Observation of the decay $\Lambda_c^+\rightarrow \Sigma^- \pi^+\pi^+\pi^0$

We report the first observation of the decay $\Lambda^+_{c}\rightarrow \Sigma^- \pi^+\pi^+\pi^0$, based on data obtained in $e^+e^-$ annihilations with an integrated luminosity of 567~pb$^{-1}$ at $\sqrt{s}=4.6$~GeV. The data were collected with the BESIII detector at the BEPCII storage rings. The absolute branching fraction $\mathcal{B}(\Lambda^+_{c}\rightarrow\Sigma^-\pi^+\pi^+\pi^0)$ is determined to be $(2.11\pm0.33({\rm stat.})\pm0.14({\rm syst.}))\%$. In addition, an improved measurement of $\mathcal{B}(\Lambda^+_{c}\rightarrow\Sigma^-\pi^+\pi^+)$ is determined as $(1.81\pm0.17({\rm stat.})\pm0.09({\rm syst.}))\%$.


Introduction
The study of hadronic decays of charmed baryons provides important information to understand both the strong and the weak interactions [1]. It also provides essential input to understand background contributions in the study of b-baryon physics, as Λ b decays dominantly to Λ + c . More than 30 years have passed since the Λ + c baryon was first observed in e + e − annihilations by the Mark II experiment [2] and the knowledge of Λ + c decays remains very poor compared to that for charmed mesons. So far, measured decay modes account for only about 60% [3] of all Λ + c decays, primarily consisting of modes with a Λ(Σ) hyperon or a proton in the final state. Decays to the Σ − hyperon are Cabibbo-allowed and are expected to have large rates. However, no experimental measurements exist except for Λ + c → Σ − π + π + [3]. Therefore, searching for additional decay modes with Σ − in the final state is important to build up knowledge on Λ + c decays. In this paper, we report the first observation of the so-far undetermined, but expected to be large, decay of Λ + c → Σ − π + π + π 0 [4]. In addition, we perform the first absolute measurement of the branching fraction for Λ + c → Σ − π + π + . The data analyzed in this work corresponds to an integrated luminosity of 567 pb −1 [5] of e + e − annihilations at center-of-mass energy (c.m.) √ s = 4.6 GeV by the BEPCII collider and collected with the BESIII detector [6]. The c.m. energy is slightly above the threshold for the production of Λ + cΛ − c , so Λ + cΛ − c pairs are produced with no additional hadrons. The analysis technique in this work, which was first applied in the Mark III experiment [7], is optimized for measuring charm hadron pairs produced near threshold. First, we select the subset of our events in which aΛ − c is reconstructed in an exclusive hadronic decay mode, designated as the single-tag (ST) sample. Events in this ST sample are then searched for the signal channel Λ + c → Σ − π + π + (π 0 ) in the system recoiling against the ST to select double tag (DT) events. In the final states of Λ + c → Σ − π + π + (π 0 ), the Σ − hyperon is detected through Σ − → nπ − . As the neutron is not reconstructed in this analysis, we deduce its kinematic properties by four-momentum conservation. The absolute branching fraction (BF) of Λ + c → Σ − π + π + (π 0 ) is derived from the probability of detecting the DT signals in the ST sample. Hence, this method provides a clean and straightforward BF measurement that is independent of the number of Λ + cΛ − c events produced.

BESIII Detector and Monte Carlo Simulation
BESIII [6] is a cylindrical detector with a coverage of 93% of the full 4π solid angle. It consists of a Helium-gas based main drift chamber (MDC), a plastic scintillator time-of-flight (TOF) system, a CsI (Tl) electromagnetic calorimeter (EMC), a superconducting solenoid providing a 1.0 T magnetic field, and a muon detection system in the iron flux return of the magnet. The charged particle momentum resolution is 0.5% at a transverse momentum of 1 GeV/c. The photon energy resolution at 1 GeV is 2.5% in the central barrel region and 5.0% in the two end caps. More details about the design and performance of the detector are given in Ref. [6].
A GEANT4-based [8] Monte Carlo (MC) simulation package, which includes the geometric description of the detector and the detector response, is used to determine the detection efficiency and to estimate the potential backgrounds. MC samples of the signal mode Λ + c → Σ − π + π + (π 0 ), together with aΛ − c decaying to specified ST modes, are generated with KKMC [9] and EVTGEN [10], taking into account initial-state radiation (ISR) [11] and final-state radiation [12] effects. The Λ + c → Σ − π + π + (π 0 ) decay is simulated by reweighting the phase-space-generated MC events to approximate observed kinematic distributions in data. To understand potential background contributions, an inclusive MC sample is used. It includes generic Λ + (s) + X production, ISR return to the charmonium states at lower masses and continuum qq processes. Previously measured decay modes of the Λ c , ψ and D (s) are simulated with EVTGEN, using BFs from the Particle Data Group (PDG) [3]. The unknown decays of the ψ states are generated with LUND-CHARM [13].

Analysis
The ST and DT selection technique that is used in our analysis follows closely the one used and described in Ref. [14]. We reconstruct theΛ − c baryons in the eleven hadronic decay modes listed in Table 1. Intermediate particles are reconstructed through their decays K 0 S → π + π − ,Λ →pπ + ,Σ 0 → γΛ withΛ →pπ + , Σ − →pπ 0 , and π 0 → γγ. The selection criteria for the proton, kaon, pion, π 0 , K 0 S andΛ candidates used in the reconstruction of the ST signals are described in Ref. [14].
The STΛ − c signals are identified using the beamenergy-constrained mass, where E beam is the beam energy and pΛ− c is the momentum of theΛ − c candidate in the rest frame of the initial e + e − system [15]. To improve the signal purity, the energy difference ∆E = E beam − EΛ− c for each candidate is required to be within approximately ±3σ of the ∆E signal peak position, where σ is the ∆E resolution and EΛ− c is the reconstructedΛ − c energy. Table 1 shows the mode-dependent ∆E requirements and the ST yields in the M BC signal region (2.280, 2.296) GeV/c 2 , which are obtained by fits to the M BC distributions. See Ref. [14] for more details. The total ST yield is N tot where the uncertainty is statistical only.
Candidates for the decay Λ + c → Σ − π + π + (π 0 ) with Σ − → nπ − are reconstructed from the tracks not used in the STΛ − c reconstruction. It is required that there are only three charged tracks in the system recoiling against theΛ − c satisfying | cos θ| < 0.93, where θ is the polar angle with respect to the beam direction. For the two π + candidates from the Λ + c , the distances of closest approach to the interaction point must be within ±10 cm along the beam direction and within 1 cm in the perpendicular plane, while the π − candidate from Σ − decay is not subjected to this requirement. Identification of charged tracks is performed by combining the dE/dx information from the MDC and the time of flight measured in the TOF to obtain the probability L h for each hadron type h. The three charged pions must satisfy L π > L K . Photon candidates are reconstructed from isolated clusters in the EMC in the regions | cos θ| ≤ 0.80 (barrel) and 0.86 ≤ | cos θ| ≤ 0.92 (end cap). The deposited energy of a neutral cluster is required to be larger than 25 (50) MeV in the barrel (end cap) region, and the angle between the photon candidate and the nearest charged track must be larger than 10 • . To suppress electronic noise and energy deposits unrelated to the event, the difference between the EMC time and the event start time is required to be within (0, 700) ns. To reconstruct π 0 candidates, the invariant mass of photon pairs is required to be within (0.110, 0.155) GeV/c 2 and, as a second step, a kinematic fit is implemented to constrain the γγ invariant mass to the nominal π 0 mass [3].
The kinematic variable is computed to characterize the reconstructed mass of the undetected neutron, where E π + π + π − (π 0 ) is the energy of the π + π + π − (π 0 ) combination and − → p π + π + π − (π 0 ) is the three-momentum of the π + π + π − (π 0 ) combination. The expected momen- wherep tag is the direction of the momentum of the STΛ − c candidate and m Λ + c is the mass of the Λ + c taken from the PDG [3]. Similarly, we to represent the reconstructed mass of the Σ − .
The distributions of M n versus M nπ − for the Λ + c → Σ − π + π + and Λ + c → Σ − π + π + π 0 candidates in data are shown in Figs. 1 (a) and (b), respectively, where clusters corresponding to signal decays are evident. To improve the resolution of the signal mass, as well as to better handle the backgrounds around the Σ − and neutron mass regions, we determine the signal yields from the distribution of the mass difference M nπ − − M n , since M nπ − and M n are highly correlated. Based on a study of the inclusive MC samples, no peaking backgrounds are expected for these two channels. We perform an unbinned maximum likelihood fit to the M nπ − − M n spectra, as shown in Figs. 1 (c) and (d).
In the fits, the signals are described by non-parametric functions extracted from the signal MC convoluted with a Gaussian function accounting for the resolution difference between data and MC, while the background shapes are described with a second-order polynomial function. The width of the Gaussian is left free in the fit, while its mean is fixed to zero. From the fits, we find the DT signal yields N obs Σ − π + π + = 161 ± 15 and N obs Σ − π + π + π 0 = 88 ± 14, where the uncertainties are statistical only. Backgrounds from non-Λ + c decays are estimated by examining the ST candidates in the M BC sideband (2.252, 2.272) GeV/c 2 in data. The backgrounds from non-Λ + c decays are found to be negligible.
With the DT technique, the BF measurement is insensitive to uncertainty in the ST efficiencies. The systematic uncertainties in measuring B(Λ + c → Σ − π + π + ) and B(Λ + c → Σ − π + π + π 0 ) mainly arise from the efficiencies of π detection and identification, fits to the M nπ − − M n distributions and the signal modelling in the MC simulation. The systematic uncertainties in the π ± tracking and identification are both determined to be 1.0% by studying a set of samples of e + e − → π + π − π + π − , e + e − → K + K − π + π − and e + e − → ppπ + π − obtained from data with c.m. en- (a) Events/0.005 GeV/c 2 (b) (d) Fig. 1: Scatter plots of M n versus M nπ − for candidates in data for (a) Λ + c → Σ − π + π + and (b) Λ + c → Σ − π + π + π 0 . Also shown are fits to the distributions of M nπ − − M n for (c) Λ + c → Σ − π + π + and (d) Λ + c → Σ − π + π + π 0 in data. Solid lines are the results of a complete fit while dashed lines reflect the background components. ergy above 4.0 GeV. The π 0 reconstruction efficiency is validated by analyzing DT events withD 0 → K + π − or K + π − π 0 versus D 0 → K − π + π 0 [16]. The difference of the π 0 reconstruction efficiencies between data and MC simulations is estimated to be 2.0%. The uncertainty from the fit to the M nπ − −M n distribution is evaluated by checking the relative changes of N obs with different choices for signal shapes (double Gaussian function), background shapes (first-order polynomial function, third-order polynomial function and a MC-derived background shape) and fit ranges ((0.19, 0.34) GeV/c 2 ). The uncertainty in modelling the signal process is obtained by varying the reweighting factors of the observed kinematic variables within their statistical uncertainties and extracting the difference of the resultant efficiencies. The difference is estimated to be 2.0% for the studied channels and is taken as the systematic uncertainty due to the signal modelling. In addition, there are systematic uncertainties in obtaining N tot Λ − c evaluated by using alternative signal shapes in the fits to the M BC spectra [14], resulting in an uncertainty of 1.0%, and in the statistical limitation of the MC samples, which is estimated to be 0.6 (0.7)% for Λ + c → Σ − π + π + (π 0 ). The uncertainties from the BFs of Σ − → nπ − and π 0 → γγ are negligible. All of the above systematic uncertainties are summarized in Table 2, and the total uncertainties are evaluated to be 5.2% and 6.4% for B(Λ + c → Σ − π + π + ) and B(Λ + c → Σ − π + π + π 0 ), respectively, by combining all items in quadrature.