the corresponding maximized likelihood of the data; \(n_{Y}\) is the number of Y signal events; and \(\varepsilon _\mathrm{all}^{Y} = \sum \varepsilon _{i}^{Y} \times \Gamma _{i}/\Gamma (p K^{-} \pi ^{+})\) (\(\varepsilon _{i}^{Y}\) being the total 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.

Fig. 5
figure 5

The \(\Lambda _{c}^{+}\bar{\Lambda }_{c}^{-}\) invariant mass spectra in data with (a) \(Y_{\eta }\) and (b) Y(4660) signals included in the fits. The solid blue lines are the best fits and the dotted red lines represent the backgrounds. The shaded cyan histograms are from the normalized \(\Lambda _{c}^{+}\) and \(\bar{\Lambda }_{c}^{-}\) mass sidebands

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There are several sources of systematic uncertainties in the branching fraction measurements. The detection efficiency relevant (DER) errors include those for tracking efficiency (0.35%/track), particle identification efficiency (1.9%/kaon, 0.9%/pion, 2.4%/proton and 2.0%/anti-proton), as well as \(\Lambda \) (3.0%) and \(K_{S}^{0}\) (1.7%) selection efficiencies. Assuming all the above systematic error sources are independent, the DER errors are summed in quadrature for each decay mode, yielding 5.8–8.3%, depending on the mode. For the four branching fraction measurements, the final DER errors are summed in quadrature over the five \(\Lambda _c\) decay modes using weight factors equal to the product of the total efficiency and the \(\Lambda _c\) partial decay width. We estimate the systematic errors associated with the fitting procedure by changing the order of the background polynomial, the range of the fit, and the values of the masses and widths of the \(Y_{\eta }\) and Y(4660) by \(\pm 1\sigma \), and by enlarging the mass resolution by 10%; the deviations from nominal in the fitted results are taken as systematic errors. Uncertainties for \(\mathcal{B}(\Lambda _c^+ \rightarrow p K^- \pi ^+)\) and \(\Gamma _{i}/\Gamma (p K^{-} \pi ^{+})\) are taken from Ref. [1]. The final errors on the \(\Lambda _c\) partial decay widths are summed in quadrature over the five modes with the detection efficiency as a weighting factor. The world average of \(\mathcal{B}(\Upsilon (4S)\rightarrow B^+B^-)\) is \((51.4\pm 0.6)\%\) [1], which corresponds to a systematic uncertainty of 1.2%. The systematic uncertainty on \(N_{\Upsilon (4S)}\) is 1.37%. Assuming all sources listed in Table 1 to be independent, the total systematic uncertainties on the branching fraction measurements are summed in quadrature.

Table 1 Relative systematic uncertainties (%) in the branching fraction measurements. Here, \(\mathcal{B}_1\equiv \mathcal{B}(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-})\), \(\mathcal{B}_2 \equiv \mathcal{B}(B^{-} \rightarrow \Xi _{c}(2930) \bar{\Lambda }_{c}^{-})\mathcal{B}(\Xi _{c}(2930) \rightarrow K^- \Lambda _{c}^+)\), \(\mathcal{B}_3 \equiv \mathcal{B}(B^- \rightarrow K^- Y_{\eta })\mathcal{B}( Y_{\eta } \rightarrow \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-} )\), and \(\mathcal{B}_4 \equiv \mathcal{B}(B^- \rightarrow K^- Y(4660))\mathcal{B}( Y(4660) \rightarrow \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-} )\)
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The following systematic uncertainties are considered for the \(\Xi _{c}(2930)\) mass and width. Half of the correction due to the fitting bias on the \(\Xi _{c}(2930)\) mass is taken conservatively as a systematic error. By enlarging the mass resolution by 10%, the difference in the measured \(\Xi _{c}(2930)\) width is 0.7 MeV, which is taken as a systematic error. By changing the background shape, the differences of 0.3 MeV/\(c^2\) and 0.9 MeV in the measured \(\Xi _{c}(2930)\) 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 of \(\Gamma _{t} = \Gamma ^{0}_{t}\times \Phi (M_{K^-\Lambda _{c}^+})/\Phi (M_{\Xi _c(2930)})\), where \(\Gamma _{t}^{0}\) is the width of the resonance, \(\Phi (M_{K^-\Lambda _c^+}) = P/M_{K^-\Lambda _c^+}\) is the phase space factor for an S-wave two-body system (P is the \(K^-\) momentum in the \(K^- \Lambda _c^+\) CMS) and \(M_{\Xi _c(2930)}\) is the \(K^- \Lambda _c^+\) invariant mass fixed at the \(\Xi _{c}(2930)\) nominal mass. The differences in the measured \(\Xi _{c}(2930)\) mass and width are 0.2 MeV/\(c^2\) and 5.3 MeV, respectively, which are taken as the systematic errors. Adding an additional possible resonance with mass and width free at around 2.85 GeV/\(c^{2}\) into the fit to the \(M(K^- \Lambda _c^+)\) spectra, the fit gives \(M_{\Xi _{c}(2930)} = (2929.3 \pm 3.1)\) MeV/\(c^{2}\) and \(\Gamma _{\Xi _{c}(2930)} = (21.7 \pm 9.3)\) MeV; the differences of \(+0.4\) MeV/\(c^{2}\) and \(+2.2\) MeV from the mass and width found without the additional resonance, respectively, are taken as systematic errors. An alternative fit to the \(M(K^- \Lambda _c^+)\) spectra with interference between the \(\Xi _{c}(2930)\) and the phase-space contribution included gives \(M_{\Xi _{c}(2930)} = (2917.0 \pm 5.5)\) MeV/\(c^{2}\) and \(\Gamma _{\Xi _{c}(2930)} = (13.8 \pm 6.9)\) MeV; the differences of \(-11.9\) MeV/\(c^{2}\) and \(-5.7\) MeV from the nominal mass and width, respectively, are taken as systematic errors. Assuming all the sources are independent, we add them in quadrature to obtain the total systematic uncertainties on the \(\Xi _{c}(2930)\) mass and width of \(^{+0.9}_{-12.0}\) MeV/\(c^2\) and \(^{+5.9}_{-7.9}\) MeV, respectively.

In summary, using \((772 \pm 11) \times 10^{6}~B\bar{B}\) pairs, we perform an updated analysis of \(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\). In the \(K^- \Lambda _{c}^+\) mass spectrum, the charmed baryon state \(\Xi _{c}(2930)^0\) is clearly observed for the first time with a statistical significance greater than 5\(\sigma \). The measured mass and width are \(M_{\Xi _{c}(2930)} =(2928.9 \pm 3.0 ^{+0.9}_{-12.0})\) MeV/\(c^{2}\) and \(\Gamma _{\Xi _{c}(2930)} = (19.5 \pm 8.4^{+5.9}_{-7.9})\) MeV. The branching fraction is \(\mathcal{B}(B^{-} \rightarrow K^{-} \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-})=(4.80 \pm 0.43 \pm 0.60)\times 10^{-4} \), which is consistent with the world average value of \((6.9 \pm 2.2) \times 10^{-4}\) [1] but with much-improved precision. We measure the product branching fraction \(\mathcal{B}(B^{-} \rightarrow \Xi _{c}(2930) \bar{\Lambda }_{c}^{-})\mathcal{B}(\Xi _{c}(2930) \rightarrow K^- \Lambda _{c}^{+})=(1.73 \pm 0.45 \pm 0.21) \times 10^{-4}\), where the first error is statistical and the second systematic. Because of the limited statistics, we do not attempt analysis of angular correlations to determine the spin parity of the \(\Xi _{c}(2930)^0\), however we expect that this will be possible with the much larger data sample which will be collected with the Belle II detector. Without this information, we are not able to identify the quark content of this state as there are many theoretical possibilities. There are no significant signals seen in the \(\Lambda _{c}^{+} \bar{\Lambda }_{c}^{-}\) mass spectrum. We place 90% C.L. upper limits for the Y(4660) and its theoretically predicted spin partner \(Y_{\eta }\) of \(\mathcal{B}(B^- \rightarrow K^- Y(4660))\mathcal{B}( Y(4660) \rightarrow \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-})<1.2\times 10^{-4}\) and \(\mathcal{B}(B^- \rightarrow K^- Y_{\eta })\mathcal{B}( Y_{\eta } \rightarrow \Lambda _{c}^{+} \bar{\Lambda }_{c}^{-})<2.0 \times 10^{-4}\) [32].

We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, the National Institute of Informatics, and the PNNL/EMSL computing group for valuable computing and SINET5 network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council; Austrian Science Fund under Grant No. P 26794-N20; the National Natural Science Foundation of China under Contracts No. 10575109, No. 10775142, No. 10875115, No. 11175187, No. 11475187, No. 11521505, No. 11575017 and No. 11761141009; the Chinese Academy of Science Center for Excellence in Particle Physics; Key Research Program of Frontier Sciences, Chinese Academy of Science, Grant No. QYZDJ-SSW-SLH011; the Ministry of Education, Youth and Sports of the Czech Republic under Contract No. LTT17020; the Carl Zeiss Foundation, the Deutsche Forschungsgemeinschaft, the Excellence Cluster Universe, and the VolkswagenStiftung; the Department of Science and Technology of India; the Istituto Nazionale di Fisica Nucleare of Italy; National Research Foundation (NRF) of Korea Grants No. 2014R1A2A2A01005286, No. 2015R1A2A2A01003280, No. 2015H1A2A1033649, No. 2016R1D1A1B01010135, No. 2016K1A3A7A09005603, No. 2016R1D1A1B02012900; Radiation Science Research Institute, Foreign Large-size Research Facility Application Supporting project and the Global Science Experimental Data Hub Center of the Korea Institute of Science and Technology Information; the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Education and Science of the Russian Federation and the Russian Foundation for Basic Research; the Slovenian Research Agency; Ikerbasque, Basque Foundation for Science and MINECO (Juan de la Cierva), Spain; the Swiss National Science Foundation; the Ministry of Education and the Ministry of Science and Technology of Taiwan; and the U.S. Department of Energy and the National Science Foundation.