Observation of $\Xi_{c}(2930)^0$ and updated measurement of $B^{-} \to K^{-} \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-}$ at Belle

We report the first observation of the $\Xi_{c}(2930)^0$ charmed-strange baryon with a significance greater than 5$\sigma$. The $\Xi_{c}(2930)^0$ is found in its decay to $K^- \Lambda_{c}^+$ in $B^{-} \to K^{-} \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-}$ decays. The measured mass and width are $[2928.9 \pm 3.0(\rm stat.)^{+0.9}_{-12.0}(\rm syst.)]$ MeV/$c^{2}$ and $[19.5 \pm 8.4(\rm stat.) ^{+5.9}_{-7.9}(\rm syst.)]$ MeV, respectively, and the product branching fraction is ${\cal B}(B^{-} \to \Xi_{c}(2930)^0 \bar{\Lambda}_{c}^{-}) {\cal B}(\Xi_{c}(2930)^0 \to K^- \Lambda_{c}^{+})=[1.73 \pm 0.45(\rm stat.) \pm 0.21(\rm syst.)]\times 10^{-4}$. We also measure ${\cal B}(B^{-} \to K^{-} \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-}) = [4.80 \pm 0.43(\rm stat.) \pm 0.60(\rm syst.)] \times 10^{-4}$ with improved precision, and 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 $Y(4660)$ nor its spin partner 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.


decays.
The measured mass and width are [2928.9 ± 3.0(stat.) +0.9 We also measure B(B − → K − Λ + (C.L.) upper limits on their production rates are determined. 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 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 Ξ c (2930) charmed-strange baryon has been reported only in the analysis of B − → K − Λ + cΛ − c by BaBar [4], where they claim a signal in the K − Λ + c invariant mass distribution with a mass of [2931 ± 3(stat.) ± 5(syst.)] MeV/c 2 and a width of [36 ± 7(stat.) ± 11(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 Ξ 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 3 P 0 mode [7], the constituent quark model [8,9], and the heavy-hadron chiral perturbation theory [10].
Belle has previously studied B − → K − Λ + cΛ − c decays [11] with a data sample of 386 × 10 6 BB pairs but the distributions of the intermediate KΛ c systems have not been presented. The full Belle data sample of (772 ± 11) × 10 6 BB pairs permits an improved study of B − → K − Λ + cΛ − c and a test for the existence of the Ξ c (2930).
The same B decay mode can be used to study the Λ + cΛ − 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 − → γ ISR Λ + −24 (stat.) +10 −21 (syst.)] MeV. As this mass is very close to that of the Y (4660) observed by Belle in the ISR process e + e − → γ ISR π + π − ψ ′ [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)ψ ′ bound state, the authors predict that it should have a spin partner-a f 0 (980)η c (2S) bound state denoted as the Y η -with a mass and width of (4613 ± 4) MeV/c 2 and around 30 MeV, respectively, and a large partial width into Λ + cΛ − c [17,19]. In this Letter, we perform an updated measurement of [20] and observe the Ξ c (2930) 0 signal with a significance of 5.1σ. This analysis is based on the full data sample collected at the Υ(4S) resonance by the Belle detector [21] at the KEKB asymmetric energy electron-positron collider [22]. Simulated signal events with B meson decays are generated using Evt-Gen [23], while the inclusive decays are generated via PYTHIA [24]. These events are processed by a detector simulation based on GEANT3 [25]. 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 are used to check the backgrounds, corresponding to more than 5 times the integrated luminosity of the data.
We reconstruct the Λ + c via the Λ + c → pK − π + , pK 0 S , Λπ + , pK 0 S π + π − , and Λπ + π + π − decay channels. When a Λ + c andΛ − c are combined to reconstruct a B candidate, at least one is required to have been reconstructed via the pK + π − orpK − π + 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 L i for species i, where i = π, K, or p [26]. Except for the charged tracks from Λ → pπ − and K 0 S → π + π − decays, a track with a likelihood ratio R π K = L K /(L K + L π ) > 0.6 is identified as a kaon, while a track with R π K < 0.4 is treated as a pion [26]. 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 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 [27] based on two sets of input variables [28]. 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].
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 χ 2 vertex from the vertex fit. We require χ 2 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 bc and the mass difference ∆M B . The beam-energy constrained mass is defined as where E beam is the beam energy and 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 where M B is the invariant mass of the B candidate and m B is the nominal B-meson mass [1]. Figure 1 shows where m Λc is the nominal mass of the Λ c baryon [1]. As the mass resolution of Λ c candidates is almost independent of the Λ c decay mode, according to the signal MC simulation, the same requirement is placed on all Λ c decay modes. The non-Λ c background in the Λ 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. To obtain the B − → K − Λ + cΛ − c signal yields, we perform an unbinned two-dimensional (2D) simultaneous extended maximum likelihood fit to the ∆M B versus M bc distributions for the five reconstructed Λ c decay modes. The model used to fit the M bc distribution is a Gaussian function for the signal shape plus an ARGUS func-tion [29] for the background. The model for the ∆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 Λ c -signal-enhanced M bc and ∆M B distributions, summing over all five reconstructed Λ c decay modes. We observe 153 ± 14 signal events with a signal significance above 10σ, and extract the branching fraction of  The B-signal-enhanced K − Λ + c mass spectrum is shown in Fig. 4. The shaded histogram is from the normalized Λ + c andΛ − c mass sidebands, and the dot-dashed line is the sum of the contributions from normalized e + e − → qq and Υ(4S) → BB generic MC samples. Since they are consistent, we take the Λ + c andΛ − c mass sidebands to represent the total background, neglecting the small possible contribution of background with real Λ + c and Λ − c . A clear Ξ c (2930) signal is observed. No structure is seen in the Λ + c andΛ − c mass sidebands, nor in the generic MC samples, nor in the wrong-sign-combination distribution of K −Λ− c . An unbinned simultaneous extended maximum likelihood fit is performed to the K − Λ + c invariant mass spectra for selected B-and Λ c -signal events and the Λ + c andΛ − To estimate the Ξ 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 − Λ + c mass spectra according to the shape of the non-Ξ 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 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 max ) value greater than or equal to the value obtained in the data. The resulting p value is 2.27 × 10 −7 , corresponding to a significance of 5.1σ.
The product branching fraction of B(Λ + c → pK − π + ) = (6.35 ± 0.33)% is the worldaverage branching fraction for Λ + is the detection efficiency from MC simulation and Γ i is the partial decay width of Λ + c → pK − π + , pK 0 S , Λπ − , pK 0 S π + π − , and 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 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. 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 Λ (3.0%) and K 0 S (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 Λ c decay modes using weight factors equal to the product of the total efficiency and the Λ 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 η and Y (4660) by ±1σ, and by enlarging the mass resolution by 10%; the deviations from nominal in the fitted results are taken as systematic errors. Uncertainties for B(Λ + c → pK − π + ) and Γ i /Γ(pK − π + ) are taken from Ref. [1]. The final errors on the Λ c partial decay widths are summed in quadrature over the five modes with the detection efficiency as a weighting factor. The world average of B(Υ(4S) → B + B − ) is (51.4 ± 0.6)% [1], which corresponds to a systematic uncertainty of 1.2%. The systematic uncertainty on N Υ(4S) is 1.37%. Assuming all sources listed in Table I to be independent, the total systematic uncertainties on the branching fraction measurements are summed in quadrature.
The following systematic uncertainties are considered for the Ξ c (2930) mass and width. Half of the correction due to the fitting bias on the Ξ c (2930) mass is taken conservatively as a systematic error. By enlarging the mass resolution by 10%, the difference in the measured Ξ 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 Ξ c (2930) Relative systematic uncertainties (%) in the branching fraction measurements.  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 − Λ + c ) spectra with interference between the Ξ c (2930) and the phasespace contribution included gives M Ξc(2930) = (2917.0 ± 5.5) MeV/c 2 and Γ Ξc(2930) = (13.8±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 Ξ c (2930) mass and width of +0.9 −12.0 MeV/c 2 and +5.9 −7.9 MeV, respectively. In summary, using (772 ± 11) × 10 6 BB pairs, we perform an updated analysis of B − → K − Λ + cΛ − c . In the K − Λ + c mass spectrum, the charmed baryon state Ξ c (2930) 0 is clearly observed for the first time with a statistical significance greater than 5σ. The measured mass and width are M Ξc(2930) = (2928.9 ± 3.0 +0.9 −12.0 ) MeV/c 2 and Γ Ξc(2930) = (19.5 ± 8.4 +5.9 −7.9 ) MeV. The branching fraction is B(B − → K − Λ + cΛ − c ) = (4.80 ± 0.43 ± 0.60) × 10 −4 , which is consistent with the world average value of (6.9 ± 2.2) × 10 −4 [1] but with muchimproved precision. We measure the product branching fraction B(B − → Ξ c (2930)Λ − c )B(Ξ c (2930) → K − Λ + c ) = (1.73 ± 0.45 ± 0.21) × 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 Ξ 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 Λ +