First measurements of absolute branching fractions of $\Xi_c^0$ at Belle

We present the first measurements of absolute branching fractions of $\Xi_c^0$ decays into $\Xi^- \pi^+$, $\Lambda K^- \pi^+$, and $p K^- K^- \pi^+$ final states. The measurements are made using a data set comprising $(772\pm 11)\times 10^{6}$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+e^-$ collider. We first measure the absolute branching fraction for $B^- \to \bar{\Lambda}_c^- \Xi_c^0$ using a missing-mass technique; the result is ${\cal B}(B^- \to \bar{\Lambda}_c^- \Xi_c^0) = (9.51 \pm 2.10 \pm 0.88) \times 10^{-4}$. We subsequently measure the product branching fractions ${\cal B}(B^- \to \bar{\Lambda}_c^- \Xi_c^0){\cal B}(\Xi_c^0 \to \Xi^- \pi^+)$, ${\cal B}( B^- \to \bar{\Lambda}_c^- \Xi_c^0) {\cal B}(\Xi_c^0 \to \Lambda K^- \pi^+)$, and ${\cal B}( B^- \to \bar{\Lambda}_c^- \Xi_c^0) {\cal B}(\Xi_c^0 \to p K^- K^- \pi^+)$ with improved precision. Dividing these product branching fractions by the result for $B^- \to \bar{\Lambda}_c^- \Xi_c^0$ yields the following branching fractions: ${\cal B}(\Xi_c^0 \to \Xi^- \pi^+)= (1.80 \pm 0.50 \pm 0.14)\%$, ${\cal B}(\Xi_c^0 \to \Lambda K^- \pi^+)=(1.17 \pm 0.37 \pm 0.09)\%$, and ${\cal B}(\Xi_c^0 \to p K^- K^- \pi^+)=(0.58 \pm 0.23 \pm 0.05)\%.$ For the above branching fractions, the first uncertainties are statistical and the second are systematic. Our result for ${\cal B}(\Xi_c^0 \to \Xi^- \pi^+)$ can be combined with $\Xi_c^0$ branching fractions measured relative to $\Xi_c^0 \to \Xi^- \pi^+$ to yield other absolute $\Xi_c^0$ branching fractions.

Half a century after the theory of Quantum Chromodynamics (QCD) was developed, understanding the non-perturbative property of the strong interaction still remains a challenge.Weak decays of charmed hadrons play a unique role in the study of strong interactions, as the charm mass scale is near the boundary between perturbative and non-perturbative QCD.The charmed-baryon sector offers an excellent laboratory for testing heavy-quark symmetry and lightquark chiral symmetry, both of which have important implications for the low-energy dynamics of heavy baryons interacting with Goldstone bosons [1].
In exclusive charm decays, the heavy-quark expansion does not work, and experimental data is needed to extract non-perturbative quantities in the decay amplitudes [2][3][4][5].Decays of charmed baryons with an additional quark and spin of 1/2 provide complementary information to that of charm-meson decays.
We subsequently measure the product branching fractions For these measurements we do not reconstruct the recoiling B + decay, as the signal decays are fully reconstructed.Dividing these product branching fractions by ).This analysis is based on the full data sample of 702.6 fb −1 collected at the Υ(4S) resonance by the Belle detector [26] at the KEKB asymmetric-energy e + e − collider [27].The detector is described in detail elsewhere [26].
To optimize signal selection criteria and calculate the signal reconstruction efficiency, we use Monte Carlo (MC) simulated events.Signal events of B meson decays are generated using evtgen [28], while inclusive Ξ 0 c decays are generated using pythia [29].The MC events are processed with a detector simulation based on geant3 [30].MC samples of Υ(4S) → B B events with B = B + or B 0 , and e + e − → q q events with q = u, d, s, c at √ s = 10.58GeV are used as background samples.To select signal candidates, well-reconstructed tracks and particle identification are performed using the same method as in Ref. [31], as well as the Λ → pπ − and K 0 S → π + π − candidates [31].
For the inclusive analysis of the Ξ 0 c decay, the tagside B + meson candidate, B + tag , is reconstructed using a neural network based on a full hadron-reconstruction algorithm [32] A double-Gaussian function (its parameters are fixed to those from a fit to the MC-simulated signal distribution) is used to model the Ξ 0 c signal shape, and a first-order polynomial is taken as the background shape.The fit results are shown in Fig. 2.   The fitted Ξ 0 c signal yield is N Ξ 0 c = 40.9± 9.0, with a statistical significance of 5.5σ.The significance is calculated using −2 ln(L 0 /L max ), where L 0 and L max are the likelihoods of the fits without and with a signal component, respectively.The B(B The number of B − → Λ− c Ξ 0 c signal events is extracted by performing an unbinned two-dimensional maximumlikelihood fit to the M bc versus ∆E distributions.For the M bc distribution, the signal shape is modeled with a Gaussian function, and the background is described using an ARGUS function [33].For the ∆E distribution, the signal shape is modeled using a double-Gaussian function, and the background is described by a first-order polynomial.All shape parameters of the signal functions are fixed to the values obtained from the fits to the MCsimulated signal distributions.The fit results are shown in Fig. 3.
Assuming that all the above sources of systematic uncertainty are independent, the reconstruction-efficiency-related uncertainties are summed in quadrature for each decay mode, yielding 4.0-8.4%,depending on the specific decay mode.For the four branching-fraction measurements, the final uncertainties related to the efficiency of the reconstruction are summed in quadrature over the two reconstructed 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 uncertainties associated with the fit by changing the order of the background polynomial, the fitting range, and by enlarging the mass resolution by 20%.The observed deviations are taken as systematic uncertainties.Uncertainties on ) are taken from Ref. [22].The final uncertainties on the two Λ− c partial decay widths are summed in quadrature with the reconstruction efficiency as a weighting factor.The uncertainty due to the B tagging efficiency is 4.2% [36].The uncertainty on B[Υ(4S) → B + B − ] is 1.2% [22].The systematic uncertainty on N Υ(4S) is 1.37% [37].For the Ξ 0 c branching fractions and the corresponding ratios, some common systematic uncertainties cancel including tracking, particle identification, Λ− c branching fractions, Λ and K 0 S selections, and N B − .The sources of uncertainty summarized in Table I are assumed to be independent and thus are added in quadrature to obtain the total systematic uncertainty.

3 FIG. 1 :
FIG. 1: The distribution of M tag bc of B + tag versus M Λ− c of selected B − → Λ− c Ξ 0 c candidates with Ξ 0 c → anything, summed over the two reconstructed Λ− c decay modes.The solid box shows the signal region, and the dashed and dashdotted boxes define the M tag bc and M Λ− c sidebands described in the text.

FIG. 2 :
FIG.2:The fit to the M rec B + tag Λ− c distribution of the selected candidate events.The points with error bars represent the data, the solid blue curve is the best fit, the dashed curve is the fitted background, the cyan shaded histogram is from the scaled M tag bc and M Λ− c sidebands, the red open histogram is from the sum of the MC-simulated contributions from the e + e − → q q with q = u, d, s, c, and Υ(4S) → B B genericdecay backgrounds with the number of events normalized to the number of events from the normalized M tag bc and M Λ− c and N B − = 2N Υ(4S) B(Υ(4S) → B + B − ), where N Υ(4S) is the number of Υ(4S) events, and the B[Υ(4S) → B + B − ] = (51.4± 0.6)% [22].The reconstruction efficiencies ε 1 and ε 2 of the two Λ− c decay modes.

FIG. 3 :
FIG. 3: The distributions of M Ξ 0 c versus M Λ− c (a), and the fits to the M bc (b) and ∆E (c) distributions of the selectedB − → Λ− c Ξ 0 c candidates with Ξ 0 c → Ξ − π + (1), Ξ 0 c → ΛK − π + (2), and Ξ 0 c → pK − K − π + (3)decays, summed over the two reconstructed Λ− c decay modes.In (a), the central solid box defines the signal region.The red dash-dotted and blue dashed boxes show the M Ξ 0 c and M Λ− c sideband regions used for the estimation of the non-Ξ 0 c and non-Λ− c backgrounds (see text).In (b) and (c), the dots with error bars represent the data, the blue solid curves represent the best fits, and the dashed curves represent the fitted background contributions.The shaded and red open histograms have the same meaning as in Fig. 2.

B
(B − → Λ− c Ξ 0 c ) is measured for the first time to be B(B − → Λ− c Ξ 0 c ) = (9.51± 2.10 ± 0.88) × 10 −4 .For the above branching fractions, the first uncertainties are statistical and the second systematic.The product branching fractions are B(B − → Λ− c Ξ 0 c )B(Ξ 0 c → Ξ − π + ) = (1.71± 0.28 ± 0.15) × 10 −5 , B(B − → Λ− c Ξ 0 c )B(Ξ 0 c → ΛK − π + ) = (1.11± 0.26 ± 0.10) × 10 −5 , and B(B − → Λ− c Ξ 0 c NN is selected.To improve the purity of the B + tag sample, we require O NN > 0.005, M tag bc > 5.27 GeV/c 2 , and |∆E tag | < 0.04 GeV, where the latter two intervals correspond to approximately 3σ in resolution.The variables M tag bc and ∆E tag are defined as M tag bc ≡ E 2 beam − | i − → p tag i | 2 and ∆E tag ≡ i E tag . Each B + tag candidate has an associated output value O NN from the multivariate analysis that ranges from 0 to 1.A candidate with larger O NN is more likely to be a true B meson.If multiple B + tag candidates are found in an event, the candidate with the largest O

TABLE I :
Summary of the measured branching fractions and ratios of Ξ 0 c decays (last column), and the corresponding systematic uncertainties (%).For the branching fractions and ratios, the first uncertainties are statistical and the second are systematic.