Observation of the Singly Cabibbo-Suppressed Decay $\Lambda_{c}^{+} \to n\pi^{+}$

The singly Cabibbo-suppressed decay $\Lambda_{c}^{+} \to n\pi^{+}$ is observed for the first time with a statistical significance of $7.3\sigma$ by using 3.9 $\mathrm{fb}^{-1}$ of $e^{+}e^{-}$ collision data collected at center-of-mass energies between 4.612 and 4.699 GeV with the BESIII detector at BEPCII. The branching fraction of $\Lambda_{c}^{+} \to n\pi^{+}$ is measured to be $(6.6\pm1.2_{\rm stat}\pm0.4_{\rm syst})\times 10^{-4}$. By taking the upper limit of branching fractions of $\Lambda_{c}^{+} \to p\pi^0$ from the Belle experiment, the ratio of branching fractions between $\Lambda_{c}^{+} \to n\pi^{+}$ and $\Lambda_{c}^{+} \to p\pi^0$ is calculated to be larger than 7.2 at the 90% confidence level, which disagrees with the current predictions of available phenomenological models. In addition, the branching fractions of the Cabibbo-favored decays $\Lambda_{c}^{+} \to \Lambda\pi^{+}$ and $\Lambda_{c}^{+} \to \Sigma^{0}\pi^{+}$ are measured to be $(1.31\pm0.08_{\rm stat}\pm0.05_{\rm syst})\times 10^{-2}$ and $(1.22\pm0.08_{\rm stat}\pm0.07_{\rm syst})\times 10^{-2}$, respectively, which are consistent with previous results.

The singly Cabibbo-suppressed decay Λ + c → nπ + is observed for the first time with a statistical significance of 7.3σ by using 3.9 fb −1 of e + e − collision data collected at center-of-mass energies between 4.612 and 4.699 GeV with the BESIII detector at BEPCII. The branching fraction of Λ + c → nπ + is measured to be (6.6 ± 1.2stat ± 0.4syst) × 10 −4 . By taking the upper limit of branching fractions of Λ + c → pπ 0 from the Belle experiment, the ratio of branching fractions between Λ + c → nπ + and Λ + c → pπ 0 is calculated to be larger than 7.2 at the 90% confidence level, which disagrees with the most predictions of available phenomenological models. In addition, the branching fractions of the Cabibbo-favored decays Λ + c → Λπ + and Λ + c → Σ 0 π + are measured to be (1.31 ± 0.08stat ± 0.05syst)×10 −2 and (1.22±0.08stat ±0.07syst)×10 −2 , respectively, which are consistent with previous results.
The decay of the ground state charmed baryon Λ + c plays an essential role in studying the nature of both strong and weak interactions in heavy-to-light baryonic transitions [1]. The hadronic decay amplitudes of Λ + c consist of factorizable and nonfactorizable components, in which the nonfactorizable effects arising from W exchange and internal W emission play an essential role [2,3]. Therefore, studies of nonfactorizable components are critical to understanding the underlining dynamics of charmed baryon decays.
In the last three decades, several different phenomenological models, e.g., current algebra [4,5] and SU(3) flavor symmetry [6][7][8], have been employed as tools to reveal the dynamics of charmed baryon decays. The non-factorizable contributions are important in these decays, in contrast to the meson case, and can be constrained by measurements. Studies of singly Cabibbo-suppressed (SCS) decay modes containing both factorizable and nonfactorizable contributions will provide information about their interference; therefore comprehensive and precise experimental inputs are required for an improved understanding of the validity of the different phenomenological models. Experimentally, great progress has been made in the study of charmed-baryon decays recently, particularly for Cabibbo-favored (CF) decays [9][10][11][12]; for example, the branching fraction of the golden mode Λ + c → pK − π + and the neutron final-state decay Λ + c → nK 0 S π + have been measured with a precision of better than 10% [13][14][15]. However, experimental studies of the SCS decays are still quite challenging due to their small branching fractions of 10 −3 or below.
To date, the branching fractions of only a few SCS decay modes have been measured, and all with limited precision [24], and those involving a neutron in the final state have never been measured. BESIII and Belle have reported the branching fractions of Λ + c → pη and the upper limit for Λ + c → pπ 0 [25,26], where for Λ + c → pπ 0 some tension exists between measurement and some of the predictions [6,7,16,19]. Therefore, an observation of the decay Λ + c → nπ + is essential for validating and constraining different dynamical models.
In this Letter, the first observation of the SCS decay Λ + c → nπ + is reported using 3.9 fb −1 e + e − collision data collected with the BESIII detector at six center-of-mass (c.m.) energies between 4.612 and 4.699 GeV. The integrated luminosities of the data samples at 4 [27], respectively. Throughout this Letter, charge-conjugate modes are implicitly included.
A detailed description of the design and performance of the BESIII detector can be found in Ref. [28]. Simulated samples are produced with a GEANT4-based [29] Monte Carlo (MC) package, which includes the geometric description of the BESIII detector. The signal MC samples of e + e − → Λ + cΛ − c withΛ − c decaying into ten specific tag modes (as described below and listed in Table I) and Λ + c → nπ + , Λπ + , and Σ 0 π + are generated for each individual c.m. energy by the generator kkmc [30] by incorporating initial-state radiation (ISR) effects and the beam energy spread. The inclusive MC sample, which consists of Λ + cΛ − c events, D (s) production, ISR re-turn to lower-mass ψ states, and continuum processes e + e − → qq (q = u, d, s), is generated to estimate the potential background, in which all the known decay modes of charmed hadrons and charmonia are modeled with evtgen [31,32] using branching fractions taken from the Particle Data Group [24], and the remaining unknown decays are modeled with lundcharm [33]. Final-state radiation from charged final-state particles is incorporated using photos [34].
Charged tracks detected in the helium-based main drift chamber (MDC) are required to be within a polar angle (θ) range of |cos θ| < 0.93, where θ is defined with respect to the beam direction. Except for those from K 0 S and Λ decays, their distances of the closest approach to the interaction point (IP) are required to be within ±10 cm along the beam direction and 1 cm in the plane perpendicular to the beam (referred to as tight track hereafter). The particle identification (PID) is implemented by combining measurements of the energy deposited in the MDC (dE/dx) and the flight time in the time-of-flight system, and every charged track is assigned a particle type of pion, kaon or proton, according to which assignment has the highest probability.
Photon candidates are identified using showers in the electromagnetic calorimeter (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. The 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 be the π 0 mass and requiring the corresponding χ 2 of the fit to be less than 200. The momenta updated by the kinematic fit are used in the further analysis.
Candidates for K 0 S andΛ mesons are reconstructed in their decays to π + π − andpπ + , respectively, where the charged tracks must have distances of closest approaches to the IP that are within ±20 cm along the beam direction (referred to as loose track hereafter). To improve the signal purity, PID is applied to the (anti)proton candidate, while the charged pion is not subjected to a PID requirement. A secondary vertex fit is performed to each K 0 S orΛ candidate, and the momenta updated by the fit are used in the further analysis. A K 0 S orΛ candidate is accepted by requiring the χ 2 of the secondary vertex fit 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, and the invariant mass to be within (0.487, 0.511) GeV/c 2 for π + π − or (1.111, 1.121) GeV/c 2 forpπ + . TheΣ 0 andΣ − candidates are reconstructed with the γΛ andpπ 0 final states, requiring the invariant masses to lie within (1.179, 1.203) and (1.176, 1.200) GeV/c 2 , respectively.
The M BC distributions of surviving candidates for the ten ST modes are illustrated in Fig. 1 for the data sample at √ s = 4.682 GeV, where clearΛ − c signals are observed in each sample. No peaking backgrounds are found with the investigation of the inclusive MC sample. To obtain the ST yields, unbinned maximum likelihood fits on these M BC distributions are performed, where the signal shapes are modeled with the MC-simulated shape convolved with a Gaussian function representing the resolution difference between data and MC simulation, and the background shapes are described by an ARGUS function [36]. The candidates with M BC ∈ (2.275, 2.31) GeV/c 2 are retained for further analysis, and the signal yields for the individual ST modes are summarized in Table I  The decay Λ + c → nπ + is searched for among the remaining tracks recoiling against the STΛ − c candidates. Only one tight charged track is allowed, which is then assigned to be the π + from the signal decay. To suppress contamination from long-lifetime particles in the final state, the candidate events are further required to be without any loose tracks. It reduces the signal efficiency of Λ + c → nπ + by 6% and background level by 50%. Meanwhile, the signal yields for Λ + c → Λπ + and Σ 0 π + will decrease significantly as the Λ and Σ 0 decays with charged particles in the final state are highly suppressed, and their decays with neutral ones mostly pass this requirement. To improve detection efficiency, the neutron is selected through the recoiling mass (M rec ) against the STΛ − c and π + : where E π + and p π + are the energy and momentum of the π + candidate, After imposing all selection conditions mentioned above, the distribution of M rec of the accepted DT candidate events from the combined six data samples at different c.m. energies is shown in Fig. 2, where a peak at the neutron mass is observed, representing the Λ + c → nπ + signal. Additionally, there are two prominent structures peaking at the Λ and Σ 0 mass regions, which represent the CF processes Λ + c → Λπ + and Λ + c → Σ 0 π + , respectively. The potential backgrounds can be classified into two categories: those directly originating from continuum hadron production in the e + e − annihilation (referred to as qq background hereafter) and those from e + e − →Λ + cΛ − c events (referred to as Λ + cΛ − c background hereafter), excluding contributions from Λ + c → nπ + , Λπ + , and Σ 0 π + signals. The distributions and magnitudes of qq and Λ + cΛ − c backgrounds are estimated with the inclusive MC sample, as shown in Fig. 2, where no peaking backgrounds are observed. The understanding of the qq background is also validated with candidate events in the M BC sideband region (2.235, 2.270) GeV/c 2 of ST candidates in data; here also, no peaking background is observed.
The signal yield N obs is obtained by performing an unbinned maximum-likelihood fit on the M rec distribution. The neutron, Λ and Σ 0 signals are modeled by the MC-simulated shapes convolved with Gaussian functions that account for the resolution difference between data and MC simulation, and where the three Gaussian functions share the same width parameters. The qq background is described by a second-order Chebyshev function with fixed parameters, which are obtained by fitting the corresponding distribution of events in the ST M BC sideband region. The shape of the Λ + cΛ − c background is taken from the inclusive MC sample. The fit distributions are depicted in Fig. 2, and correspond to signal yields of 50 ± 9, 376 ± 22, and 343 ± 22 for the decays Λ + c → nπ + , Λπ + , and Σ 0 π + , respectively, where the uncertainties are statistical. The statistical significance of Λ + c → nπ + is 7.3σ, which is calculated from the change of the likelihood values between fits with and without the signal component included, and accounting for the change in the number of degrees of freedom.
The Λ + c decay branching fractions (B) are determined as  Table I for  The systematic uncertainties for the branching fraction measurements comprise those associated with the ST yields, the π + tracking and PID efficiencies, the requirement of zero loose tracks, the determination of the DT signal yields, the decay branching fractions of Λ and Σ 0 (for Λ + c → Λπ + and Σ 0 π + only) and the statistical uncertainties from the MC samples. The DT approach on which the measurement is based means that uncertainties associated with the ST selection efficiency cancel out.
The uncertainty in the ST yields is 0.5%, which arises from the statistical uncertainty and a systematic component coming from the fit to the M BC distribution. The uncertainties associated with the π + tracking and PID efficiencies are determined from studies of a control sample J/ψ → π + π − π 0 decays, as explained in Ref. [38], and are assigned to be 1.0% and 2.0%, respectively. The uncertainty due to the zero loose-track requirement is 1.7%, which is assigned from studies of a control sample of e + e − → Λ + cΛ − c with Λ + c → pK − π + and theΛ − c decaying into ten tag decay modes. The uncertainties from the determination of the DT yields are 5.6%, 2.5% and 2.1% for the decays Λ + c → nπ + , Λπ + , and Σ 0 π + , respectively, including those from the fit range and the modeling of qq and Λ + cΛ − c backgrounds, which are estimated from varying the range and alternative polynomial descriptions for the qq and Λ + cΛ − c backgrounds, respectively. The uncertainties in the DT efficiencies due to the branching fractions of Λ and Σ 0 are 1.4% and 1.4% for the decays Λ + c → Λπ + and Σ 0 π + , respectively. Uncertainties arising from the MC modeling are investigated by reweighting the MC distribution to data, and comparing the results obtained between the original and reweighted samples. The resultant uncertainties in the MC modeling are 0.8% for Λ + c → nπ + and 3.8% for Λ + c → Σ 0 π + , but negligible for Λ + c → Λπ + . The uncertainties associated with the finite size of the signal MC samples are 0.2%. All other uncertainties are negligible. Assuming that all the sources of bias are uncorrelated, the total uncertainties are then taken to be the quadratic sum of the individual values, which are 6.3%, 4.0%, and 5.4% for the decays Λ + c → nπ + , Λπ + , and Σ 0 π + , respectively. In summary, the singly Cabibbo-suppressed decay Λ + c → nπ + is observed with a statistical significance of 7.3σ by using e + e − collision data samples corresponding to a total integrated luminosity of 3.9 fb −1 collected at c.m. energies between 4.612 and 4.699 GeV with the BE-SIII detector. The branching fraction of Λ + c → nπ + is measured to be (6.6±1.2 stat ±0.4 syst )×10 −4 , this is a firsttime measurement. Meanwhile, the branching fractions of the Cabibbo-favored decays Λ + c → Λπ + and Λ + c → Σ 0 π + are measured to be (1.31±0.08 stat ±0.05 syst )×10 −2 and (1.22 ± 0.08 stat ± 0.07 syst ) × 10 −2 , respectively, which are consistent with previous BESIII results [14]. The measured branching fraction of Λ + c → nπ + is consistent with the prediction in Ref. [20], but twice as large as that in Ref. [18], implying that the nonfactorization contributions are overestimated. Taking the upper limit of the branching fraction of Λ + c → pπ 0 from the Belle experiment, B(Λ + c → pπ 0 ) < 8.0 × 10 −5 at the 90% confidence level [26], the ratio of branching fractions between Λ + c → nπ + and Λ + c → pπ 0 is calculated to be larger than 7.2 at the 90% confidence level, which disagrees with the most predictions of phenomenological models [6,7,16,[18][19][20]23]. The results from this analysis provide an essential input for the phenomenological studies on the underlying dynamics of charmed baryon decays. In order to obtain an improved understanding it is desirable to perform improved studies of these decays, in particular concerning the Λ + c → pπ 0 branching fraction in the future [39].