Measurement of the absolute branching fraction of the inclusive semileptonic $\Lambda_c^+$ decay

Using a data sample corresponding to an integrated luminosity of 567 pb$^{-1}$ collected at a center-of-mass energy of $\sqrt{s}=4.6$ GeV with the BESIII detector, we measure the absolute branching fraction of the inclusive semileptonic $\Lambda_c^+$ decay with a double-tag method. We obtain $\mathcal{B}(\Lambda_c^+ \rightarrow X e^+ \nu_e) = (3.95\pm0.34\pm0.09)\%$, where the first uncertainty is statistical and the second systematic. Using the known $\Lambda_c^+$ lifetime and the charge-averaged semileptonic decay width of nonstrange charmed measons ($D^0$ and $D^+$), we obtain the ratio of the inclusive semileptonic decay widths $\Gamma(\Lambda_c^+ \rightarrow X e^+ \nu_e)/\bar{\Gamma}(D\rightarrow X e^+ \nu_e)= 1.26\pm0.12$.

Using a data sample corresponding to an integrated luminosity of 567 pb −1 collected at a center-ofmass energy of √ s = 4.6 GeV with the BESIII detector, we measure the absolute branching fraction of the inclusive semileptonic Λ + c decay with a double-tag method. We obtain B(Λ + c → Xe + νe) = (3.95 ± 0.34 ± 0.09)%, where the first uncertainty is statistical and the second systematic. Using the known Λ + c lifetime and the charge-averaged semileptonic decay width of nonstrange charmed measons (D 0 and D + ), we obtain the ratio of the inclusive semileptonic decay widths Γ(Λ + c → Xe + νe)/Γ(D → Xe + νe) = 1.26 ± 0.12.
PACS numbers: 14.20.Lq, 13.30.Ce, 12.38.Qk Since the first observation of the Λ + c baryon, the lightest baryon containing a charm quark, in 1979 [1], its hadronic decays have been studied extensively. However, information about semileptonic decays of the Λ + c baryon is sparse [2][3][4][5][6]. The branching fraction of Λ + c → Λe + ν e was first measured by the ARGUS collaboration [3] and then measured by the CLEO collaboration [4] more than 20 years ago. Recently, the BESIII collaboration measured the absolute branching fraction of Λ + c → Λe + ν e to be (3.63 ± 0.43)% [5]. A comparison of this exclusive branching fraction and the inclusive semileptonic decay branching fraction of the Λ + c baryon will guide searches for new semileptonic decay modes. The branching fraction of the inclusive semileptonic decay has been measured previously by the MARK II collaboration 35 years ago, with a result of (4.5 ± 1.7)% [7]. The uncertainty is much larger than that of the exclusive decay. Thus, a more precise measurement for the inclusive semileptonic decay is required. In addition, using the known Λ + c lifetime, the semileptonic decay width Γ(Λ + c → Xe + ν e ), where X refers to any particle system with baryon number one, can be determined. Comparing Γ(Λ + c → Xe + ν e ) with the charge-averaged nonstrange D semileptonic decay widthΓ(D → Xe + ν e ), the ratio Γ(Λ + c → Xe + ν e )/Γ(D → Xe + ν e ) can be obtained. Using current data results in Γ(Λ + c → Xe + ν e )/Γ(D → Xe + ν e ) = 1.44 ± 0.54 [8,9]. This ratio is predicted to be 1.67 [9,10] using an effective-quark theory calculation and about 1.2 based on a calculation using the heavyquark expansion [11]. Therefore, a more precise measurement of B(Λ + c → Xe + ν e ) is desirable to test these theoretical predictions.
In this Letter, we present the first absolute measurement of the branching fraction of the inclusive semileptonic Λ + c decay using a double-tag method. This analysis is based on a data sample corresponding to an integrated luminosity of 567 pb −1 , which is the largest Λ + c sample taken just above the Λ + cΛ − c production threshold collected up to now. The data sample was accumulated at a center-of-mass energy √ s = 4.6 GeV and recorded with the BESIII detector [12] at the Beijing Electron-Positron Collider II (BEPCII). A detailed description of the BESIII detector can be found in Ref. [12].
A GEANT4-based [13] Monte Carlo (MC) simulation is used to estimate the signal efficiency, optimize the selection criteria and understand the backgrounds. In the simulation, the effects of beam-energy spread and initial state radiation (ISR) are incorporated using kkmc [14], and the final-state radiation (FSR) is modeled by photos [15]. The 'inclusive' MC samples consist of Λ + (s) pairs, ISR to lower-mass charmonium (ψ) states, and continuum QED and QCD processes e + e − → qq (q = u, d, s). All known decay modes of Λ + c , D ( * ) (s) and ψ are generated with the branching fractions taken from the Particle Data Group (PDG) [8] by evtgen [16,17], and the remaining unknown decay modes of ψ are generated by lundcharm [18]. The equivalent luminosities of the simulated data samples are several times that of real data.
Since the data are taken just above the production threshold of Λ + cΛ − c , no additional hadrons are produced. The double-tag technique, first developed by the MARK III collaboration [19], is used to determine the absolute branching fraction of the inclusive semileptonic decay. First, we fully reconstruct oneΛ − c [referred to as the single-tag (ST)], and then search for candidates of the signal decay in the rest of the event that is recoiling against the taggedΛ − c . Hence, the absolute branching fraction of the inclusive semileptonic decay can be measured without knowing the number of Λ + cΛ − c pairs produced, thus eliminating the related systematic uncertainty from the measurement. The ST candidates are reconstructed through the decaysΛ − c →pK 0 S andΛ − c →pK + π − , which have large branching fractions and low backgrounds. The charge conjugated modes are implied throughout this Letter unless otherwise stated.
The charged tracks, except those from K 0 S , are required to have a polar angle θ with respect to the beam direction within the multilayer drift chamber (MDC) acceptance | cos θ| < 0.93, and a distance of closest approach to the interaction point (IP) within 10 cm along the beam direction and 1 cm in the plane transverse to the beam direction. Particle identification (PID) for charged pions, kaons and protons is performed by exploiting time-offlight (TOF) information and specific ionization energy loss dE/dx measured by the MDC. The confidence level (C.L.) under each particle hypothesis (p, K, or π) is calculated; each charged track is assigned the particle type with the largest PID C.L. The K 0 S meson candidates are reconstructed from two oppositely charged tracks to which no PID criteria are applied and which are assigned the pion mass hypothesis. The charged tracks from the K 0 S candidate must satisfy | cos θ| < 0.93. Furthermore, due to the long lifetime of the K 0 S meson, there is a less stringent criterion on the distance of the closest approach to the IP in the beam direction of less than 20 cm and there is no requirement on the distance of closest approach in the plane transverse to the beam direction. The invariant mass of the track pair is required to be in the range (0.487, 0.511) GeV/c 2 . Furthermore, the π + π − pair is constrained to be consistent with originating from a common decay vertex by means of a vertex fit. In addition, the decay length, which is the distance between the IP and the decay vertex, is required to be larger than twice its resolution.
To suppress combinatorial backgrounds, two kinematic variables are used to select the ST candidates. These are the energy difference ∆E ≡ EΛ− c − E beam and the beam-constrained mass and pΛ− c are the reconstructed energy and three momentum of the ST candidate in the rest frame of the e + e − system, respectively. We require ∆E to be within (−3σ, 3σ) of the peak of the ∆E distribution, where σ is the resolution of the ∆E distribution. Table I gives the ∆E requirements for each ST mode. If there are multiple candidates for the same tag mode in a given event, only the combination with the smallest |∆E| is retained for further analysis.
To determine the ST yields, we apply a fit to the M BC distributions, as shown in Fig. 1. In the fits, the signal shape is modeled by the shape obtained from the MC convolved with a Gaussian function that describes the resolution difference between data and MC simulation; the combinatorial background is described by an ARGUS function [20]. We obtain the ST yields by subtracting the integral of the background function in the signal region 2.282 < M BC < 2.300 GeV/c 2 from the total number of events in the same region. The tails of the M BC distribution above the nominal Λ + c mass are due to the effects of ISR and FSR. The ST yields and the corresponding detection efficiencies are summarized in Table I.
In the selected ST sample ofΛ − c candidates, we search for charged tracks consistent with being an electron or positron. To ensure that the charged tracks originate from the IP, the same distance of closest approach selection criteria are used as for the non-K 0 S daughters of the ST candidates. The track is required to satisfy | cos θ| < 0.8 to ensure that it lies within the acceptance The PID of the selected tracks is implemented with the information of the dE/dx, TOF and EMC, and the C.L. under each particle hypothesis (e, π, K or p) is calculated. Positron candidates must satisfy CL(e) > 0.001 and CL(e)/(CL(e) + CL(π) + CL(K) + CL(p)) > 0.8. To further suppress the backgrounds from charged pions, E e /p e > 0.8 is required, where E e and p e are the deposited energy in the EMC and momentum measured by the MDC, respectively. The remaining selected charged tracks are assigned the hadron type corresponding to the highest C.L. that is greater than 0.001. The track is rejected if it does not have a C.L. greater than 0.001 for any hypothesis.
The identified positron sample contains sizable backgrounds from misidentified hadrons. To evaluate these backgrounds, knowledge of their yields and corresponding misidentification probabilities is required. The real RS and WS positron yields are determined individually by unfolding the matrix [21][22][23] where N obs a is the observed yield of particle species a (a denotes e, π, K or p), P a→b is the probability to identify particle a as particle b, and N true a is the true yield of particle a in the studied sample. The elements of the PID efficiency matrix P a→b are obtained by studying corresponding control samples selected from data. The charged pion and proton samples are selected from  Fig. 2. The muon component is omitted in the unfolding procedure due to its small yields (almost the same as the positron yields), the small mis-PID probability from muon to positron (similar to that from pion to positron, shown in Fig. 2) and the negligible effect on the branching fraction measurement. In addition, because the selected pion sample contains the muon component due to their similar PID behaviour in the BESIII detector, the muon component is implicitly taken into account.
To estimate the contribution from non-Λ + c decays in the signal region, the unfolded positron yield in the M BC sideband region is scaled by a factor of 0.78 that accounts for the relative amount of background in the sideband and signal regions determined by the fit to the M BC distribution. Since low-background ST modes are used, the contribution from non-Λ + c decays is small (3.8%). The RS sample contains primary positrons, which directly originate from Λ + c decays, and secondary positrons, not directly arising from Λ + c decays and originating predominantly from γ conversions and π 0 Dalitz decays. Detailed MC studies indicate that the secondary positrons are charge symmetric, hence their yield can be evaluated from the WS positron sample and subtracted from the total RS positron yields. The reliability of the WS subtraction has been validated by MC studies.
The tracking efficiency in a given momentum interval, including the track reconstruction efficiency, selection efficiency and resolution effects, is corrected by unfolding the following matrix equation where the tracking efficiency matrix T (i|j) describes the probability of positrons produced in the j-th momentum interval to be reconstructed in the i-th momentum interval, N pro j is the number of primary positrons produced in the j-th momentum interval and N true i is the true yield of positron reconstructed in the i-th momentum interval. The tracking efficiency matrix is obtained by studying the positron MC sample selected from Λ + c semileptonic events. After this procedure, we obtain the efficiency-corrected positron momentum spectrum above 200 MeV/c in the laboratory frame. Table II summarizes the positron yields obtained after each correction step.
The fraction of positrons below 200 MeV/c is obtained by fitting the efficiency-corrected positron momentum spectrum with the sum of the spectra of the exclusive decay channels (Table III), as shown in Fig. 3. In the fit, the branching fraction of each component is allowed to vary within the given uncertainty. From the fit, we obtain the fraction of positrons below 200 MeV/c to be (5.6 ± 1.5)%, where the uncertainty is systematic derived from variations of the fit assumptions. The branching fraction of the inclusive semileptonic decay of the Λ + c baryon is then calculated with where N pro   [5] and the uncertainty of the unobserved decay channels are 100% of the predicted branching fractions. The form factor of Λ + c → Λe + νe decay is from QCD sum rules [24] and the other two, unobserved, semileptonic decay modes are generated by pythia [27]   The systematic uncertainties in this analysis are listed in Table IV. The tag yield systematic uncertainty is estimated to be 1.0% by using alternative fits to the M BC distribution with different signal shapes, background parameters and fitting ranges. The systematic uncertainty related to the tracking efficiency is estimated to be 1.0% by studying radiative Bhabha events [5]. The systematic uncertainty in the positron identification efficiency is estimated by comparing the positron PID efficiencies in different MC simulated semileptonic Λ + c decays. The largest relative difference of the positron PID efficiency is assigned as the systematic uncertainty. The uncertainties in the other elements of the PID efficiency matrix are estimated by comparing the matrix elements obtained from Λ + cΛ − c pair MC samples with those obtained from radiative Bhabha, J/ψ → ppπ + π − and J/ψ → K + K − K + K − MC samples. Adding them in quadrature, we assign 0.9% as the systematic uncertainty related to PID. The uncertainty associated with the M BC sideband subtraction is estimated to be 0.5% by using an alternative M BC sideband region. To estimate the uncertainty in the extrapolation of the positron momentum spectrum, we perform an alternative fit in which the branching fraction of each fit component is unconstrained. In addition, we use an alternative form-factor model and repeat the fit. Adding these effects in quadrature, we attribute 1.5% as the systematic uncertainty related to the extrapolation procedure. The uncertainty due to limited statistics of data and MC simulation used to determine the PID efficiency matrix and tracking efficiency matrix is estimated by repeating the PID unfolding procedure and correction of tracking efficiency. In each repetition, we vary each element of the PID efficiency matrix and tracking efficiency matrix within the corresponding error. The corresponding systematic uncertainty is derived from 10, 000 independent repetitions and is estimated to be 0.4%. Adding all uncertainties in quadrature, the total systematic uncertainty is determined to be 2.3%. The absolute branching fraction of the inclusive semileptonic decays of the Λ + c baryon is determined to be B(Λ + c → Xe + ν e ) = (3.95 ± 0.34 ± 0.09)%, where the first and second uncertainties are statistical and systematic, respectively. Compared with the branching fraction of Λ + c → Λe + ν e measured by the BESIII collabration [5], the ratio B(Λ + c →Λe + νe) B(Λ + c →Xe + νe) is determined to be (91.9 ± 12.5 ± 5.4)%, where the systematic uncertainty related to the tracking efficiency of the positron cancels. Using the known Λ + c lifetime [8], we obtain the semileptonic decay width Γ(Λ + c → Xe + ν e ) = (1.98 ± 0.18) × 10 11 s −1 . Comparing this with the charge-averaged semileptonic decay width of nonstrange charmed measonsΓ(D → Xe + ν e ) [8], the ratio Γ(Λ + c →Xe + νe) Γ(D→Xe + νe) is determined to be 1.26 ± 0.12. A comparison of the branching fraction and ratio of the semileptonic decay width between experimental measurements and theoretical predictions can be found in Table V. In summary, by analysing a data sample corresponding to an integrated luminosity of 567 pb −1 taken at a centerof-mass energy √ s = 4.6 GeV, we report the absolute measurement of the inclusive semileptonic Λ + c decay branching fraction B(Λ + c → Xe + ν e ) = (3.95 ± 0.34 ± 0.09)%. The uncertainty is reduced by a factor of four compared to the MARK II result [7]. Based on the BE-SIII measurements [5], we obtain the ratio of the branch-TABLE V. Comparison of the branching fraction (in 10 −2 ) and ratio of the semileptonic decay width between experimental measurements and theoretical predictions.