First observation of $\Lambda_c^+\rightarrow\Lambda K^+\pi^0$ and evidence of $\Lambda_c^+\rightarrow\Lambda K^+\pi^+\pi^-$

We present the first observation of the singly Cabibbo-suppressed decay $\Lambda_c^+ \rightarrow \Lambda K^+\pi^0$ with a significance of $5.7\sigma$ and the first evidence of $\Lambda_c^+ \rightarrow \Lambda K^+\pi^+\pi^-$ decay with a significance of $3.1\sigma$, based on $e^+e^-$ annihilation data recorded by the BESIII detector at the BEPCII collider. The data correspond to an integrated luminosity of $6.4~{\rm fb^{-1}}$, in the center-of-mass energy range from $4.600~{\rm GeV}$ to $4.950~{\rm GeV}$. We determine the branching fractions of $\Lambda_c^+ \rightarrow \Lambda K^+\pi^0$ and $\Lambda_c^+ \rightarrow \Lambda K^+\pi^+\pi^-$ relative to their Cabibbo-favored counterparts to be $\frac{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda K^+\pi^0)}{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda \pi^+\pi^0)} = (2.09\pm0.39_{\mathrm{stat.}}\pm0.07_{\mathrm{syst.}}) \times 10^{-2}$ and $\frac{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda K^+\pi^+\pi^-)}{\mathcal{B}(\Lambda_c^+ \rightarrow \Lambda \pi^+\pi^+\pi^-)} = (1.13\pm0.41_{\mathrm{stat.}}\pm0.06_{\mathrm{syst.}}) \times 10^{-2}$, respectively. Moreover, by combining our measured result with the world average of $\mathcal{B}(\Lambda^+_c\to \Lambda\pi^+\pi^0)$, we obtain the branching fraction $\mathcal{B}(\Lambda_c^+ \to \Lambda K^+\pi^0) = (1.49\pm0.27_{\mathrm{stat.}}\pm0.05_{\mathrm{syst.}}\pm0.08_{\mathrm{ref.}}) \times 10^{-3}$. This result significantly departs from theoretical predictions based on quark $SU(3)$ flavor symmetry, which is underpinned by the presumption of meson pair $S$-wave amplitude dominance.

overestimated.However, the measured BF of Λ þ c → ΛK þ is around 40% of the expectations derived from quark SUð3Þ flavor symmetry [8], constituent quark models [9] or current algebra [7], indicating that the nonfactorizable contribution in this decay is poorly estimated.Experimental investigations of additional SCS decays of Λ þ c are essential for improving our understanding of the mechanisms responsible for the behavior of this baryon.
To date, the decay Λ þ c → ΛK þ π 0 has not been observed in any experiment.Based on quark SUð3Þ flavor symmetry, the S-wave meson pair MM 0 configurations, where MðM 0 Þ denotes the meson octets, are assumed to dominate in the final state, and the BF of this decay is predicted to be ð4.5 AE 0.8Þ × 10 −3 in Ref. [10] and ð3.5 AE 0.6Þ × 10 −3 in Ref. [11], where the latter result incorporates an additional constraint stemming from the magnitude of the S-wave and P-wave interference term α [12].In Ref. [13] the BABAR experiment report a null search for Λ þ c → ΛK þ π þ π − , in which an upper limit on the BF ratio BðΛ þ

II. DETECTOR AND SIMULATION
The BESIII detector [16] records symmetric e þ e − collisions provided by the BEPCII storage ring [17] in the c.m. energy range from 2.0 to 4.95 GeV, with a peak luminosity of 1 × 10 33 cm −2 s −1 achieved at ffiffi ffi s p ¼ 3.77 GeV.BESIII has collected large data samples in these energy regions [18][19][20][21][22].The cylindrical core of the BESIII detector covers 93% of the full solid angle and consists of a helium-based multilayer drift chamber (MDC), 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 magnetic field.The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identification modules interleaved with steel.The charged-particle momentum resolution at 1 GeV=c is 0.5%, and the dE=dx resolution 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, while that in the end cap region is 60 ps [23].
Monte Carlo (MC) simulation is performed with GEANT4 based software [24], which contains a description of the geometry and response of the BESIII detector [25].To estimate detection efficiency, the KKMC generator [26] is used to generate signal MC samples.This generator includes the effects of initial-state radiation and the beam-energy spread, and incorporates the Born cross section line shape of e þ e − → Λ þ pairs without associated hadrons is prevalent.This environment lends itself to the adoption of the single-tag method, where only one Λ þ c is reconstructed within an event, with no condition on the recoil side.This approach is favored for its efficiency, thereby enabling the retention of a greater number of Λ þ c candidates.Charged tracks detected in the MDC are required to be within a polar angle (θ) range of j cos θj < 0.93, where θ is defined with respect to the z axis, which is the symmetry axis of the MDC.For charged tracks not originating from Λ decays, the nearest distance between tracks to the e þ e − interaction point (IP) must be no more than 10 cm along the z axis, jV z j, and less than 1 cm in the transverse plane, jV xy j.Particle identification (PID) is implemented by combining information on the specific ionization energy loss in the MDC (dE=dx) and the flight time in the TOF to form the likelihoods LðhÞ (h ¼ p, π, K) for each hadron h hypothesis.Tracks are identified as protons when the proton hypothesis satisfies the requirements LðpÞ > LðπÞ and LðpÞ > LðKÞ.Charged pions and kaons are discriminated based on comparing the likelihoods for the hypotheses, LðπÞ > LðKÞ and LðKÞ > LðπÞ, respectively.The Λ candidates are reconstructed from a pair of oppositely charged proton and pion candidates, identified with relatively loose PID requirements.In this case, the charged tracks must have a closest distance to the IP within AE20 cm, with no transverse distance requirement imposed.The daughter tracks are constrained to originate from the same decay vertex with a χ 2 value less than 100, and this vertex is required to be displaced from the IP by a distance at least twice larger than the measurement uncertainty.It is demanded that the Λ candidates have a pπ − invariant mass within 1.111 < M pπ − < 1.121 GeV=c 2 , which corresponds to three standard deviations of the reconstruction resolution around the known Λ mass [28].Electromagnetic showers produced in the EMC, not associated with any charged tracks, are identified as photon candidates.The deposited energy is required to be greater than 25 MeV in the barrel region (j cos θj < 0.80) and greater than 50 MeV in the end cap region (0.86 < j cos θj < 0.92).To further suppress background from beam and electronic noise, the difference of EMC time with respect to the collision time is required to be within 700 ns.Showers are required to be separated from other charged tracks by an angle greater than 10°in order to eliminate activity induced by tracks.Then, the π 0 candidates are reconstructed from photon pairs with invariant mass within 0.115 < M γγ < 0.150 GeV=c 2 .To improve the π 0 momentum resolution, the mass of the π 0 candidate is constrained to the PDG value [28] via a one-constraint kinematic fit.Combinations satisfying χ 2 < 200 are preserved, and the refined momenta are utilized for subsequent studies.
By analyzing the inclusive MC samples with the tool TOPOANA [34], we find several processes with the same final states as the signals contaminate the selection.For , we veto events where the invariant mass of the Λπ 0 pair satisfies 1.290 To further mitigate the effects of combinatorial background, two kinematic variables are employed: ΔE and the beam-constrained mass, M BC .The variable ΔE is defined as c and E beam is the beam energy.The beam-constrained mass, M BC , is a crucial parameter used for determining signal yields.It is defined as The ΔE distributions in the data are illustrated in Fig. 2. In case where multiple E (GeV) ' , where S is the expected signal yield in the signal region M BC ∈ ½2.282; 2.291 GeV=c 2 and B is the background yield in the same region estimated from the inclusive MC sample.The number of SðBÞ is normalized to the integrated luminosity of the data sample.

IV. RELATIVE BF MEASUREMENT
Figure 3 shows the M BC spectra of accepted events of and Fig. 4 shows the corresponding distribution for Signal peaks are evident for the SCS modes above the distributions of background events.To minimize systematic uncertainty, the BF of each signal decay is measured relative to its CF counterpart by where i represents each energy point, N is the observed signal yield in data and ϵ denotes the detection efficiency obtained from signal MC samples.To determine R, an unbinned maximum likelihood fit is performed on these M BC spectra, in which R is a common fit parameter between the energy points.Table I lists the relative detection efficiencies and the signal yields of the reference modes.
To extract the signal yield of each mode, the simultaneous fit is performed on the M BC distributions at different energy points.In the fit, the signal shapes of the four modes are described with the MC-simulated signal shapes convoluted with a Gaussian function that is used to compensate for the resolution difference between data and MC simulation.To obtain a pure signal, we employ the truth-match method.This method involves comparing the reconstructed tracks of two photons in the π 0 and the charged tracks K AE and π AE with their corresponding truth information.
The angle θ truth is defined as the opening angle between each reconstructed and the corresponding simulated tracks.The signal shape is derived from the events with θ truth < 20°for all tracks.For the signal decay modes, the parameters of the Gaussian functions are shared with those of the corresponding reference decay modes due to low number of events in the signal peaks.
For the signal decay modes, the background shapes consist of an ARGUS function [35] to describe the combinatorial components, a shape extracted from exclusive MC simulations to describe the remaining peaking background and a shape extracted from signal MC samples to describe the wrongly reconstructed events.The peaking backgrounds arise from the following specific decay processes: The corresponding yields of these peaking backgrounds are determined using exclusive MC samples.As there are no significant sources of peaking contamination for the reference modes, here the background is described with only an ARGUS function and the unmatched background shape.The ARGUS function has an endpoint fixed at E beam and a floating slope parameter shared between signal modes and reference modes for better precision.Unmatched events, studied through the signal MC samples, shows a distribution that is not flat.In the simultaneous fit, the determination of yields associated with these unmatched events relies on evaluating the ratio between matched signal yields and unmatched background yields, where the ratio is determined from MC simulation.
By maximizing the likelihood of the simultaneous fit, we obtain where the uncertainties are statistical only.

V. SYSTEMATIC UNCERTAINTY
The significant sources of systematic uncertainty in the R measurement comprise those associated with the tracking and PID of charged tracks, the π 0 reconstruction, the ΔE requirement, the simultaneous fit, MC modeling, the understanding of the peaking backgrounds and the performance of truth matching.The relative quantities associated with these uncertainties are detailed in Table II.The uncertainties from the total number of c pairs and the BF of Λ → pπ − are canceled in the relative measurement.
We study the uncertainty from the tracking with a control sample of 178 GeV, where the tracking efficiency is measured both in data and MC simulation.We reweight the efficiency for kaon and pion according to their transverse momenta, and use the new efficiency to get the deviations in the obtained value of R, which is 0.2% for 178 GeV.We determine the PID efficiencies of kaon and pion identification both in data and MC simulations and reweight the efficiencies according to their momenta.In this way, the uncertainties for and 1.6%, respectively.The reconstruction efficiency of π 0 is studied through the D → Kππ 0 mode.Since the π 0 momentum in our signal and reference modes are not fully the same, we reweight them according to the π 0 momentum and obtain the associated uncertainty 0.8% for Λ þ c → ΛK þ π 0 .In the nominal fit, the parameters of the Gaussian function are shared between the signal and reference modes, and the uncertainty associated with these parameters is neglected due to the clear signal in the reference modes.The uncertainty related to the background shape is assessed by varying the ARGUS end point by AE0.15 MeV.The alternative fit results in an uncertainty of 1.2% for The uncertainty due to the fixed contribution of the peaking background yields in the fit is investigated by varying the fixed yields within AE1σ of the PDG BFs of individual background sources.The largest differences observed in the fitted signal yield are assigned as the The detection efficiency is determined after applying the ΔE requirements to the signal MC samples.Possible differences between the data and MC samples in the ΔE distributions are studied using the reference modes.The signal MC samples are smeared according to data, and the BF difference between nominal and smeared samples are assigned as the uncertainties, which are 0 The systematic uncertainties associated with MC modeling are evaluated by generating alternative signal MC samples.We add some possible resonances to the signal MC samples, for instance, , respectively.The efficiency differences obtained with the nominal and alternative signal MC samples are assigned as the uncertainties, which are 1.8% and 0.1% for We investigate the uncertainty linked to the performance of the truth matching by varying the θ truth requirement by 20°AE 1°in the signal MC.The relative differences obtained from these variations are then utilized to estimate the corresponding systematic uncertainties which are assigned to be 2.1% for The statistical significance of the signal is calculated by , where L max and L 0 are the maximal likelihood of the fits with and without the signal contribution, respectively.To account for additive systematic uncertainties, which include the M BC fit, peaking background and performance of truth matching, and under the assumption of their independence, we obtain quadratic sums of 2.8% for R ΛK þ π 0 and 4.5% for R ΛK þ π þ π −.Taking these systematic uncertainties into consideration, the signal significance is found to be 5.7σ for the

VI. SUMMARY
In this paper, we report the first observation of the SCS decay Λ þ c → ΛK þ π 0 with a significance of 5.7σ and the with a significance of 3.1σ.The BFs are measured relative to their CF counterparts, which are  [28], we obtain the BFs BðΛ c → ΛK þ π 0 Þ to be ð4.5 AE 0.8Þ × 10 −3 [10] and ð3.5 AE 0.6Þ × 10 −3 [11].Our measured value deviates from these predictions by 3.5σ and 3.0σ, respectively.Our result of Þ is consistent with the measurement by the BABAR experiment [13].The precision of both measurements is currently dominated by the statistical uncertainty.Improved precision for these two SCS decays will be achievable from the larger datasets that are expected to be collected in the near future, following the upgrade of the BEPCII collider [19,36].These improved measurements will provide valuable insights into the properties of these decays and help in refining our understanding of charmed baryon decays.
exist, the one with the minimum jΔEj is
13 AE 1.48 stat AE 0.20 syst AE 0.33 ref Þ × 10 −4 .Two recent theoretical works which are based on the quark SUð3Þ flavor symmetry predict the BðΛ þ

TABLE I .
Relative detection efficiencies for and signal yields for reference modes at different energy points.Uncertainties are statistical only.