First measurements of absolute branching fractions of the $\Xi_c^+$ baryon at Belle

We present the first measurements of the absolute branching fractions of $\Xi_c^+$ decays into $\Xi^- \pi^+ \pi^+$, $p K^- \pi^+$, and $p \bar{K}^{*}(892)^{0}$ final states. Our analysis is based on a data set of $(772\pm 11)\times 10^{6}$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+e^-$ collider. We measure the absolute branching fraction of $\bar{B}^{0} \to \bar{\Lambda}_{c}^{-} \Xi_{c}^{+}$ with the $\Xi_c^+$ signal recoiling against $\bar{\Lambda}_c^-$ in $\bar{B}^0$ decays resulting in ${\cal B}(\bar{B}^{0} \to \bar{\Lambda}_{c}^{-} \Xi_{c}^{+}) = [1.16 \pm 0.42(\rm stat.) \pm 0.15(\rm syst.)] \times 10^{-3}$. We then measure the product branching fractions ${\cal B}(\bar{B}^{0} \to \bar{\Lambda}_c^- \Xi_c^+){\cal B}(\Xi_c^+ \to \Xi^- \pi^+ \pi^+)$, ${\cal B}(\bar{B}^{0} \to \bar{\Lambda}_c^- \Xi_c^+){\cal B}(\Xi_c^+ \to p K^- \pi^+)$, and ${\cal B}(\bar{B}^{0} \to \bar{\Lambda}_c^- \Xi_c^+){\cal B}(\Xi_c^+ \to p \bar{K}^{*}(892)^{0})$. Dividing these product branching fractions by $\bar{B}^{0} \to \bar{\Lambda}_{c}^{-} \Xi_{c}^{+}$ yields: ${\cal B}(\Xi_c^+ \to \Xi^- \pi^+ \pi^+) = [2.86 \pm 1.21(\rm stat.) \pm 0.38(\rm syst.)]\%$, ${\cal B}(\Xi_c^+ \to p K^- \pi^+)=[0.45 \pm 0.21(\rm stat.) \pm 0.07(\rm syst.)]\%$, and ${\cal B}(\Xi_c^+ \to p \bar{K}^{*}(892)^{0}) = [0.25 \pm 0.16(\rm stat.) \pm 0.04(\rm syst.)]\%$. Our result for ${\cal B}(\Xi_c^+ \to \Xi^- \pi^+ \pi^+)$ can be combined with $\Xi_c^+$ branching fractions measured relative to $\Xi_c^+ \to \Xi^- \pi^+ \pi^+$ to set the absolute scale for many $\Xi_c^+$ branching fractions.

In recent decades there has been significant experimental progress of the measurements of the weak decays of charmed baryons [1].However, the large nonperturbative effects of Quantum Chromodynamics make it impossible to reliably calculate the decay amplitudes of charmed baryons from first principles.Furthermore, in exclusive charmed-baryon decays the heavy quark expansion does not work.Hence experimental data are needed to extract the non-perturbative quantities in the decay amplitudes [2][3][4][5] and provide important information to constrain phenomenological models of such decays [6][7][8][9][10][11][12][13].
However, the absolute branching fraction of the remaining member of the charmed-baryon SU(3) flavor antitriplet, the Ξ + c , has not been measured.Branching fractions of Ξ + c decays have been measured relative to the Ξ − π + π + mode.A measurement of the absolute branching fraction B(Ξ + c → Ξ − π + π + ) is needed to infer the absolute branching fractions of other Ξ + c decays.The comparison of Ξ + c decays with those of Λ + c and Ξ 0 c can also provide an important test of SU(3) flavor symmetry [17].
A few models have been developed to predict the decay rates of Ξ + c .For example, the B(Ξ + c → Ξ − π + π + ) has been predicted to be (1.47 ± 0.84)% based on the SU(3) flavor symmetry [18].Experimental information is crucial to not only validate these models, but also to constrain the model parameters.
Along with the reference mode Ξ + c → Ξ − π + π + , Ξ + c → pK − π + is a particularly important decay mode as it is the one most often used to reconstruct Ξ + c candidates at hadron collider experiments, such as LHCb.For example, the decay has been used to study the properties of Ξ b and to search for higher excited Ξ b states via [19][20][21], to search for new Ω * c states in the Ξ + c K − mode [22], to measure the doubly charmed baryon via Ξ ++ cc → Ξ + c π + [23], and to measure the ratio of fragmentation fractions of b → Ξ 0 b relative to b → Λ 0 b [24,25].Theory predicts B(Ξ + c → pK − π + ) to be (2.2 ± 0.8)% using the measured ratio [25,26].In experiments, the decay Ξ + c → pK − π + has been observed by the FOCUS and SELEX Collaborations and the branching fraction ratio is measured to be B(Ξ , which proceeds via a b → ccs transition, has been predicted to have a branching fraction of the order 10 −3 [30], but there has been no experimental measurement.The world average of the product branching fraction B( B0 [1,31,32]. In this Letter, we perform an analysis of B0 → Λ− c Ξ + c with Λ− c reconstructed via its pK + π − decay, and Ξ + c reconstructed both inclusively and exclusively via the decay modes Ξ − π + π + , pK − π + , and p K * (892) 0 [33].We present first a measurement of the absolute branching fraction for B0 → Λ− c Ξ + c using a missing-mass technique.For this analysis we fully reconstruct the tag-side B 0 decay.
We subsequently measure the product branching fractions B( B0 ) without reconstructing the recoiling B 0 decay in the event as the signal decays are fully reconstructed.Dividing these product branching fractions by the result for B( B0 This analysis is based on the full data sample of 711 fb −1 collected at the Υ(4S) resonance by the Belle detector [34] at the KEKB asymmetric-energy e + e − collider [35].
To determine detection efficiency and optimize signal event selections, B meson signal events are generated using evtgen [36] and Ξ + c inclusive decays are generated using pythia [37].The events are then processed by a detector simulation based on geant3 [38].Monte Carlo (MC) simulated 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 a center-of-mass energy of √ s = 10.58GeV are used to examine possible peaking backgrounds.
Selection of signal and Λ → pπ − candidates uses well reconstructed tracks and particle identification as in Ref. [39].
For the inclusive analysis of the Ξ + c decay, the tagside B 0 meson candidate, B 0 tag , is reconstructed using a neural network based on a full hadron-reconstruction algorithm [40].Each B 0 tag candidate has an associated output value O NN from the multivariate analysis, which ranges from 0 to 1.A candidate with larger O NN is more likely to be a true B 0 meson.If multiple B 0 tag candidates are found in an event, the candidate with the largest O NN value is selected.To improve the purity of the B 0 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 3 standard deviations, 3σ.M tag bc and ∆E tag are defined as where ) is the four-momentum of the B 0 tag daughter i in the e + e − center-of-mass system (CMS).Λ− c → pK + π − candidates are selected using the same method as in Ref. [16].A 3σ Λ− c signal region is defined by Here and throughout the text, M i represents a measured invariant mass and m i represents the nominal mass of the particle i [1].
The mass recoiling against the Λ− To improve the recoil-mass resolution we use M rec Here, P CMS , P B 0 tag , and P Λ− c are four-momenta of the initial e + e − system, the tagged B 0 meson, and the reconstructed Λ− c baryon, respectively.Figure 1   To extract the Ξ + c signal yields we perform an unbinned maximum likelihood fit to the M rec A double-Gaussian function with its parameters fixed to those from a fit to the MC-simulated signal distribution is used to model the Ξ + c signal shape and a first-order polynomial is used for the background shape since we find no peaking background in the M tag bc and M Λ− c sideband events.The fit results are shown in Figure 1 (right).
The fitted number of Ξ + c signal events is N Ξ + c = 18.8 ± 6.8.This corresponds to a statistical significance of 3.2σ estimated using −2 ln(L 0 /L max ), where L 0 and L max are the maximum likelihood values of the fits without and with a signal component, respectively.The branching fraction is where is the number of Υ(4S) events, and B(Υ(4S) → B 0 B0 ) = 0.486 [1].The reconstruction efficiency, ε inc , is obtained from the MC simulation.The B( Λ− c → pK + π − ) is taken from Ref. [1].
For the analysis of the exclusive Ξ + c decays, we reconstruct Ξ + c from Ξ − π + π + with Ξ − → Λπ − (Λ → pπ − ) and Ξ − → pK − π + modes, with no B 0 tag .The daughters of the B0 , Ξ + c , and Ξ − candidates are fit to common vertices.If there is more than one B0 candidate in an event, the one with the smallest χ 2 vertex /n.d.f.background is described using an ARGUS function [41].For the ∆E distribution, the signal shape is a double-Gaussian and the background is a first-order polynomial.All shape parameters of the signal functions are fixed to the values obtained from the fits to the MC simulated signal distributions.The fit results are shown in Figure 2.
To extract the Ξ + c → p K * (892) 0 → pK − π + signal yields, we do an unbinned, three-dimensional, maximumlikelihood fit to the M K − π + , M bc , and ∆E distributions.For the M bc and ∆E distributions, the same fitting functions are taken as in the 2D fit for the signal and background events described above.For the M K − π + distribution, the signal shape is a P -wave relativistic Breit-Wigner (RBW) function with shape parameters fixed to the values obtained from fitting the MC simulated distribution, and the background shape is a first-order polynomial plus an additional P -wave RBW for a possible peaking background contribution with a K * (892) 0 signal.We show the fit results in Figures 2(df).The fitted signal yield is N p K * (892) 0 = 8.9 ± 3.9 (3.3σ significance).The measured B( B0 We divide the above product branching fractions by the value of B( B0 → Λ− c Ξ + c ) and for the first time measure ), and the ratios between them.These are shown in Table I.
There are several sources of systematic uncertainties in the branching fraction measurements.
The uncertainties related to reconstruction efficiency include those for tracking efficiency (0.35% per track), particle identification efficiency (0.9% per kaon, 0.9% per pion, and 3.3% per proton), as well as Λ reconstruction efficiency (3.0% per Λ [42]).We assume these reconstruction-efficiency-related uncertainties are independent and sum them in quadrature.We estimate the systematic uncertainties associated with the fitting procedures by changing the order of the background polynomial, the range of the fit, and by enlarging the mass resolution by 10%.The observed deviations from the nominal fit results are taken as systematic uncertainties.The uncertainty on B( Λ− c → pK + π − ) is taken from Ref. [1].The uncertainty due to the B 0 tagging efficiency is 4.5% [43].A relative systematic uncertainty on B(Υ(4S) → B 0 B0 ) is 1.23% [1].The systematic uncertainty on N Υ(4S) is 1.37% [44].For the Ξ + c branching fractions and the corresponding ratios, some common systematic uncertainties, including tracking, particle identification, Λ− c decay branching fraction, Λ selection, and the total number of B B pairs, cancel.We summarize the sources of systematic uncertainties in Table I, assume them to be independent, and add them in quadrature to obtain the total systematic uncertainties.
We report the first measurements of the absolute branching fractions where the first uncertainties are statistical and the second systematic.The measured B(Ξ + c → Ξ − π + π + ) value is consistent with the theoretical prediction within uncertainties [18].
The measured central value of B(Ξ + c → pK − π + ) is smaller than that of the theoretical prediction [25,26], perhaps indicating a large Uspin symmetry breaking effect in the singly-Cabibbosuppressed charmed-baryon decays.
The branching fraction B( B0 → Λ− c Ξ + c ) is measured for the first time to be [1.16 ± 0.42(stat.)± 0.15(syst.)]× 10 −3 and agrees well with that of B − → Λ− c Ξ 0 c [16]   , the red open histograms are 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 generic-decay backgrounds with the number of events normalized to the number of events from the normalized M Ξ + c and M Λ− c sidebands.

< 2 .
(left) shows the distribution of M tag bc of the B 0 tag candidates versus M Λ− c of the selected B0 → Λ− c Ξ + c signal candidates after all selection requirements in the studied Ξ + c mass region of 2.4 < M rec 53 GeV/c 2 .Candidates B0 → Λ− c Ξ + c are observed in the signal region defined by the solid box.To check possible peaking backgrounds, we define M tag bc and M Λ− c sideband regions, which are represented by the dashed and dash-dotted boxes.The normalized contribution of the M tag bc and M Λ− c sidebands is estimated as being half the number of events in the blue dashed boxes minus one fourth the number of events in the red dash-dotted boxes.The M rec B 0 tag Λ− c distribution in the signal and the sideband boxes is shown in Figure 1 (right).

FIG. 1 :
FIG. 1: The distribution of M tag bc of the B 0 tag versus M Λ− c for selected B0 → Λ− c Ξ + c candidates with Ξ + c → anything and Λ− c → pK − π + (left) and the fit to the M rec B 0 tag Λ− c

FIG. 2 :
FIG. 2: The distributions of (a) M Ξ + c versus M Λ− c , and the fits to the (b) M bc and (c) ∆E distributions of the selected B0 → Λ− c Ξ + c candidates for (b1-c1) the Ξ + c → Ξ − π + π + and (b2-c2) the Ξ + c → pK − π + decay modes.Plots (d-f) show the fit to (d) the M K − π + , (e) the M bc , and (f) the ∆E distributions for the Ξ + c → p K * (892) 0 → pK − π + decay mode.In plots (a1-a2), the central solid boxes are the signal regions, and the red dash-dotted and blue dashed boxes show the M Ξ + c and M Λ− c sideband regions used to estimate of the backgrounds (see text).The dots with error bars are the data, the blue solid curves represent the best fits, and the dashed curves represent the fit background contributions.The shaded histograms are the normalized as in the text M Ξ + c and M Λ− c sidebands, the red open histograms are 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 generic-decay backgrounds with the number of events normalized to the number of events from the normalized M Ξ + c and M Λ− c sidebands.

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