A Study of Excited Charm-Strange Baryons with Evidence for new Baryons \Xi_c(3055)^+ and \Xi_c(3123)^+

We present a study of excited charm-strange baryon states produced in $e^+e^-$ annihilations at or near a center-of-mass energy of $10.58\mathrm{Ge\kern -0.1em V}$, in a data sample with an integrated luminosity of $384 fb^{-1}$ recorded with the BABAR detector at the PEP-II $e^+e^-$ storage rings at the Stanford Linear Accelerator Center. We study strong decays of charm-strange baryons to $\Lambda_c^+K^0_{\scriptscriptstyle S}$, $\Lambda_c^+K^-$, $\Lambda_c^+K^-\pi^+$, $\Lambda_c^+K^0_{\scriptscriptstyle S}\pi^-$, $\Lambda_c^+K^0_{\scriptscriptstyle S}\pi^-\pi^+$, and $\Lambda_c^+K^-\pi^+\pi^-$. This study confirms the existence of the states $\Xi_c(2980)^+$, $\Xi_c(3077)^+$, and $\Xi_c(3077)^0$, with a more accurate determination of the $\Xi_c(2980)^+$ mass and width. We also present evidence for two new states, $\Xi_c(3055)^+$ and $\Xi_c(3123)^+$, decaying through the intermediate resonant modes $\Sigma_c(2455)^{++}K^-$ and $\Sigma_c(2520)^{++}K^-$, respectively. For each of these baryons, we measure the yield in each final state, determine the statistical significance, and calculate the product of the production cross-section and branching fractions. We also measure the masses and widths of these excited charm-strange baryons.


H. Neal
Yale University, New Haven, Connecticut 06511, USA We present a study of excited charm-strange baryon states produced in e + e − annihilations at or near a center-of-mass energy of 10.58 GeV, in a data sample with an integrated luminosity of 384 fb −1 recorded with the BABAR detector at the PEP-II e + e − storage rings at the Stanford Linear Accelerator Center. We study strong decays of charm-strange baryons to Λ + c K 0 S , Λ + c K − , Λ + c K − π + , Λ + c K 0 S π − , Λ + c K 0 S π − π + , and Λ + c K − π + π − . This study confirms the existence of the states Ξc(2980) + , Ξc(3077) + , and Ξc(3077) 0 , with a more accurate determination of the Ξc(2980) + mass and width. We also present evidence for two new states, Ξc(3055) + and Ξc(3123) + , decaying through the intermediate resonant modes Σc(2455) ++ K − and Σc(2520) ++ K − , respectively. For each of these baryons, we measure the yield in each final state, determine the statistical significance, and calculate the product of the production cross-section and branching fractions. We also measure the masses and widths of these excited charm-strange baryons.

I. INTRODUCTION
With the observation of the Ω * c (css) baryon [1] by the BABAR Collaboration, every predicted SU(4) groundstate single-charm baryon has been experimentally observed. Several excited Λ c (cqq), Σ c (cqq), and Ξ c (csq) baryons have also been experimentally observed [2]. The spins and parities of these are assigned based on a comparison of the measured masses and natural widths with predictions of theoretical models.
Both the BABAR and Belle collaborations have searched for ground-state double-charm baryons decaying to the final state Λ + c K − π + [3-5]. These searches reveal no evidence for such states. However, the Belle Collaboration finds evidence for two excited charm-strange baryon states, Ξ c (2980) +,0 and Ξ c (3077) +,0 , decaying strongly to Λ + c K 0 S π − and Λ + c K − π + [5]. Although these new states have the same or similar decay modes as those used in the search for weak decays of double-charm baryons, they are identified as charm-strange states based on the measured masses, natural widths (which indicate strong decays), and charges of the members of the isospin doublet.
Previously known excited Ξ c baryons have been observed only in decays to a lower-mass Ξ c baryon plus a pion or photon. In contrast, the Ξ c (2980) +,0 and Ξ c (3077) +,0 baryons are observed in decays in which the charm and strange quarks are in separate hadrons. The observed decay modes may have implications for the internal quark dynamics of these new states. Several excited charm-strange baryons with J P = {(1/2) ± , (3/2) ± } are predicted, with masses ranging from about 2800 MeV/c 2 to 3150 MeV/c 2 [6,7]. Other authors [8][9][10] consider J P = (5/2) + states and radial excitations, and use the measured natural widths and decay modes in assigning possible quantum numbers for the new Ξ c (2980) +,0 and Ξ c (3077) +,0 states.
In this paper, we report measurements of excited charm-strange baryon properties based on a data sample corresponding to an integrated luminosity of 384 fb −1 recorded with the BABAR detector at the PEP-II asymmetric-energy e + e − storage rings at the Stanford Linear Accelerator Center. We search for decays to the three-body final states Λ + c K − π + and Λ + c K 0 S π − , the two-body final states Λ + c K 0 S and Λ + c K − , and the fourbody final states Λ + c K 0 S π − π + and Λ + c K − π − π + . Significant signals are found only in decays to three-body final states. We confirm the existence of the states Ξ c (2980) + , Ξ c (3077) + , and Ξ c (3077) 0 , with an improvement over existing measurements of the Ξ c (2980) + mass and width. * Deceased † Now at Tel Aviv University, Tel Aviv, 69978, Israel ‡ Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy § Also with Università della Basilicata, Potenza, Italy ¶ Also with Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain For the three-body final states, we also search for decays through intermediate resonant Σ c (2455) ++ K − , Σ c (2455) 0 K 0 S , Σ c (2520) ++ K − , and Σ c (2520) 0 K 0 S channels. The Σ c (2455) and Σ c (2520) baryons decay exclusively to Λ + c π. We find evidence for two additional new states Ξ c (3055) + and Ξ c (3123) + decaying through the intermediate-resonant channels Σ c (2455) ++ K − and Σ c (2520) ++ K − , respectively. We measure the mass, natural width, yield, and the product of production cross section and decay branching fractions when there is evidence for an excited charm-strange baryon. Also, where applicable, the intermediate resonant decay fractions are measured.

II. ANALYSIS OVERVIEW
This analysis relies primarily on the charged-particle tracking and particle-identification capabilities of the BABAR detector. A detailed description of the BABAR detector is presented in Ref. [11]. The charged-particle tracking system consists of a five-layer double-sided silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH). Discrimination between charged pions, kaons, and protons relies on ionization energy loss (dE/dx) in the DCH and SVT, and on Cherenkov photons detected in a ring-imaging detector (DIRC). A CsI(Tl) crystal calorimeter is used to identify electrons and photons. These four detector subsystems are mounted inside a 1.5-T solenoidal superconducting magnet. The instrumented flux return for the solenoidal magnet provides muon identification.
We produce samples of simulated events using the Monte Carlo (MC) generators JETSET74 [12] and EVT-GEN [13] with a full detector simulation based on GEANT4 [14]. We produce about four million simulated e + e − → cc events in which at least one of the primary charm quarks hadronizes into an excited charm-strange baryon that decays according to one of the studied decay channels. All particle decays are generated according to phase space. Reconstruction efficiencies are estimated based on the excited charm-strange baryon kinematic distributions from JETSET74. The simulated samples are also used to estimate measured invariant-mass resolutions.
In data, we study the invariant-mass region between 2.91 GeV/c 2 and 3.15 GeV/c 2 for potential Ξ c states. We do not examine candidates in this region while optimizing the selection criteria in order to minimize potential experimenters' bias. Selection criteria are chosen to maximize the expected significance of signal events averaged over five reconstructed Λ + c decay modes: pK − π + , pK 0 S , pK 0 S π − π + , Λπ + , and Λπ + π − π + . The expected significance of each decay mode is estimated based on the efficiency measured with samples of simulated signal events, and the number of candidates in upper (above 3.15 GeV/c 2 ) and lower (below 2.91 GeV/c 2 ) Ξ c invariantmass side-bands in data.
The selection criteria are based on proton, kaon, and pion particle identification, among several other reconstruction parameters. Reconstructed tracks in the entire candidate decay chain are simultaneously fit with vertex constraints and with the Λ + c , Λ, and K 0 S candidate masses constrained to their world-average values [2]. The total χ 2 probability of the fitted track vertices in the decay chain is required to be greater than 1%. The vertex-constrained Λ + c mass (with no mass constraint) is required to be within 1.75 times the mass resolution (∼ 5 MeV/c 2 ) of the world-average Λ + c mass [2]. The vertex-constrained Λ and K 0 S masses are required to be within 6.5 MeV/c 2 and 10.0 MeV/c 2 , respectively, of their world-average values [2]. The measured Λ and K 0 S flight lengths divided by their errors are required to be greater than 2.5 and 3.0, respectively. The momentum of the Ξ c candidate in the e + e − center-of-mass frame (p * ) is required to be above 2.9 GeV/c. This p * requirement significantly reduces background from random combinations of tracks.
For each Ξ c decay mode, the selected candidates in data are divided into five samples based on the reconstructed Λ + c decay mode. The signal yields in each sample are extracted with an extended, unbinned, maximumlikelihood fit. All five samples are fit simultaneously. The signal probability density functions (PDF) share the values of parameters that describe the signal shape and, for three-body final states, the intermediate-resonant decay fractions. For Λ + c decay mode m, the corresponding portion of the likelihood function L m has the form where S η m is the number of candidates in signalcomponent η, B κ m is the number of candidates in background-component κ, a and b are the shape parameters for the N s signal-PDF components (P η s ) and the N b background-PDF components (P κ b ), and x i m represents the measured masses for the N m candidates in decay mode m. The mass, natural width, and resonant fraction results listed in Table I are the measured shape parameters a for the respective signal PDFs. Combining the five L m , the full extended likelihood function L has the form (2) Each parameter is allowed to vary over a range that is large enough so that it does not constrain any of the final results; in particular, the number of signal candidates is allowed to be negative. For each signal-PDF component (P η s ), the numbers of measured candidates with Λ + c decay mode m (S η m ) are summed together to determine the total yields listed in Table I or to determine the products of cross-sections and branching fractions listed in Tables III and IV. Statistically significant signals for excited charmstrange baryons are observed only in the analysis of threebody final states. For the two-body and four-body final states, we only search for the baryons observed in the three-body final states. The Ξ c masses and widths measured with the three-body candidates are used as Gaussian constraints in the fits to samples of two-body and four-body candidates by multiplying the likelihood function in Eq. (2) by where M is the mass and Γ is the natural width of the Ξ c state measured from the fit to three-body candidates, σ M and σ Γ are the corresponding uncertainties, and µ and γ are the constrained signal mean and width parameters.
The studies of the three-body final states Λ + . The experimental resolution for these two-and three-body invariant masses varies from about 1.0 MeV/c 2 to 2.5 MeV/c 2 . With these two-dimensional mass distributions, we can incorporate the intermediate resonances Σ c (2455) ++,0 and Σ c (2520) ++,0 in the fits. No other known intermediate resonances are kinematically allowed. We fit a region defined by the kinematically allowed mass thresholds, and Λ + c K 0 S π − and Λ + c K − π + invariant masses up to 3150 MeV/c 2 . Two-dimensional mass plots for candidates in the fit region are shown in Fig. 1(a) for Λ + c K − π + candidates and in Fig. 2(a) for Λ + c K 0 S π − candidates. For the two-dimensional maximum-likelihood fit we use a PDF with background components (P b ) and signal components (P s ) used to describe four candidate categories: resonant combinatoric background, non-resonant combinatoric background, resonant signal, and nonresonant signal. We use a double-Voigtian resonance shape (a non-relativistic Breit-Wigner distribution convolved with a resolution function that is the sum of two Gaussian functions) to describe each peak in invariant mass. These peaks include the Ξ c states as well as the Σ c states associated with both Ξ c decays and backgrounds. The double-Voigtian resonance shape does not account for possible interference effects due to overlapping resonances. All resolution parameters are fixed to values measured in the MC samples. The masses and widths of the Σ c (2455) ++ and Σ c (2520) ++ are free parameters in the fits, while the masses and widths of the Σ c (2455) 0 and Σ c (2520) 0 are fixed to the world average values [2] because of the limited statistical sensitivity of the data to these states. The double-Voigtian resonance shape that accounts for excited charm-strange baryon decays through an intermediate Σ c resonance is multiplied by a two-body phase-space factor, and the double-Voigtian resonance shape that accounts for direct three-body decays is multiplied by a three-body phase-space factor. The non-Σ c backgrounds are modeled with a threshold function proportional to where M is the mass variable in the distribution of which there is a minimum kinematic threshold, t is the value of the threshold, and α and β are shape parameters. The free parameters ( a) of the signal-PDF components include the masses, natural widths, and resonant fractions of the excited charm-strange baryon signals.
Projections of the Λ + c K − π + invariant-mass distribution, for all five reconstructed Λ + c decay modes combined, are shown in Figs. 1(b) and (c) with the combined components of the fit shown. The fit allows for four excited charm-strange baryon states; the masses and widths are free parameters in the fit. The data and fit projections correspond to M (Λ + c π + ) ranges within 3.0 natural widths of the Σ c (2455) ++ mass ( Fig. 1(b)) and 2.0 natural widths of the Σ c (2520) ++ mass ( Fig. 1(c)) [2]. These M (Λ + c π + ) ranges are delineated by the horizontal lines in Fig. 1(a). A two-dimensional (M (Λ + c π + ) and M (Λ + c K − π + )) binned χ 2 probability of 88% is calculated for the fit using roughly 300 equally sized bins each containing over 10 candidates. Four excited charm-strange states are observed at the approximate M (Λ + c K − π + ) invariant-masses of 2970 MeV/c 2 , 3055 MeV/c 2 , 3077 MeV/c 2 , and 3123 MeV/c 2 . We use the change in maximum ln-likelihood value when a signal is removed from the fit, and the number of free parameters in each signal PDF component, to estimate statistical significances of > 9.0 σ (∆ ln L = 81), 6.4 σ (∆ ln L = 31), > 9.0 σ (∆ ln L = 91), and 3.6 σ (∆ ln L = 15) for each state, in order of increasing mass. These estimated significances do not statistically account for fluctuations in background level across the entire range of invariant masses over which the study was conducted. This means that these significances do not correspond to those of a search. Rather, they correspond to significances of signals incorporated into the PDF after evidence for the corresponding states had been observed.
The newly identified Ξ c (3055) + and Ξ c (3123) + baryons are found to have statistically significant signals with widths that are larger in value than our mass resolution, p * values distributed toward higher momenta than the combinatoric background, and consistent signal decay rates between the five Λ + c final states. Four additional samples are studied for possible sources of peaking background that could be mistaken for any of the excited charm-strange baryon signals. These four samples are a "wrong-sign" Λ + c K + π − data sample, a Λ + c masssideband data sample, a MC sample of e + e − → cc events, and a data sample in which the Λ + c K − π + invariant mass is recalculated substituting a pion mass for the kaon mass (Λ + c π − π + ). The last data sample would reveal excited Λ + c decays in which the π − has been misidentified as a K − ; no evidence for such decays is found. We also determined that misidentifed excited Λ + c decays result in peaks that are asymmetric in mass and are much broader than the signals observed in data. The wrong-sign data sample could show evidence of peaking backgrounds due to Σ 0 c decays that are reconstructed with an additional kaon, but no such evidence is found. The Λ + c masssideband data sample and the generic-cc MC sample are searched for unexpected sources of peaking background. No sources of peaking background are found. We conclude from these studies that the signals for Ξ c (2980) + , Ξ c (3055) + , Ξ c (3077) + , and Ξ c (3123) + are not peaking backgrounds. These studies also confirm that the threshold function in Eq. (4) accurately models non-peaking background shapes.
Projections of the Λ + c K 0 S π − invariant-mass distribution, for all five reconstructed Λ + c decay modes combined, are shown in Figs. 2(b) and (c). Projections of the combined compenents of the fit are also shown. The data and fit projections correspond to M (Λ + c π − ) ranges within 3.0 natural widths of the Σ c (2455) 0 mass ( Fig. 2(b))and 2.0 natural widths of the Σ c (2520) 0 mass (Fig. 2(c)) [2]. These M (Λ + c π − ) ranges are delineated by the horizontal lines in Fig. 2(a). The fit shown in Fig. 2   for two excited charm-strange baryons: Ξ c (2980) 0 and Ξ c (3077) 0 . A two-dimensional binned χ 2 probability of 62% is calculated (in the same way as described for the fit to Λ + c K − π + data) for the fit when both the Ξ c (2980) 0 and Ξ c (3077) 0 PDF components are included, while a 54% χ 2 probability is calculated when only the Ξ c (3077) 0 PDF component is included. Estimated statistical sig-nificances of 1.7 σ (∆ ln L = 8) and 4.5 σ (∆ ln L = 21) are found for the Ξ c (2980) 0 and Ξ c (3077) 0 states, respectively, based on changes in ln-likelihood values and the number of free parameters in each signal PDF component. Despite the low statistical significance of the Ξ c (2980) 0 signal, we use the prior assumption that this state exists as the isospin partner of the Ξ c (2980) + and include the Ξ c (2980) 0 PDF components for all measurements based on the sample of Λ +

C. Systematic Uncertainties
Several sources of systematic uncertainty are investigated and quantified for the measurements of charmstrange baryons decaying to Λ + c K − π + and Λ + c K 0 S π − final states; they are listed in Table II. Uncertainties in PDF modeling are estimated from additional fits to the data with different mass resolution parameters, background shapes, and phase-space threshold masses. Because of their relatively low statistical significances, we include the effects of excluding a Ξ c (2980) 0 or Ξ c (3123) + PDF component in the relevant fits. Systematic uncertainties on the measured mass, associated with SVT misalignments, angular dependence of tracking performance, energy loss in detector material, the magnetic field, and material magnetization, were extensively studied in BABAR for a precision measurement of the Λ + c mass [15]. Since the Q-values of the excited charm-strange baryon decays in this analysis are similar to those of the Λ + c decays used in the mass measurement, we assign the same systematic error of 0.14 MeV/c 2 . This uncertainty is much smaller than those from other sources.
The systematic uncertainties are added in quadrature and are listed along with the measurements of masses, widths, yields, and intermediate-resonant decay fractions in Table I. To determine the effect of systematic uncertainties on the estimated significance of the Ξ c (3055) + and Ξ c (3123) + states, the change in ln-likelihood is recalculated with the same PDF modeling changes described in the previous paragraph. Only for the Ξ c (3123) + do any of these changes reduce the significance of the signal; the modified background shapes reduce the significance from 3.6 to 3.0 σ (∆ ln L = 12). This lower significance is listed in parentheses in Table I.

D. Products of Cross-Section and Branching Fractions
Reconstruction efficiencies are estimated from JET-SET74 simulations of the e + e − production of excited charm-strange baryons. The efficiencies are studied as a function of the kinematic variables M (Λ + c K) 2 , M (Kπ ± ) 2 , and M (Λ + c π ± ) 2 , where K denotes K − or K 0 S .  0 and Ξc(3077) 0 baryons decaying to Λ + c K 0 S π − . The first errors are statistical and the second errors are systematic. All signal candidates are required to have p * greater than 2.9 GeV/c. The rows labeled "Resonant" give the fraction of each signal that decays through intermediate resonances. The Ξc(3077) + resonant fraction is a 90% confidencelevel lower limit. The row labeled "Σc(2455)" gives the fraction of resonant decays that proceed through Σc(2455)K. The only state for which systematic uncertainties reduce the calculated significance at the stated precision is the Ξc(3123) + ; the lower significance is given in parentheses. A slight 6% relative variation in efficiency is found only at large values of M (Λ + c π + ) 2 . Therefore, we use an efficiency for each Λ + c K − π + candidate that depends on the measured value of M (Λ + c π + ) 2 . Reconstruction efficiencies for states that decay through Λ + c K − π + range from about 1% to 9%, depending on the reconstructed Λ + c decay mode. Reconstruction efficiencies for states that decay through Λ + c K 0 S π − range from about 0.4% to 3.2%.
For each excited charm-strange baryon state, the number of baryons produced in the BABAR detector that decay to Λ + c K − π + or Λ + c K 0 S π − , where Λ + c → pK − π + , is estimated using the signal yields for all five Λ c decay modes, the reconstruction efficiencies, the Λ + c branchingfraction ratios [2], and a "Best Linear Unbiased Estimate" (BLUE) method [16]. The BLUE method accounts for correlated errors between the five signal yields from the five reconstructed Λ + c decay modes, as well as correlated errors between the five estimated efficiencies. The estimated number of excited charm-strange baryons produced with p * > 2.9 GeV/c and the integrated luminosity are used to calculate the product of cross-section and branching fractions for each excited charm-strange II: Systematic uncertainties on the masses, widths, yields, resonant fractions (R1), and Σc(2455) resonant fractions (R2) determined from the samples of Λ + c K − π + and Λ + c K 0 S π − candidates. Uncertainties associated with mass resolution, background-PDF shapes, phase-space thresholds, the inclusion of the Ξc(3123) + or Ξc(2980) 0 signal shapes, and the mass scale are listed. The systematic errors from each source are added in quadrature. NA indicates that a source of systematic uncertainty is not applicable.

Mass
Width where Ξ * c is an excited charm-strange baryon, X is the unreconstructed portion of the e + e − event, and Y is Λ + c K − π + or Λ + c K 0 π − . With these calculations, it is assumed that 34.6% of the K 0 mesons decay as K 0 S → . The measured products of cross-section and branching fractions are listed in Table III. Upper limits at 90% confidence level are calculated on the product of cross-section and branching fractions for the neutral states Ξ c (2980) 0 , Ξ c (3055) 0 , and Ξ c (3123) 0 . The upper limits are determined from numerical integration of posterior probability densities calculated from the likelihood distributions, with a uniform positive prior for the product of cross-section and branching fractions greater than zero and a zero prior below. Gaussian constraints on efficiencies and Λ + c branching-fraction ratios are included in the likelihood functions; these modified likelihood functions constrain the ratios of fitted yields from each Λ + c decay mode and incorporate systematic uncertainties from these ratios of yields. Also, in calculating each upper limit, the signal shape parameters of the baryon are given Gaussian constraints based on the measured values in Table I. For Ξ c (3055) 0 and Ξ c (3123) 0 parameters, we use the values of the parameters measured for their isospin partners. All Gaussian constraints involve a factor analogous to that in Eq. (3). The upper limits on the products of cross-section and branching fractions are listed in Table III.
The studies of decays to the two-body final states Λ + c K 0 S and Λ + c K − are based on one-dimensional fits to the distributions of M (Λ + c K 0 S ) and M (Λ + c K − ). In each case, the invariant-mass range between 2.91 GeV/c 2 to 3.15 GeV/c 2 is fit. The PDF component that accounts for a possible resonance (P s ) is a double-Voigtian resonance shape with free parameters a, which are the mass and natural width of the signal. In the likelihood function, the means and widths of the resonance shapes are given Gaussian constraints (Eq. (3)) based on the values measured with three-body decays. For each of the five Λ + c decay modes, the background distribution in Λ + c K 0 S is modeled with a first-order polynomial (P b ). Background distributions in Λ + c K − are modeled with functions proportional to Eq. (4).
Invariant-mass resolutions and reconstruction efficiencies are calculated from MC samples. Mass resolutions are about 2.5 MeV/c 2 . Reconstruction efficiencies range from about 0.7% to 5.0% for signals that decay through Λ + c K 0 S , depending on the reconstructed Λ + c decay mode, and from about 1.5% to 12% for signals that decay through Λ + c K − . Neither the Λ + c K 0 S nor the Λ + c K − invariant-mass distributions exhibit evidence for statistically significant peaking structures corresponding to any of the charmstrange baryons found in the three-body final states. Figure 3 shows background-only fits to the Λ + c K 0 S and Λ + c K − invariant-mass distributions for all five reconstructed Λ + c decay modes combined. The same method described for three-body final states is used to determine 90% confidence-level upper limits for the products of crosssection and branching fractions described by Eq. (5), where Y is now Λ + c K 0 or Λ + c K − . The upper limits on the products of cross-section and branching fractions are listed in Table IV.
The studies of decays to the four-body final states Λ + c K 0 S π − π + and Λ + c K − π + π − are based on fits to the one-dimensional distributions of M (Λ + c K 0 S π − π + )  and M (Λ + c K − π + π − ). The invariant-mass region from the minimum kinematic threshold (≈ 3063 MeV/c 2 for Λ + c K 0 S π − π + and ≈ 3059 MeV/c 2 for Λ + c K − π + π − ) to 250 MeV/c 2 above the threshold is fit in each case. The PDF component that accounts for possible resonances is a double-Voigtian resonant function multiplied by a third-order polynomial that models the rapidly changing four-body phase space. In the likelihood function, the means and widths of the resonance shapes are given Gaussian constraints (Eq. (3)) based on the values measured with three-body decays. The rapidly rising fourbody phase-space function and the proximity of any resonances to the kinematic thresholds lead to possibly significant contributions of Ξ c (3077) 0 and Ξ c (3077) + signals throughout each fitted 250 MeV/c 2 range. In quoting upper limits for Ξ c (3077) 0 and Ξ c (3077) + , we consider the integrated yield up to 3093 MeV/c 2 and 3089 MeV/c 2 , respectively (≈ 30 MeV/c 2 above threshold in each case). Each range includes the peaking signal but not the higher mass range where efficiencies and possible effects from intermediate-resonant decays are unknown. Background distributions are modeled by (M − α)(M − t) 2 , where M is the mass variable, t is the kinematic threshold, and α is a free parameter.
Invariant-mass resolutions and reconstruction efficiencies are again calculated from MC samples. Mass resolutions are about 1.0 MeV/c 2 . Reconstruction efficiencies range from about 0.3% to 2.4% for signals that decay through Λ + c K 0 S π − π + , depending on the reconstructed Λ + c decay mode. Reconstruction efficiencies range from about 0.8% to 5.5% for signals that decay through Λ + c K − π + π − . Neither the Λ + c K 0 S π − π + nor the Λ + c K − π − π + invariant-mass distributions exhibit evidence for statistically significant peaking structures corresponding to any of the charm-strange baryons found in the three-body final states. Figure 4 shows background-only fits to these invariant-mass distributions for all five reconstructed Λ + c decay modes combined. The same method described for three-body final states is used to determine 90% confidence-level upper limits for the products of cross- Distributions of (a) M (Λ + c K 0 S π − π + ) and (b) M (Λ + c K − π + π − ), for all five reconstructed Λ + c decay modes combined. The curves correspond to fits with no signal PDFs. Signals were searched for around the invariant-mass values indicated by the dashed vertical lines. section and branching fractions described by Eq. (5), where Y is now Λ + c K 0 π − π + or Λ + c K − π + π − . The upper limits on the products of cross-section and branching fractions are listed in Table IV.
For the Λ + c K 0 S π − final state, the only statistically significant signal corresponds to the Ξ c (3077) 0 baryon, which is presumably the isospin partner to the Ξ c (3077) + ; its mass, width, and product of cross-section and branching fractions are measured. Like the Ξ c (3077) + state, the Ξ c (3077) 0 is observed to decay mostly through the Σ c (2455) 0 K 0