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Charmed baryons provide an excellent laboratory for studying the properties of QCD in the case where a heavy quark couples to two light quarks. Currently, we do not have reliable phenomenological models to describe these complex baryon decays. More than two decades ago, a general formulation of a topological-diagram scheme for the nonleptonic weak decays of baryons was proposed to calculate the amplitudes of different topological diagrams [1]. The factorizable external W-emission amplitude T and internal W-emission amplitude C, as well as the non-factorizable inner W-emission amplitude
C′ and W-exchange amplitude E are introduced in the representation of these diagrams. In this scheme, one amplitude can be factorized into two parts, the decay constant of the emitted meson and the heavy-to-light transition form factor, which can be directly calculated. By way of example, the topological diagrams forΛ+c→nπ+π0 can be seen in Fig. 1. We know that here the non-factorizable contribution is essential for understanding the weak decays of charmed baryons, in contrast to the negligible effect they contribute in heavy-meson decays [2]. Hence, studies of charmed baryon decays involving non-factorizable components are critical for understanding the underlying dynamics of charmed-baryon decays in general.
Figure 1. Topological diagrams of the decay
Λ+c→nπ+π0 via (a) externalW -emissionT , (b) internalW -emissionC , (c) innerW -emissionC′ , and (d)W -exchange diagramE .In addition, an alternative and model-inpendent approach based on quark flavor SU(3) symmetry has been proposed to describe charmed-baryon decays. Even though it is an approximate method, it is a powerful and reliable tool to extract useful information about these transitions [3–10]. Improved measurements of charmed-baryon decays will be important in further testing the validity of this method.
Many experimental studies of various
Λ+c decays have been reported, with a focus on decays to two-body hadronic final states [11–21]. However, more studies of multi-body hadronic decays are required to gain deeper insight into the nature of non-perturbative QCD, as these involve rich intermediate processes and the branching fractions (BF) are in general higher. There is a significant discrepancy between the predicted BFs ofΛ+c→NˉKππ decays reported in Ref. [22] and the measured values forΛ+c→pK−π+π0 andΛ+c→pˉK0π+π− [23]. Clarifying this tension requires knowledge of the BFs of hadronicΛ+c decays to final states involving a neutron. Fewer studies have been performed for these decays because of the difficulty of direct neutron detection.The BESIII collaboration has measured the BFs of the Cabibbo-favored (CF) decay
Λ+c→nK0Sπ+ [14] and the Cabibbo-suppressed (CS) decayΛ+c→nπ+ [18]. These studies provide critical tests for isospin and SU(3) symmetries in charmed-baryon decays, the violation of which could lead to enhancedCP -violation effects [24, 25]. Taking the BFs ofΛ+c→nK0Sπ+ ,Λ+c→pK0Sπ0 andΛ+c→pK−π+ from the Particle Data Group (PDG) [23], the amplitudes of these three decays satisfy the triangle relation and obey isospin symmetry [3]. However, the ratio of the BF ofΛ+c→nπ+ to that ofΛ+c→pπ0 is measured to be larger than 7.2 which disagrees with the SU(3) flavor symmetry model prediction [3, 6, 26]. Precise measurements of the BFs of additionalΛ+c decays to final states involving a neutron, such asΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ , andΛ+c→nK−π+π+ , are highly desirable to allow for futher tests of isospin and SU(3) symmetries in charmed-baryon decays. Throughout this paper, charge-conjugate modes are implicitly assumed.In this paper, two CS decays
Λ+c→nπ+π0 ,Λ+c→nπ+π−π+ , and the CF decayΛ+c→nK−π+π+ are studied by employing the double-tag (DT) method [27], where the neutron is reconstructed via the missing-mass technique. Our analysis is based on electron-positron annihilation data samples collected at seven center-of-mass (c.m.) energies from√s=4599.53MeV to4698.82MeV by the BESIII detector. These data samples correspond to an integrated luminosity of 4.5 fb−1 [28–31], as listed in Table 1. Within this energy range, the electron-positron collisions provide a clean environment for the productionΛ+cˉΛ−c pairs, which offers a unique opportunity to carry out model-independent measurements of the BFs of variousΛ+c decays involving neutrons. The DT method allows us to measure the BFs without any theoretical input or external information on the cross section ofΛ+c production.√s /MeV
Int. luminosity/pb −1 
4599.53 586.90±0.10±3.90 
4611.86 103.65±0.05±0.55 
4628.00 521.53±0.11±2.76 
4640.91 551.65±0.12±2.92 
4661.24 529.43±0.12±2.81 
4681.92 1667.39±0.21±8.84 
4698.82 535.54±0.12±2.84 
Table 1. The c.m. energies and integrated luminosities for the data samples.
The
ˉΛ−c baryons are reconstructed with twelve exclusive hadronic decay modes, as listed in Table 2. This data set is referred to as the single-tag (ST) sample. Theπ0 ,K0S ,ˉΛ ,ˉΣ0 , andˉΣ− particles are reconstructed via individual dominant decay modes. Those events in which any of the signal decaysΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ , andΛ+c→nK−π+π+ are reconstructed in the system recoiling against the STˉΛ−c candidates are denoted as DT candidates.Tag mode ΔE 
/MeV 
NSTi 
εSTi(%) 
εDTi(E)(%) 
εDTi(D)(%) 
εDTi(F)(%) 
ˉpK0S 
(−21,18) 
3376±61 48.6 
12.58 
11.55 
18.50 
ˉpK+π− 
(−29,26) 
17508±147 47.1 
10.77 
10.59 
16.61 
ˉpK0Sπ0 
(−49,34) 
1785±63 19.7 
4.74 
4.65 
7.15 
ˉpK0Sπ−π+ 
(−34,31) 
1511±57 20.7 
4.22 
4.13 
5.99 
ˉpK+π−π0 
(−60,41) 
5111±128 17.8 
⋯ 
4.13 
6.60 
ˉΛπ− 
(−23,21) 
2074±48 41.3 
9.95 
9.12 
15.08 
ˉΛπ−π0 
(−50,41) 
4380±88 18.2 
4.05 
3.85 
6.00 
ˉΛπ−π+π− 
(−40,36) 
2059±61 13.9 
2.80 
2.67 
3.93 
ˉΣ0π− 
(−33,31) 
1398±42 25.9 
6.31 
5.89 
8.46 
ˉΣ−π0 
(−67,32) 
879±43 22.5 
5.78 
5.21 
8.22 
ˉΣ−π−π+ 
(−40,32) 
3027±88 22.1 
5.40 
5.21 
7.77 
ˉpπ−π+ 
(−26,20) 
1596±80 53.6 
⋯ 
⋯ 
17.35 
Table 2. Requirements on
ΔE , ST yields, ST and DT efficiencies for the signal decays ofΛ+c→nπ+π0 (E ),Λ+c→nπ+π−π+ (D ) andΛ+c→nK−π+π+ (F ) at√s=4681.92MeV . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs. Entries of "⋯ " are for the cases where knowledge of the DT efficiencies is not required in the analysis. -
The BESIII detector [32] records symmetric
e+e− collisions provided by the BEPCII storage ring [33], which operates in the center-of-mass energy range from 2.0GeV to 4.95GeV . BESIII has collected large data samples in this energy region [34]. 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 at1GeV/c is0.5 %, and the specific ionization energy loss (dE/dx) resolution is6 % for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of2.5 % (5 %) at1 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 [35–37]. High-statistics Monte Carlo (MC) simulation samples for the processe+e−→inclusive are produced with the KKMC generator [38] by incorporating the initial-state radiation (ISR) effects and the beam-energy spread. The inclusive MC simulation sample, which consists ofΛ+cˉΛ−c events,D(∗)(s) production, ISR return to lower-mass ψ states, and continuum processese+e−→qˉq (q=u,d,s ), is generated to determine the ST detection efficiencies and estimate the potential background. For this MC simulation sample, all the known decay modes of charmed hadrons and charmonia are modeled with evtgen [39, 40] using BFs taken from the PDG [23], and the remaining unknown decays are modeled with LUNDCHARM [41]. Furthermore, exclusive DT signal MC simulation events, where theˉΛ−c decays into any of the tag modes and theΛ+c decays into any of the signal modes ofnπ+π0 ,nπ+π−π+ ornK−π+π+ , are used to determine the DT dectection efficiencies. The Born cross sections are taken into account when producing the MC simulation sample ofΛ+cˉΛ−c pairs. TheΛ+c→nπ+π0 andΛ+c→nπ+π−π+ signal MC samples are simulated evenly distributed in phase space since the angular distributions, momentum distributions and the two-body invariant mass distributions of the final state particles of the signal MC simulation samples are in good agreement with data with the current size of data set. For the signal MC simulation sample ofΛ+c→nK−π+π+ , the key kinematic distributions mentioned above have been reweighted to agree with those of data. All final tracks and photons are fed into a GEANT4-based [42, 43] detector simulation package, which includes the geometric description of the BESIII detector. -
Charged tracks detected in the MDC must satisfy
|cosθ|<0.93 (where θ is defined with respect to the z-axis, which is the symmetry axis of the MDC) and have a distance of closest approach to the interaction point (IP) of less than 10 cm along the beam axis and less than 1 cm in the perpendicular plane, except for those used for reconstructingK0S andˉΛ decays. Particle identification (PID) for charged tracks combines measurements of the energy deposited in the MDC (dE/ dx) and the flight time in the TOF to form likelihoodsL(h)(h=p,K,π) for each hadron h hypothesis. Tracks are identified as protons when their likelihoods satisfyL(p)>L(K) andL(p)>L(π) , while charged kaons and pions are identified by comparing the likelihoods for the kaon and pion hypotheses,L(K)>L(π) orL(π)>L(K) , respectively.Neutral showers are reconstructed in the EMC. Showers not associated with any charged track are identified as photon candidates. The deposited energy of each shower in the EMC must be greater than
25MeV in the barrel region, corresponding to the polar angle|cosθ|<0.80 , and greater than50MeV in the end-cap region, corresponding to0.86<|cosθ|<0.92 . The EMC time difference from the event start time is required to be less than 700 ns, to suppress electronic noise and showers unrelated to the event. Theπ0 candidates are reconstructed from photon pairs with invariant masses within115MeV/c2<M(γγ)<150MeV/c2 . To improve momentum resolution, a kinematic fit constraining the photon pairs to theπ0 known mass is performed and the resulting four-momentum of theπ0 candidate is used for further analysis.Candidates for
K0S andˉΛ decays are formed byπ+π− andˉpπ+ combinations, respectively. For these tracks, their distances of closest approaches to the IP must be within± 20 cm along the beam direction. No distance constraint in the transverse plane is required. The charged pion is not subjected to the PID requirement described above, while the proton PID is imposed. The two final-state tracks are constrained to originate from a common decay vertex by requiring theχ2 of the 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. The fitted momenta of theπ+π− andˉpπ+ combinations are used in the subsequent analysis. We require487MeV/c2<M(π+π−)<511MeV/c2 and1111MeV/c2<M(ˉpπ+)<1121MeV/c2 to selectK0S andˉΛ candidates, respectively, which corresponds to a window of about three times the standard deviations either side of the known masses. TheˉΣ0 andˉΣ− candidates are reconstructed with theγˉΛ andˉpπ0 combinations with invariant masses being in the intervals of1179MeV/c2<M(γˉΛ)<1203MeV/c2 and1176MeV/c2<M(ˉpπ0)<1200MeV/c2 , respectively.For the tag modes
ˉΛ−c→ ˉpK0Sπ0 ,ˉΛ−c→ˉpK0Sπ−π+ ,ˉΛ−c→ˉΣ−π−π+ , andˉΛ−c→ ˉpπ−π+ , possible backgrounds withˉΛ→ˉpπ+ are rejected by requiringM(ˉpπ+) to be outside the range(1110,1120)MeV/c2 . In the selection ofˉΛ−c→ˉpK0Sπ0 decays, candidate events within the range1170MeV/c2<M(ˉpπ0)<1200MeV/c2 are excluded to suppress background fromˉΣ− decays. To removeK0S decays in the selection ofˉΛ−c→ˉΛπ−π+π− ,ˉΛ−c→ˉΣ−π0 ,ˉΛ−c→ˉΣ−π−π+ , andˉΛ−c→ ˉpπ−π+ candidates, the invariant masses of anyπ+π− andπ0π0 pairs are required to lie outside of the range(480,520)MeV/c2 . MC simulation studies indicate that peaking backgrounds and cross feeds among the twelve ST modes are negligible after applying the above veto procedures.The ST
ˉΛ−c baryons are identified using the beam-constrained massMBC≡√E2beam/c4−p2/c2 , whereEbeam is the average value of thee+ ande− beam energies and p is the measuredˉΛ−c momentum in the c.m. system of thee+e− collision. To improve the signal purity, the energy differenceΔE≡E−Ebeam for theˉΛ−c candidate is required to fulfil a mode-dependentΔE requirement shown in Table 2, corresponding to approximately three times the resolutions. Here, E is the total reconstructed energy of theˉΛ−c candidate. For each ST mode, if more than one candidate satisfies the above requirements, we select the one with the minimal|ΔE| . Figure 2 shows theMBC distributions of various ST modes for the data sample at√s=4681.92MeV , where a clearˉΛ−c signal peak can be seen in each mode.
Figure 2. (color online) The
MBC distributions of various ST modes for the data sample at√s =4681.92MeV . The points with error bars represent data. The (red) solid curves indicate the fit results and the (blue) dashed curves describe the fitted background shapes. The ranges between green dashed lines are the signal regions.To obtain the ST yields, unbinned maximum-likelihood fits are performed to the
MBC distributions, 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 [44]. The fit results for the data sample at√s= 4681.92 MeV are shown in Fig. 2. The fits to theMBC distributions for the other six data samples at different c.m. energies are shown in Appendix B. Candidates withMBC∈(2275,2300)MeV/c2 for the data sample at√s=4599.53MeV ,MBC∈(2275,2306)MeV/c2 for the data samples at√s= 4611.86 MeV, 4628.00 MeV, 4640.91 MeV, andMBC∈(2275,2310)MeV/c2 for the data samples at√s= 4661.24 MeV, 4681.92 MeV, 4698.82 MeV are retained for further analysis. The differences in selection requirements between data sets are necessary as the resolution and effects of ISR vary with collision energy. The fitted ST yields, ST and DT efficiencies for each ST mode at√s=4681.92 MeV are summarized in Table 2; those for the other c.m. energy points can be found in Appendix B.Searches are performed for the decays
Λ+c→nπ+π0 ,Λ+c→nπ+π−π+ andΛ+c→nK−π+π+ among the remaining tracks and showers recoiling against the STˉΛ−c candidates. In the case ofΛ+c→nπ+π0 , the event is allowed to contain only one pion with opposite charge to the taggedˉΛ−c satisfying the same selection criteria as described above. Theπ0 candidate giving rise to the smallestχ2 for the mass-constrained kinematic fit is retained. When searching forΛ+c→nπ+π−π+ andΛ+c→nK−π+π+ decays, events are selected with only three remaining charged tracks, satisfying the desired charge and PID criteria. In each of the decays, the kinematic variableMmiss≡√E2miss/c4−|→pmiss|2/c2 is used to infer the presence of the undetected neutron. Here,Emiss and→pmiss are calculated byEmiss≡Ebeam−Erec and→pmiss≡→pΛ+c−→prec , whereErec (→prec ) is the energy (momentum) of the reconstructed final-state particles in thee+e− c.m. system. The momentum of theΛ+c baryon→pΛ+c is calculated by→pΛ+c≡−ˆptag√E2beam/c2−m2Λ+cc2 , whereˆptag is the momentum direction of the STˉΛ−c andmΛ+c is the known mass of theΛ+c baryon [23]. In the case ofΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ , andΛ+c→nK−π+π+ decays, theMmiss(π+π0) ,Mmiss(π+π−π+) andMmiss(K−π+π+) spectra are expected to peak around the known mass of the neutroni.e. at939.6MeV/c2 [23]. A study of the inclusive MC simulation sample reveals that the dominant background events for the signal modeΛ+c→nπ+π0 are from the processesΛ+c→Λπ+ withΛ→nπ0 ,Λ+c→Σ+π0 withΣ+→nπ+ andΛ+c→Σ0π+ withΣ0→γΛ(→nπ0) . In order to reject these background events forΛ+c→nπ+π0 , the following selection criteria are applied:Mmiss(π+)> 1300MeV/c2 andMmiss(π0)> 1370MeV/c2 . For the signal modeΛ+c→nπ+π−π+ , the peaking backgrounds from the decaysΛ+c→nK0S(→π+π−)π+ ,Λ+c→Σ+(→nπ+)π+π− , andΛ+c→Σ−(→nπ−)π+π+ are suppressed by requiringMπ+π−∉(487,511)MeV/c2 ,Mmiss(π+π−)∉(1150,1250)MeV/c2 andMmiss(π+π+)∉(1150,1250)MeV/c2 . Note that, based on the study of the inclusive MC simulation sample, ten ST modes (after excludingˉΛ−c→ˉpK+π−π0 andˉΛ−c→ˉpπ−π+ ) are used in the analysis of the decayΛ+c→nπ+π0 , and eleven ST modes (after excludingˉΛ−c→ˉpπ−π+ ) are used in the analysis of the decayΛ+c→nπ+π−π+ to improve the background level in theMmiss spectra.The resulting
Mmiss distributions of the DT candidate events summed over all data samples at seven c.m. energies are shown in Fig. 3. A peak around the neutron mass is observed in Fig. 3(a) representing theΛ+c→nπ+π0 signal. Moreover, there are two prominent structures peaking around the Λ andΣ0 mass regions, which correspond to the CF decaysΛ+c→Λπ+π0 andΛ+c→Σ0π+π0 , respectively. Significant signal peaks around the neutron mass are also observed forΛ+c→nπ+π−π+ andΛ+c→nK−π+π+ in Fig. 3(b) and Fig. 3(c), respectively.
Figure 3. (color online) The
Mmiss distributions of the surviving DT candidate events for (a)Λ+c→nπ+π0 , (b)Λ+c→nπ+π−π+ and (c)Λ+c→nK−π+π+ decays with fit results overlaid. The points with error bars are data combined from seven c.m. energy points. The solid black curves are the fit results. The red, cyan, and pink dashed curves indicate the neutron, Λ, and Σ signal shapes, respectively. The brown dashed curve is theΛ+cˉΛ−c background shape forΛ+c→nπ+π0 . The blue dashed curves represent the fitted combinatorial background shape. The green histograms are the simulated combinatorial background shapes from the inclusive MC sample. The plots in the bottom of each graphs show the pull value of each bin, in which the values are expected to fluctuate around 0.The total DT signal yield is obtained by performing an unbinned maximum-likelihood fit on the
Mmiss distribution. The neutron, Λ andΣ0 signals are modeled by individual MC-derived shapes convolved with Gaussian functions that account for the shift and resolution difference between data and MC simulation. The Gaussian-function parameters are left free and are shared by the three signal processes in the fit to theMmiss(π+π0) spectra. The potential background events in theMmiss distributions are classified into two categories. Those directly originating from continuum hadron production in thee+e− annihilation are denoted asqˉq background. Those frome+e−→Λ+cˉΛ−c events excluding the contributions from the corresponding signal process are referred to asΛ+cˉΛ−c background. In the fit to theMmiss(π+π0) distribution, theqˉq background is described by a second-order Chebyshev polynomial with free parameters and theΛ+cˉΛ−c backgroud shape is taken from the inclusive MC simulation sample. For the fit to theMmiss(π+π−π+) spectrum, only one first-order Chebyshev polynomial with free parameters is used to model all the background. Similarly, for theMmiss(K−π+π+) distribution, one second-order Chebyshev function with fixed parameters is taken as the background shape where the parameters are derived from the fit to the inclusive MC simulation sample. The DT signal and background yields are left free in the fit to theMmiss(π+π0) ,Mmiss(π+π−π+) andMmiss(K−π+π+) spectra. Figure 3 shows the results of the fits to theMmiss distributions. From these fits, we determine the DT signal yields ofΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ , andΛ+c→nK−π+π+ to beNDTnπ+π0=150.9±21.4 ,NDTnπ+π−π+=120.6±17.9 andNDTnK−π+π+=805.8±33.1 , respectively, where the uncertainties are statistical only. The statistical significances of theΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ andΛ+c→nK−π+π+ signals are7.9σ ,7.8σ , and>10σ , respectively, which are evaluated by the changes in the likelihoods between the nominal fit and the fit with the signal yield set to zero, and accounting for the change in the number of degrees of freedom.The BFs of the decays
Λ+c→nπ+π0 ,Λ+c→nπ+π−π+ , andΛ+c→nK−π+π+ are determined asB=NDT∑ijNSTij⋅(ϵDTij/ϵSTij)⋅Bint,
(1) where i and j represent the ST modes and the data samples at different c.m. energies, respectively. The factor
Bint is(98.823±0.034) %, which is the BF ofπ0→γγ [23], is only present forΛ+c→nπ+π0 .NSTij ,ϵSTij , andϵDTij are the ST yields, ST efficiencies, and DT efficiencies, respectively. The detection efficienciesϵSTij andϵDTij are estimated from the inclusive MC simulation sample and exclusive DT signal MC simulation samples, respectively. The ST and DT efficiencies for the data sample at√s=4681.92 MeV are summarized in Table 2. The detection efficiencies for the other data samples are summarized in Appendix B. The obtained BFs are summaried in Table 3.Signal decay B(%) 
Λ+c→nπ+π0 
0.64±0.09±0.02 
Λ+c→nπ+π−π+ 
0.45±0.07±0.03 
Λ+c→nK−π+π+ 
1.90±0.08±0.09 
Table 3. The obtained BFs, where the first uncertainties are statistical and the second are systematic.
Most systematic uncertainties from the ST side cancel in the determination of the BFs, as is clear from Eq. (1). However, effects from the signal side can lead to systematic bias, for example, the requirement of no extra charged track, tracking efficiency, PID efficiency,
π0 reconstruction, peaking background veto,Mmiss fit, STˉΛ−c yield, MC modeling, and MC sample size. The systematic uncertainty due to the requirement of no extra charged track is assigned as 1.1% from the study of a control sample ofe+e−→Λ+cˉΛ−c withΛ+c→nK−π+π+ andˉΛ−c decays to tag modes. The systematic uncertainties associated with the efficiencies of the tracking and PID of charged particles are estimated to be1 % by using control samples ofe+e−→π+π+π−π− ande+e−→K+K−π+π− events collected at c.m. energies above√s=4.0GeV . The systematic uncertainty due to theπ0 reconstruction efficiency is assigned to be1.0 % [12]. The systematic uncertainty associated with the BF ofπ0→γγ is0.03 % [23], which is negligible. In order to estimate the systematic uncertainties arising from the veto of peaking backgrounds involving Λ,Σ+ ,Σ0 ,K0S , andΣ− , the corresponding resolutions in the MC simulation samples are corrected to agree with those in data, and the BFs are then re-evaluated with the updated MC simulation samples. The deviations from the baseline BF measurements are taken as the associated systematic uncertainties forΛ+c→nπ+π0 andΛ+c→nπ+π−π+ , which are 1.6% and 1.0%, respectively. The systematic uncertainties from the fitted DT yields are 1.3%, 2.2%, and 0.9% forΛ+c→nπ+π0 ,nπ+π−π+ , andnK−π+π+ , respectively, which are estimated from varying the alternative polynomial descriptions for theqˉq andΛ+cˉΛ−c backgrounds, respectively. The systematic uncertainty in the total STˉΛ−c yield is 0.1% forΛ+c→nπ+π0 , and 0.2% forΛ+c→nπ+π−π+ , andnK−π+π+ . These uncertainties arise from the fluctuation of background together with a component coming from the fit to theMBC distribution. The systematic uncertainties arising from the MC modeling are investigated by reweighting the MC distribution to data, and they are assigned as the efficiency differences between the original and reweighted samples. The systematic uncertainties due to limited sample sizes of the MC samples are estimated to be 0.2%. Assuming that all the sources are uncorrelated, the total uncertainties are then taken to be the quadratic sums of the individual values, which are 3.1%, 5.6%, and 4.5% forΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ , andΛ+c→nK−π+π+ , respectively. All the above systematic uncertainties are summarized in Table 4.Source nπ+π0(%) 
nπ+π−π+(%) 
nK−π+π+(%) 
No extra charged track 1.1 1.1 1.1 Tracking 1.0 3.0 3.0 PID 1.0 3.0 3.0 π0 reconstruction
1.0 − 
− 
Background veto 1.6 1.0 − 
Mmiss fit
1.3 2.2 0.9 ST ˉΛ−c yield
0.1 0.2 0.2 MC model 1.1 2.6 ⋯ 
MC sample size 0.2 0.2 0.2 Total 3.1 5.6 4.5 Table 4. Relative systematic uncertainties in BF measurements. "
⋯ " means the uncertainty is negligible. "− " indicates cases where there is no uncertainty. -
In summary, by analyzing 4.5
fb−1 of data collected at c.m. energies between 4599.53 and 4698.82 MeV, we report for the first time the observation ofΛ+c→nπ+π0 ,Λ+c→nπ+π−π+ andΛ+c→nK−π+π+ . The BFs of these decays are determined to beB(Λ+c→nπ+π0)=(0.64±0.09±0.02) %,B(Λ+c→nπ+π−π+)=(0.45±0.07±0.03) %, andB(Λ+c→nK−π+π+)=(1.90±0.08±0.09) %, where the first uncertainties are statistical and the second systematic. These observations are important additions to our knowledge ofΛ+c decays. Comparison of these results to those of decays involving protons provides crucial inputs for understanding the mechanisms in the charmed baryon decays under the SU(3) flavor symmetry. TakingB(Λ+c→pπ−π+)=(0.461±0.028) % from the PDG [23], we can calculateB(Λ+c→pπ−π+)/B(Λ+c→nπ0π+)=0.72±0.11 . This result provides useful input to test of isospin symmetry in the charm baryon sector. TakingB(Λ+c→nπ+)=(6.6±1.3)×10−4 [18], the ratioB(Λ+c→nπ+π0)/B(Λ+c→nπ+) is calculated to be9.7±2.4 , indicating an order-of-magnitude difference in the rates of the two decays. This ratio is greater thanB(Λ+c→pK0Sπ0)/B(Λ+c→pK0S)=(1.24±0.10) . To further understand this behavior, amplitude analysis will be needed to decouple the intermediate resonances contributions forΛ+c→nπ+π0 andΛ+c→pK0Sπ0 . The ratio ofB(Λ+c→nπ+π−π+)/B(Λ+c→nK−π+π+)=(0.24±0.04) which is consistent with the ratio of Cabibbo-Kobayashi-Maskawa matrix elements|Vcd|/|Vcs|=(0.224±0.005) offers a new constraint on the CS and CF decay dynamics. The results from this analysis provide an essential input for the phenomenological studies on the underlying dynamics of charmed bayond decays. -
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. The authors are grateful to Fusheng Yu for enlightening discussions.
-
Figures A1 and A2 show the topological diagrams of
Λ+c→nπ+π−π+ andΛ+c→nK−π+π+ , respectively.
Figure A1. Topological diagrams of
Λ+c→nπ+π−π+ via (a) external W-emission T, (b) internal W-emission C, (c) inner W-emissionC′ , and (d) W-exchange diagram E.
Figure A2. Topological diagrams of
Λ+c→nK−π+π+ via (a) external W-emission T, (b) internal W-emission C, (c) W-exchange diagram E. -
Figures B1–B6 show the fits for the
MBC distributions of the STˉΛ−c candidates for various tag modes from the data samples at√s= 4599.53, 4611.86, 4628.00, 4640.91, 4661.24, and 4698.82 MeV, respectively.
Figure B1. (color online) The
MBC distributions of the STˉΛ−c candidates of various tag modes for the data sample at√s=4599.53MeV . The points with error bars represent data. The red solid curves indicate the fit results and the blue dashed curves describe the background shapes. The ranges between green dashed lines are the signal regions.
Figure B2. (color online) The
MBC distributions of the STˉΛ−c candidates of various tag modes for the data sample at√s=4611.86MeV . The points with error bars represent data. The red solid curves indicate the fit results and the blue dashed curves describe the background shapes. The ranges between green dashed lines are the signal regions.
Figure B3. (color online) The
MBC distributions of the STˉΛ−c candidates of various tag modes for the data sample at√s=4628.00MeV . The points with error bars represent data. The red solid curves indicate the fit results and the blue dashed curves describe the background shapes. The ranges between green dashed lines are the signal regions.
Figure B4. (color online) The
MBC distributions of the STˉΛ−c candidates of various tag modes for the data sample at√s=4640.91MeV . The points with error bars represent data. The red solid curves indicate the fit results and the blue dashed curves describe the background shapes. The ranges between green dashed lines are the signal regions.
Figure B5. (color online) The
MBC distributions of the STˉΛ−c candidates of various tag modes for the data sample at√s=4661.24MeV . The points with error bars represent data. The red solid curves indicate the fit results and the blue dashed curves describe the background shapes. The ranges between green dashed lines are the signal regions.
Figure B6. (color online) The
MBC distributions of the STˉΛ−c candidates of various tag modes for the data sample at√s=4698.82MeV . The points with error bars represent data. The red solid curves indicate the fit results and the blue dashed curves describe the background shapes. The ranges between green dashed lines are the signal regions.Tables B1–B6 show the ST yields, ST and DT efficiencies for various tag modes from the data samples at
√s= 4599.53, 4611.86, 4628.00, 4640.91, 4661.24, and 4698.82 MeV, respectively.Tag mode NSTi 
εSTi(%) 
εDTi(nπ+π0)(%) 
εDTi(nπ+π−π+)(%) 
εDTi(nK−π+π−)(%) 
ˉpK0S 
1277±36 
56.1 
14.27 
13.49 
20.87 
ˉpK+π− 
6806±91 
51.5 
11.25 
11.53 
17.64 
ˉpK0Sπ0 
606±34 
23.0 
5.17 
5.25 
7.34 
ˉpK0Sπ−π+ 
613±34 
23.5 
4.51 
4.76 
6.89 
ˉpK+π−π0 
2197±78 
20.6 
⋯ 
4.57 
6.83 
ˉΛπ− 
757±28 
48.4 
11.62 
10.9 
17.08 
ˉΛπ−π0 
1742±56 
21.6 
4.52 
4.43 
6.42 
ˉΛπ−π+π− 
769±36 
15.6 
2.86 
2.90 
4.17 
ˉΣ0π− 
520±26 
29.4 
7.30 
6.96 
11.20 
ˉΣ−π0 
320±25 
23.7 
6.47 
6.05 
8.38 
ˉΣ−π−π+ 
1186±49 
25.4 
5.84 
5.82 
8.81 
ˉpπ−π+ 
598±47 
64.3 
⋯ 
⋯ 
22.04 
Table B1. ST yields, ST and DT efficiencies of various tag modes for the data sample at
√s=4599.53MeV . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs. Entries of "⋯ " are for the cases where knowledge of the DT efficiencies are not required in the analysis.Tag mode NSTi 
εSTi(%) 
εDTi(nπ+π0)(%) 
εDTi(nπ+π−π+)(%) 
εDTi(nK−π+π−)(%) 
ˉpK0S 
239±16 
53.7 
13.89 
12.71 
20.09 
ˉpK+π− 
1166±39 
51.0 
11.34 
11.27 
16.98 
ˉpK0Sπ0 
127±17 
22.2 
5.04 
4.91 
7.20 
ˉpK0Sπ−π+ 
106±16 
21.9 
4.35 
4.33 
6.04 
ˉpK+π−π0 
364±34 
19.9 
⋯ 
4.40 
6.25 
ˉΛπ− 
123±11 
46.9 
11.29 
10.22 
15.27 
ˉΛπ−π0 
302±23 
19.8 
4.34 
4.17 
6.08 
ˉΛπ−π+π− 
139±15 
13.6 
2.68 
2.75 
3.69 
ˉΣ0π− 
102±13 
26.6 
6.89 
6.53 
8.65 
ˉΣ−π0 
73±10 
22.6 
6.47 
5.9 
8.46 
ˉΣ−π−π+ 
218±22 
25.5 
5.74 
5.63 
8.47 
ˉpπ−π+ 
155±22 
71.4 
⋯ 
⋯ 
21.82 
Table B2. ST yields, ST and DT efficiencies of various tag modes for the data sample at
√s=4611.86MeV . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs. Entries of "⋯ " are for the cases where knowledge of the DT efficiencies are not required in the analysis.Tag mode NSTi 
εSTi(%) 
εDTi(nπ+π0)(%) 
εDTi(nπ+π−π+)(%) 
εDTi(nK−π+π−)(%) 
ˉpK0S 
1054±35 
51.8 
13.27 
12.17 
18.98 
ˉpK+π− 
5886±39 
49.2 
10.98 
10.97 
16.77 
ˉpK0Sπ0 
616±36 
20.7 
4.94 
4.79 
6.73 
ˉpK0Sπ−π+ 
510±32 
20.6 
4.21 
4.17 
6.01 
ˉpK+π−π0 
1589±69 
18.7 
⋯ 
4.32 
6.95 
ˉΛπ− 
675±28 
43.2 
10.69 
9.84 
14.72 
ˉΛπ−π0 
1454±54 
19.1 
4.18 
3.98 
5.90 
ˉΛπ−π+π− 
587±33 
13.6 
2.70 
2.65 
3.67 
ˉΣ0π− 
413±23 
27.2 
6.62 
6.24 
8.41 
ˉΣ−π0 
263±23 
23.4 
6.20 
5.65 
9.10 
ˉΣ−π−π+ 
994±20 
23.6 
5.54 
5.47 
8.24 
ˉpπ−π+ 
517±45 
61.6 
⋯ 
⋯ 
19.75 
Table B3. ST yields, ST and DT efficiencies of various tag modes for the data sample at
√s=4628.00MeV . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs.Entries of "⋯ " are for the cases where knowledge of the DT efficiencies are not required in the analysis.Tag mode NSTi 
εSTi(%) 
εDTi(nπ+π0)(%) 
εDTi(nπ+π−π+)(%) 
εDTi(nK−π+π−)(%) 
ˉpK0S 
1107±36 
50.7 
13.14 
12.08 
19.12 
ˉpK+π− 
6250±89 
48.5 
10.91 
10.86 
16.83 
ˉpK0Sπ0 
599±36 
20.7 
4.82 
4.77 
7.02 
ˉpK0Sπ−π+ 
522±33 
20.8 
4.21 
4.15 
6.50 
ˉpK+π−π0 
1632±70 
18.1 
⋯ 
4.23 
6.62 
\bar{\Lambda}{}\pi^- 
705\pm29 
42.7 
10.51 
9.55 
14.24 
\bar{\Lambda}{}\pi^-\pi^0 
1613\pm54 
19.1 
4.14 
3.95 
5.46 
\bar{\Lambda}{}\pi^-\pi^+\pi^- 
745\pm36 
14.2 
2.70 
2.67 
4.20 
\bar{\Sigma}{}^{0}\pi^- 
445\pm25 
26.2 
6.43 
6.09 
8.97 
\bar{\Sigma}{}^{-}\pi^0 
298\pm24 
24.6 
6.01 
5.52 
7.70 
\bar{\Sigma}{}^{-}\pi^-\pi^+ 
1077\pm49 
23.4 
5.43 
5.38 
8.01 
\bar{p}{}\pi^-\pi^+ 
552\pm47 
59.7 
\cdots 
\cdots 
22.97 
Table B4. ST yields, ST and DT efficiencies of various tag modes for the data sample at
\sqrt{s}=4640.91 \,{\rm{MeV}} . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs. Entries of "\cdots " are for the cases where knowledge of the DT efficiencies are not required in the analysis.Tag mode N_{i}^{\rm{ST}} 
\varepsilon_{i}^{\rm{ST}}(\%) 
\varepsilon_{i}^{\rm{DT}}(n\pi^+\pi^0)(\%) 
\varepsilon_{i}^{\rm{DT}}(n\pi^{+}\pi^{-}\pi^{+})(\%) 
\varepsilon_{i}^{\rm{DT}}(nK^{-}\pi^{+}\pi^{-})(\%) 
\bar{p}{}K_{S}^0 
1119\pm35 
49.6 
12.82 
11.78 
18.58 
\bar{p}{}K^{+}\pi^- 
5938\pm86 
48.2 
10.93 
10.85 
16.47 
\bar{p}{}K_{S}^0\pi^0 
594\pm36 
20.1 
4.86 
4.75 
7.12 
\bar{p}{}K_{S}^0\pi^-\pi^+ 
537\pm33 
20.2 
4.29 
4.17 
6.27 
\bar{p}{}K^{+}\pi^-\pi^0 
1700\pm73 
18.1 
\cdots 
4.15 
6.36 
\bar{\Lambda}{}\pi^- 
668\pm27 
41.7 
10.15 
9.41 
14.98 
\bar{\Lambda}{}\pi^-\pi^0 
1491\pm51 
18.9 
4.15 
3.91 
5.91 
\bar{\Lambda}{}\pi^-\pi^+\pi^- 
780\pm36 
14.1 
2.71 
2.63 
4.04 
\bar{\Sigma}{}^{0}\pi^- 
454\pm25 
26.3 
6.56 
5.94 
9.20 
\bar{\Sigma}{}^{-}\pi^0 
298\pm25 
23.2 
5.96 
5.35 
8.22 
\bar{\Sigma}{}^{-}\pi^-\pi^+ 
1066\pm49 
23.2 
5.48 
5.34 
8.04 
\bar{p}{}\pi^-\pi^+ 
590\pm48 
60.2 
\cdots 
\cdots 
20.06 
Table B5. ST yields, ST and DT efficiencies of various tag modes for the data sample at
\sqrt{s}=4661.24 \,{\rm{MeV}} . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs. Entries of "\cdots " are for the cases where knowledge of the DT efficiencies are not required in the analysis.Tag mode N_{i}^{\rm{ST}} 
\varepsilon_{i}^{\rm{ST}}(\%) 
\varepsilon_{i}^{\rm{DT}}(n\pi^+\pi^0)(\%) 
\varepsilon_{i}^{\rm{DT}}(n\pi^{+}\pi^{-}\pi^{+})(\%) 
\varepsilon_{i}^{\rm{DT}}(nK^{-}\pi^{+}\pi^{-})(\%) 
\bar{p}{}K_{S}^0 
958\pm33 
47.5 
12.29 
11.25 
17.86 
\bar{p}{}K^{+}\pi^- 
5167\pm80 
46.3 
10.62 
10.49 
16.16 
\bar{p}{}K_{S}^0\pi^0 
471\pm34 
18.9 
4.66 
4.52 
6.62 
\bar{p}{}K_{S}^0\pi^-\pi^+ 
462\pm31 
19.5 
4.21 
4.11 
6.33 
\bar{p}{}K^{+}\pi^-\pi^0 
1389\pm74 
17.5 
\cdots 
4.02 
6.63 
\bar{\Lambda}{}\pi^- 
538\pm25 
39.4 
9.80 
8.81 
13.64 
\bar{\Lambda}{}\pi^-\pi^0 
1301\pm49 
17.9 
3.93 
3.73 
5.82 
\bar{\Lambda}{}\pi^-\pi^+\pi^- 
639\pm34 
14.6 
2.73 
2.63 
3.82 
\bar{\Sigma}{}^{0}\pi^- 
371\pm22 
24.3 
6.12 
5.75 
8.4 
\bar{\Sigma}{}^{-}\pi^0 
251\pm24 
22.2 
5.62 
5.18 
7.90 
\bar{\Sigma}{}^{-}\pi^-\pi^+ 
956\pm48 
22.2 
5.25 
5.07 
8.16 
\bar{p}{}\pi^-\pi^+ 
459\pm47 
55.9 
\cdots 
\cdots 
19.66 
Table B6. ST yields, ST and DT efficiencies of various tag modes for the data sample at
\sqrt{s}=4698.82 \,{\rm{MeV}} . The uncertainties are statistical only. The quoted efficiencies do not include any subdecay BFs. Entries of "\cdots " are for the cases where knowledge of the DT efficiencies are not required in the analysis.
Observations of the Cabibbo-Suppressed decays Λ+c→nπ+π0 , nπ+π−π+ and the Cabibbo-Favored decay Λ+c→nK−π+π+
- Received Date: 2022-10-10
- Available Online: 2023-02-15
Abstract: Using electron-positron annihilation data samples corresponding to an integrated luminosity of 4.5 fb
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