Measurement of the absolute branching fraction of the singly Cabibbo suppressed decay Λ + c → pη (cid:48)

The singly Cabibbo suppressed decay Λ + c → pη (cid:48) is measured using 4.5 fb − 1 of e + e − collision data collected at center-of-mass energies between 4.600 and 4.699 GeV with the BESIII detector at BEPCII. Evidence for Λ + c → pη (cid:48) with a statistical signiﬁcance of 3 . 6 σ is reported with a double-tag approach. The Λ + c → pη (cid:48) absolute branching fraction is determined to be (5 . 62 +2 . 46 − 2 . 04 ± 0 . 26) × 10 − 4 , where the ﬁrst and second uncertainties are statistical and systematic, respectively. Our result is consistent with the branching fraction obtained by the Belle collaboration within the uncertainty of 1 σ .


I. INTRODUCTION
The weak decays of the ground state charmed baryon Λ + c play an essential role in understanding the interplay of weak and strong interactions in the charm region [1].In addition, information about the lightest charmed baryon provides key input for investigations of heavier charmed baryons [2] and bottom baryons [3,4].In contrast to charmed meson decays, which are usu-ally dominated by factorizable amplitudes, decays of charmed baryons receive sizable non-factorizable contributions which arise from internal W -emission and Wexchange [5,6].
The complicated physics in charmed baryon decays is described by phenomenological model calculations, which strongly rely on experimental results.Experimentally, some Cabibbo favored decays [7][8][9][10][11][12] have been measured with relatively high precision, while the singly Cabibbo suppressed (SCS) decays are limited by statistics.Recently, measurements of SCS decay branching fractions have been carried out by the BESIII and Belle Collaborations [13][14][15].The SCS decay Λ + c → nπ + was observed for the first time at BESIII [16], and the measured branching fraction is consistent with the SU(3) prediction [17] but twice as large as that from current algebra [18].
The Belle Collaboration reported the first observation of the SCS decay Λ + c → pη with a statistical significance of 5.4σ and measured its decay branching fraction with respect to the Λ + c → pK − π + to be B(Λ + c → pη )/B(Λ + c → pK − π + ) = (7.54± 1.32 ± 0.75) × 10 −3 [19].The two-body SCS decay Λ + c → pη can proceed via the internal W -emission and W -exchange mechanisms, with the lowest-order Feynman diagrams shown in Fig. 1.The branching fraction of Λ + c → pη is predicted to be in the range of 10 −3 − 10 −4 [18].To improve the knowledge of charmed baryons, more experimental studies of SCS decays are highly desirable.In this paper we report a measurement of the absolute branching fraction of the SCS decay Λ + c → pη using 4.5 fb −1 of e + e − collision data collected with the BESIII detector at seven center-of-mass (CM) energies between 4.600 and 4.699 GeV.The Λ + c Λ− c data sets are above Λ + c Λ− c threshold and provide a clean environment with which to measure the absolute branching fractions of Λ + c .The CM energy and the integrated luminosity for each energy point are listed in Table 1 [20][21][22].Throughout the text, the charge conjugate states are always implied.

II. BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector [23] records symmetric e + e − collisions provided by the BEPCII storage ring [24] in the CM energy range from 2.0 to 4.95 GeV [25], with a peak luminosity of 1 × 10 33 cm −2 s −1 achieved at CM energy of 3.77 GeV.BESIII has collected large data samples in this energy region [25].The cylindrical core of the BESIII detector covers 93% of the full solid angle and consists of a multilayer drift chamber (MDC) operating with a helium-based gas mixture, a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T of magnetic field.The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identification modules interleaved with steel.The chargedparticle momentum resolution at 1 GeV/c is 0.5%, and the resolution of the ionization energy loss in the MDC (dE/dx) is 6% for electrons from Bhabha scattering.The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region.The time resolution in the TOF barrel region is 68 ps.The end cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [26].
Simulated data samples are produced with geant4based [27] Monte Carlo (MC) software, which describes the geometry of the BESIII detector and simulates the performance of the detector.The signal MC samples of e + e − → Λ + c Λ− c with Λ− c decaying into ten specific tag modes (as described below and listed in Table 2) and Λ + c → pη , which are used to determine the detection efficiencies, are generated for each individual CM energy using the generator kkmc [28] incorporating initial-state radiation (ISR) effects and the beam energy spread.The Λ + c → pη decay is modeled with a uniform phase-space distribution.The inclusive MC samples, which consist of (s) pair production, ISR return to the charmonium(-like) ψ states at lower masses, and continuum processes e + e − → q q (q = u, d, s), are generated to estimate the potential background.Particle decays are modeled with evtgen [29,30] using branching fractions taken from the Particle Data Group (PDG) [31], when available, or otherwise estimated with lundcharm [32,33].Final state radiation from charged final state particles is incorporated using photos [34].

III. METHODOLOGY
A double-tag (DT) approach [35] is implemented to study the SCS decay Λ + c → pη .A data sample of Λ− c baryons, referred to as the single-tag (ST) sample, is reconstructed with ten exclusive hadronic decay modes, as listed in Table 2. Events in which the signal decay Λ + c → pη is reconstructed in the system recoiling against the Λ− c candidates of the ST sample are denoted as DT candidates.The branching fraction of Λ + c → pη is determined as where N sig is the signal yield of the DT candidates and B inter is the η decay branching fraction taken from the PDG [31].The subscripts i and j represent the ST modes and the data samples at different CM energies, respectively.The parameters N ST ij , ST ij and DT ij are the ST yields, ST and DT detection efficiencies, respectively.

IV. SINGLE TAG EVENT SELECTIONS
The selection criteria of ST events are same as the Ref. [16].Charged tracks detected in the MDC are required to be within a polar angle (θ) range of |cos θ| < 0.93, where θ is defined with respect to the z-axis, which is the symmetry axis of the MDC.Except for tracks from K 0 S and Λ decays, their distances of closest approach to the interaction point (IP) must be less than 10 cm along the z-axis, and less than 1 cm in the transverse plane (referred to as a tight track hereafter).Particle identification (PID) is implemented by combining the measurements of dE/dx in the MDC and the flight time in the TOF, and each charged track is assigned a particle type of pion, kaon or proton, according to which assignment has the highest probability.
Photon candidates are identified from showers in the EMC.The deposited energy of each shower must be more than 25 MeV in the barrel region (|cos θ| ≤ 0.80) or more than 50 MeV in the end cap region (0.86 ≤ |cos θ| ≤ 0.92).To suppress electronic noise and showers unrelated to the event, the difference between the EMC time and the event start time is required to be within [0, 700] ns.A π 0 candidate is reconstructed with a photon pair within the invariant mass region (0.115, 0.150) GeV/c 2 .To improve the resolution, a kinematic fit is performed by constraining the invariant mass of the photon pair to the world average π 0 mass [31].The momentum updated by the kinematic fit is used in further analysis.
Candidates for K 0 S and Λ are reconstructed in their decays to π + π − and pπ + , respectively, where the charged tracks must have the distances of closest approach to the IP within 20 cm along the z-axis (referred to as a loose track hereafter).To improve the signal purity, PID is required for the anti-proton candidate, but not for the charged pion.The two daughter tracks are constrained to originate from a common decay vertex, and the χ 2 of the vertex fit is required to be less than 100.Furthermore, the decay vertex is required to be separated from the IP by a distance of at least twice the fitted vertex resolution.The momenta of the K 0 S or Λ candidates updated by the fit are used in further analysis, and the invariant masses are required to be within (0.487, 0.511) GeV/c 2 for π + π − and (1.111, 1.121) GeV/c 2 for pπ + .The Σ0 and Σ− candidates are reconstructed with the γ Λ and pπ 0 final states with invariant masses being within (1.179, 1.203) and (1.176, 1.200) GeV/c 2 , respectively.
The ST Λ− c candidates are identified using the beam constrained mass , where E beam is the beam energy and E Λ− c and p Λ− c are the energy and momentum of the Λ− c candidate, respectively.The Λ− c candidates are required to satisfy tag-mode dependent asymmetric ∆E requirements, listed in Table 2, which take into account the effects of ISR and correspond to three times the resolution around the peak.If there is more than one candidate satisfying the above requirements for a specific tag mode, the one with the minimum |∆E| is kept, and those with M BC ∈ (2.275, 2.310) GeV/c 2 are retained for further analysis.For the Λ− c → pK 0 S π 0 ST mode, candidate events with M pπ + ∈ (1.100, 1.125) GeV/c 2 and M pπ 0 ∈ (1.170, 1.200) GeV/c 2 are vetoed to avoid double counting with the Λ− mode, candidate events with M π + π − ∈ (0.490, 0.510) GeV/c 2 and M pπ + ∈ (1.110, 1.120) GeV/c 2 are rejected to avoid double counting with the Λ− c → pK 0 S π 0 or Λ− c → Λπ − π 0 ST modes, respectively.In the Λ− c → pK 0 S π + π − and Λπ − π + π − selections, candidate events with M pπ + ∈ (1.100, 1.125) GeV/c 2 and M π + π − ∈ (0.490, 0.510) GeV/c 2 are rejected, respectively.
The M BC distributions of candidates for the ten ST modes with the data set 4682 are illustrated in Fig. 2, where clear Λ− c signals are observed in each ST mode.No peaking background is found with the investigation of the inclusive MC samples.To obtain the ST yields, unbinned maximum likelihood fits on these M BC distributions are performed, where the signal shape is modeled with the MC-simulated shape convolved with a Gaussian function representing the resolution difference between data and MC simulation.The parameters of the Gaussian function are float and determined in the fit, and the resultant standard deviations are varied between 0.1 and 0.7 MeV/c 2 for different ST modes.The background shape is described by an ARGUS function [36], fixing the endpoint parameter to the corresponding E beam .The signal yields for the individual ST modes are summarized in Table 2.The same procedure is performed for the other six data samples at different CM energies, and the results can be found in Ref. [16] and its supplemental material.The sum of ST yields for all data samples at different CM energies is (1.0524 ± 0.0038) × 10 5 , where the uncertainty is statistical.
The MBC distributions of the ST modes for the data set 4680.The points with error bars represent data.The (red) solid curves indicate the fit results and the (blue) dashed curves describe the background shapes.
For both η decay modes, the signal side is required to include exactly three tight tracks, which are then identified with PID to be p, π + , π − .To suppress contamination from long-lifetime particles in the final state, the candidate events are further required to not contain any loose tracks.Possible background from Λ → pπ − is rejected completely by requiring M pπ − > 1.125 GeV/c 2 , and candidate events with M π + π − ∈ (0.490, 0.510) GeV/c 2 are vetoed to reduce the K 0 S → π + π − background by 86%.For the reconstruction mode of η → π + π − η, to increase the detection efficiency, the neutral decays of η are not reconstructed with individual final states, but considered as missing.Thus, the η signal is selected in the system recoiling against the ST Λ− c , p, π + and π − .To improve the mass resolution, we use is the recoiling mass against the ST Λ− c , p, π + and π − , M Λ− c is the reconstructed mass of the Λ− c candidate, and m Λ + c is the world average Λ + c mass [31].The M rec( Λ− c pπ + π − ) variable is required to be within the η mass interval (0.533, 0.561) GeV/c 2 , corresponding to 1σ resolution of the recoiling mass, to reject the Λ + c → pK 0 L π + π − background.The recoiling mass against the ST Λ− c is required to be within (2.275, 2.310) GeV/c 2 .Finally, the signal yield of Λ + c → pη is determined by fitting the distribution of M rec( Λ− c p) , which is defined as the recoiling mass against the ST Λ− c and p, as presented in Fig. 3(a).

VI. BACKGROUND ANALYSIS
The potential background events are classified into two categories: those directly originating from continuum hadron production in the e + e − annihilation (denoted as q q background hereafter) and those from the hereafter).The distributions and magnitudes of q q and Λ + c Λ− c backgrounds are estimated with the inclusive MC samples.The main residual background sources are c p) and M π + π − γ distributions of the accepted candidates in data are depicted in Fig. 3.There are small peaks in the η signal regions for both decay modes.The simulated shapes, which display no peaking background, describe the backgrounds well.

VII. BRANCHING FRACTION MEASUREMENT
The branching fraction of Λ + c → pη is determined with Eq. ( 1) by performing a simultaneous unbinned maximum likelihood fit on the distributions of M rec( Λ− c p) and M π + π − γ in the two η decay modes, constrained to the same B(Λ + c → pη ) and taking into account different detection efficiencies and branching fractions of η .The signal shapes are modeled by the MC-simulated shapes.The background shapes are described by second-order polynomial functions with fixed parameters, which are obtained by fitting the corresponding distributions of inclusive MC samples, and the background yields are floating.The fit curves are depicted in Fig. 3.In Eq. ( 1), the B inter values are (30.7±0.4)% and (29.5±0.4)% for the modes of η → π + π − η and η → π + π − γ, respectively, the ST detection efficiency ST ij is obtained with the same procedure as in Ref. [16], and the DT detection efficiency DT ij is derived with the signal MC samples.The efficiencies are summarized in Table 3 and Table 4 for the η → π + π − η and π + π − γ decay modes, respectively.The statistical significance of Λ + c → pη is 3.6σ, which is calculated from the change of the likelihood values between the fits with and without the signal component included, and accounting for the change in the number of degreesof-freedom.The branching fraction of Λ + c → pη is determined to be B(Λ + c → pη ) = (5.62 +2.46 −2.04 ) × 10 −4 , corresponding to signal yields of 4.9 +3.2 −2.6 and 4.3 +2.6 −2.2 for the η → π + π − η and π + π − γ modes, where the uncertainties are statistical.yield (N sig ).As the DT technique is adopted, the systematic uncertainties originating from reconstructing the ST side largely cancel.The systematic uncertainties are evaluated relative to the measured branching fraction.
The details are described in the following.The uncertainties associated with the tracking and PID efficiencies for the proton and π are determined with the control samples J/ψ → ppπ + π − [37] and J/ψ → π + π − π 0 [38], respectively.The systematic uncertainties for tracking and PID are both assigned to be 1.0% for each proton and π, respectively.
The uncertainty in the reconstruction efficiency for the γ in the η → π + π − γ decay mode is assigned to be 1.0% based on a study with the control sample J/ψ → ρ 0 π 0 events [39].
The uncertainty in the ST yields is 0.5%, which arises from the statistical uncertainty and the fits to the M BC distributions.The uncertainty in the fitting procedure is evaluated by floating the truncation parameter of the ARGUS function and changing the single Gaussian function to a double Gaussian function.
The systematic uncertainty of the M rec( Λ− c pπ + π − ) requirement for the η → π + π − η decay mode is estimated by correcting the variable M rec( Λ− c pπ + π − ) in the MC samples according to the observed resolution difference between data and MC simulation.The resolution difference is studied with the control sample Λ + c → pK 0 L π + π − .The change of the obtained efficiency of the corrected MC samples from the nominal efficiency, 1.3%, is taken as the corresponding systematic uncertainty.
The systematic uncertainty due to the ∆E pπ + π − γ requirement for the η → π + π − γ decay mode is studied with the control sample Λ + c → Σ 0 π + with Σ 0 → Λγ, which has a similar final state as the signal process.The difference between the efficiency in MC simulation and that in the control sample, 1.1%, is assigned to be the systematic uncertainty.
The systematic uncertainties arising from the M rec( Λ− c pπ + π − ) and α γ requirements for the η → π + π − γ decay mode are studied with the control sample Λ + c → pK 0 S π 0 .The differences of the efficiencies between data and MC simulation, 1.3% and 0.8%, are taken as the systematic uncertainties due to the M rec( Λ− c pπ + π − ) and α γ requirements, respectively.
The uncertainty in the fit strategy of M rec( Λ− c p) and M π + π − γ is assigned to be 2.9%, which is estimated by shifting the fit range higher by 50 MeV and varying the background shape to a third-order polynomial function.
The systematic uncertainties due to the signal shape for the η → π + π − η and η → π + π − γ decay modes are studied with the control samples Λ + c → pK 0 S and Λ + c → Σ 0 π + with Σ 0 → Λγ, respectively.The distributions of M rec( Λ− c p) and M Σ 0 are fitted by MC shapes, with or without a convolution with a Gaussian function.The differences of yields between the two cases, 0.6% and 0.1%, are taken as the corresponding systematic uncertainties for the two modes, respectively.
The systematic uncertainty arising from the signal modeling is investigated by generating a new set of signal MC Λ + c → pη events, with proton polar angle distribution parameterized by 1 + αcos 2 θ [40] with decay parameter α = ±1.Here θ is the polar angle of the proton with respect to the Λ + c in the e + e − CM system.Comparing the differences in detection efficiencies between the nominal and alternative samples, the resultant uncertainties are obtained to be 1.0% for the η → π + π − γ decay mode, and 0.1% for the η → π + π − η mode.
According to Eq. ( 1), the uncertainty related to the ST efficiency mostly cancels.However, due to different multiplicities, the ST efficiencies estimated with the generic and signal MC samples are expected to differ from each other slightly and result in a so called "tag bias" uncertainty.The difference between the ST efficiencies given by the generic and signal MC samples, 0.9%, is assigned as the corresponding uncertainty.
Table 5 summarizes the individual relative systematic uncertainties, where the correlated systematic uncertainties are listed in the top and the uncorrelated systematic uncertainties are listed in the bottom.

IX. SUMMARY
In summary, the SCS decay Λ + c → pη is observed with a statistical significance of 3.6σ by using e + e − collision data samples corresponding to a total integrated luminosity of 4.5 fb −1 collected at seven CM energies between 4.600 and 4.699 GeV with the BESIII detector.The absolute branching fraction Λ + c → pη is measured to be (5.62 +2.46  −2.04 ± 0.26) × 10 −4 , where the first and second uncertainties are statistical and systematic, respectively.The branching fraction measured in this work is consistent with the Belle result [19] and the predictions in Refs.[17,41], but significantly higher than that in Ref. [42], as shown in Table 6.The result from this analysis provides an input to understand the dynamics of charmed baryon decays, and helps to improve different theoretical models.

Fig. 3 :
Fig. 3: Simultaneous fit to (a) the M rec( Λ− c p) distribution in the η → π + π − mode and (b) the M π + π − γ distribution in the η → π + π − γ mode with the combined seven data samples.The black points with error bars are data.The red and blue dashed lines indicate the curves for the signal and background, respectively.The black line is the sum over all the components in the fit.The brown and green hatched histograms for the two background components are from the inclusive MC samples.

π 0 3
UNCERTAINTYThe systematic uncertainties for the branching fraction measurement comprise those associated with the ST yields (N ST ij ), detection efficiencies of the ST Λ− c ( ST ij ), detection efficiencies of the DT events ( DT ij ) and signal

Table 1 :
The CM energy and the integrated luminosity (Lint) for each energy point.The first and the second uncertainties are statistical and systematic, respectively.

Table 3 :
The DT detection efficiencies in percentage in the η → π + π − η mode for the ten tag modes and seven data sets at different CM energies.The statistical uncertainties are lower than 0.3%.

Table 4 :
The DT detection efficiencies in percentage in the η → π + π − γ mode for ten tag modes and seven data sets at different CM energies.The statistical uncertainties are lower than 0.3%.

Table 6 :
Comparison of the measured branching fraction (in 10 −4 ) of Λ + c → pη to theoretical predictions and the Belle result.