CLNS 94/1269 CLEO 94–4 January 17, 1994

Study of the Decay Λ_{c}^{+} → Λℓ^{+}ν_{l}

T. Bergfeld,^{1} B.I. Eisenstein,^{1} G. Gollin,^{1} B. Ong,^{1} M. Palmer,^{1} M. Selen,^{1} J. J. Thaler,^{1} A.J. Sadoff,^{2} R. Ammar,^{3} S. Ball,^{3} P. Baringer,^{3} A. Bean,^{3} D. Besson,^{3} D. Coppage,^{3}

N. Copty,^{3} R. Davis,^{3} N. Hancock,^{3} M. Kelly,^{3} N. Kwak,^{3} H. Lam,^{3} Y. Kubota,^{4} M. Lattery,^{4} J.K. Nelson,^{4} S. Patton,^{4} D. Perticone,^{4} R. Poling,^{4} V. Savinov,^{4} S. Schrenk,^{4}

R. Wang,^{4} M.S. Alam,^{5} I.J. Kim,^{5} B. Nemati,^{5} J.J. O’Neill,^{5} H. Severini,^{5} C.R. Sun,^{5} M.M. Zoeller,^{5} G. Crawford,^{6} C. M. Daubenmier,^{6} R. Fulton,^{6} D. Fujino,^{6} K.K. Gan,^{6} K. Honscheid,^{6} H. Kagan,^{6} R. Kass,^{6} J. Lee,^{6} R. Malchow,^{6} F. Morrow,^{6} Y. Skovpen,^{6}^{∗}

M. Sung,^{6} C. White,^{6} F. Butler,^{7} X. Fu,^{7} G. Kalbfleisch,^{7} W.R. Ross,^{7} P. Skubic,^{7} J. Snow,^{7} P.L. Wang,^{7} M. Wood,^{7} D.N. Brown,^{8} J.Fast ,^{8} R.L. McIlwain,^{8} T. Miao,^{8} D.H. Miller,^{8} M. Modesitt,^{8} D. Payne,^{8} E.I. Shibata,^{8} I.P.J. Shipsey,^{8} P.N. Wang,^{8} M. Battle,^{9} J. Ernst,^{9}

Y. Kwon,^{9} S. Roberts,^{9} E.H. Thorndike,^{9} C.H. Wang,^{9} J. Dominick,^{10} M. Lambrecht,^{10} S. Sanghera,^{10} V. Shelkov,^{10} T. Skwarnicki,^{10} R. Stroynowski,^{10} I. Volobouev,^{10} G. Wei,^{10}

P. Zadorozhny,^{10} M. Artuso,^{11} M. Goldberg,^{11} D. He,^{11} N. Horwitz,^{11} R. Kennett,^{11} R. Mountain,^{11} G.C. Moneti,^{11} F. Muheim,^{11} Y. Mukhin,^{11} S. Playfer,^{11} Y. Rozen,^{11}

S. Stone,^{11} M. Thulasidas,^{11} G. Vasseur,^{11} G. Zhu,^{11} J. Bartelt,^{12} S.E. Csorna,^{12} Z. Egyed,^{12} V. Jain,^{12} K. Kinoshita,^{13} K.W. Edwards,^{14} M. Ogg,^{14} D.I. Britton,^{15}

E.R.F. Hyatt,^{15} D.B. MacFarlane,^{15} P.M. Patel,^{15} D.S. Akerib,^{16} B. Barish,^{16} M. Chadha,^{16}

S. Chan,^{16} D.F. Cowen,^{16} G. Eigen,^{16} J.S. Miller,^{16} C. O’Grady,^{16} J. Urheim,^{16} A.J. Weinstein,^{16} D. Acosta,^{17} M. Athanas,^{17} G. Masek,^{17} H.P. Paar,^{17} J. Gronberg,^{18}

R. Kutschke,^{18} S. Menary,^{18} R.J. Morrison,^{18} S. Nakanishi,^{18} H.N. Nelson,^{18} T.K. Nelson,^{18}

C. Qiao,^{18} J.D. Richman,^{18} A. Ryd,^{18} H. Tajima,^{18} D. Schmidt,^{18} D. Sperka,^{18} M.S. Witherell,^{18} M. Procario,^{19} R. Balest,^{20} K. Cho,^{20} M. Daoudi,^{20} W.T. Ford,^{20}

D.R. Johnson,^{20} K. Lingel,^{20} M. Lohner,^{20} P. Rankin,^{20} J.G. Smith,^{20} J.P. Alexander,^{21} C. Bebek,^{21} K. Berkelman,^{21} K. Bloom,^{21} T.E. Browder,^{21} D.G. Cassel,^{21} H.A. Cho,^{21}

D.M. Coffman,^{21} P.S. Drell,^{21} R. Ehrlich,^{21} M. Garcia-Sciveres,^{21} B. Geiser,^{21} B. Gittelman,^{21} S.W. Gray,^{21} D.L. Hartill,^{21} B.K. Heltsley,^{21} C.D. Jones,^{21} S.L. Jones,^{21} J. Kandaswamy,^{21} N. Katayama,^{21} P.C. Kim,^{21} D.L. Kreinick,^{21} G.S. Ludwig,^{21} J. Masui,^{21} J. Mevissen,^{21} N.B. Mistry,^{21} C.R. Ng,^{21} E. Nordberg,^{21} J.R. Patterson,^{21} D. Peterson,^{21}

D. Riley,^{21} S. Salman,^{21} M. Sapper,^{21} F. Würthwein,^{21} P. Avery,^{22} A. Freyberger,^{22} J. Rodriguez,^{22} R. Stephens,^{22} S. Yang,^{22} J. Yelton,^{22} D. Cinabro,^{23} S. Henderson,^{23}

T. Liu,^{23} M. Saulnier,^{23} R. Wilson,^{23} and H. Yamamoto^{23}

(CLEO Collaboration)

1University of Illinois, Champaign-Urbana, Illinois, 61801 2Ithaca College, Ithaca, New York 14850 3University of Kansas, Lawrence, Kansas 66045 4University of Minnesota, Minneapolis, Minnesota 55455 5State University of New York at Albany, Albany, New York 12222 6Ohio State University, Columbus, Ohio, 43210 7University of Oklahoma, Norman, Oklahoma 73019 8Purdue University, West Lafayette, Indiana 47907 9University of Rochester, Rochester, New York 14627 10Southern Methodist University, Dallas, Texas 75275 11Syracuse University, Syracuse, New York 13244 12Vanderbilt University, Nashville, Tennessee 37235

13Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 14Carleton University, Ottawa, Ontario K1S 5B6 and the Institute of Particle Physics, Canada 15McGill University, Montréal, Québec H3A 2T8 and the Institute of Particle Physics, Canada

16California Institute of Technology, Pasadena, California 91125 17University of California, San Diego, La Jolla, California 92093 18University of California, Santa Barbara, California 93106 19Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 20University of Colorado, Boulder, Colorado 80309-0390 21Cornell University, Ithaca, New York 14853 22University of Florida, Gainesville, Florida 32611 23Harvard University, Cambridge, Massachusetts 02138

Abstract

Using the CLEO II detector at CESR we observe 500 Λℓ^{+} pairs consistent with the semileptonic decay Λ_{c}^{+} → Λℓ^{+}ν_{l}. We measure σ(e^{+}e^{−} → Λ_{c}^{+}X) · B(Λ_{c}^{+} → Λℓ^{+}ν_{l}) = 4.77 ± 0.25 ± 0.66pb. Combining with the charm semileptonic width and the lifetime of the Λ_{c} we also obtain B(Λ_{c}^{+} → pK^{−}π^{+}). We find no evidence for Λℓ^{+}ν_{l} final states in which there are additional Λ_{c}^{+} decay products. We measure the decay asymmetry parameter of Λ_{c}^{+} → Λe^{+}ν_{e} to be α_{Λ_{c}} = −0.89_{−0.11}^{+0.17} _{−0.05}^{+0.09}.

∗Permanent address: INP, Novosibirsk, Russia

Charm semileptonic decays allow an absolute measurement of the heavy quark decay form factors because the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V_{cs} is known from unitarity. In the spectator model, Λ-type baryon semileptonic decays are simpler than charm meson semileptonic decays. In the meson case, either a K^{∗} or a K is produced depending on whether the quark spins are parallel or anti-parallel. Conversely, the Λ_{c} spin is carried by the c quark, since the (ud) combination is spin and isospin zero, so that only a Λ is formed when the c quark decays. The simplicity of Λ-type semileptonic decays allows for more reliable predictions, within the framework of Heavy Quark Effective Theory (HQET) [1], concerning heavy quark to light quark transitions [2] [3] than is the case for mesons. In addition, as the Λ_{c} semileptonic decay branching ratio can be reliably predicted from the known inclusive charm semileptonic width and the Λ_{c} lifetime, a measurement of σ(e^{+}e^{−} → Λ_{c}^{+}X) · B(Λ_{c}^{+} → Λℓ^{+}ν_{l}) provides an absolute normalization for all Λ_{c} decays.

In this paper we report a measurement of σ(e^{+}e^{−} → Λ_{c}^{+}X) · B(Λ_{c}^{+} → Λℓ^{+}ν_{l}). From this we obtain B(Λ_{c}^{+} → pK^{−}π^{+}). Finally, we use the decay Λ → pπ as a polarization analyzer to measure the decay asymmetry in Λ_{c}^{+} → Λe^{+}ν_{e}.

The data sample used in this study contains some 2 million e^{+}e^{−} → c \overline{c} events collected with the CLEO II detector [4] at the Cornell Electron Storage Ring (CESR). The integrated luminosity consists of 1.1 fb^{−1} taken at the Υ(4S) resonance and 0.5 fb^{−1} taken just below the B\overline{B} threshold.

We search for the decay Λ_{c}^{+} → Λℓ^{+}ν_{l} by detecting a Λℓ^{+} (right sign) pair with invariant mass in the range m_{Λ} < m_{Λℓ} < m_{Λ_{c}} [5]. A background source of right sign Λℓ pairs is the semileptonic decay of the heavier charm baryons Ξ_{c}^{0}, Ξ_{c}^{+}, and Ω_{c}^{0} . Secondary background sources that can produce both right and wrong sign Λℓ pairs are the continuum production of Λ’s not associated with charm baryons, denoted by “c\overline{c}”, and B decays at the Υ(4S), denoted by “B\overline{B}”. The majority of Λℓ^{−} (wrong sign) pairs will be produced either from e^{+}e^{−} → Λ_{c}\overline{Λ}_{c} where one Λ_{c} decays to a Λ and the other decays semileptonically or from e^{+}e^{−} → Λ_{c}\overline{M}_{c}\overline{N} where \overline{M_{c}} is a charm meson that decays semileptonically. In both of these cases the Λℓ invariant mass will often satisfy m_{Λℓ} > m_{Λ_{c}}. The wrong sign sample is used to normalize our Monte Carlo (MC) simulation of secondary background sources.

We search each event for a Λℓ combination. All tracks are required to come from the region of the event vertex. Electrons are identified using a likelihood function which incorporates information from the calorimeter and dE/dx systems, and muons are identified by their ability to penetrate an iron absorber and reach detection planes at a depth of at least five nuclear absorption lengths [4]. The minimum allowed momentum is 0.7 GeV/c for electrons and 1.4 GeV/c for muons. Leptons are required to have been detected in the so-called barrel region, i.e. | cos θ| < 0.71, where θ is the angle of the lepton momentum with the beam line. To reduce the background from B decays, we require R_{2} = H_{2}/H_{0} > 0.2 where H_{i} are Fox-Wolfram event shape variables [6].

The Λ is reconstructed through its decay to pπ. We require the point of intersection of the two charged tracks, measured in the r − ϕ plane, to be greater than 0.5 cm away from the primary vertex. In addition, we require the sum of the p and π momentum vectors to extrapolate back to the beamline. The dE/dx measurement of the proton is required to be consistent with the expected value. We reject combinations which satisfy interpretation as a K_{s}^{0}. Finally, we require the momentum of the pπ pair to be greater than 0.8 GeV/c in order to reduce background from secondary sources.

These Λ candidates are then combined with leptons, and the sum of Λ and ℓ momentum, p_{Λℓ}, is required to be greater than 1.4 GeV/c. This cut reduces our dependence on the shape of the Λ_{c} fragmentation function at low momentum, which is poorly known. The invariant mass of the Λℓ pair is required to satisfy 1.3 < m_{Λℓ} < 2.3 GeV/c^{2}. To determine the number of events in the signal region we fit the pπ invariant mass distribution with a function consisting of a Gaussian, whose width is determined by a MC simulation, and a polynomial background. The fits for the electron and muon samples, in both right sign and wrong sign combinations, are shown in Figure 1 and the results of the fits are given in Table I.

In addition to background from the sources outlined above, Λℓ pairs are also produced by combining real leptons with fake Λ’s and fake leptons with real Λ’s. The first of these is already taken into account by fitting to the Λ mass to determine the yield. Care must be taken in calculating the wrong sign fake background because antiprotons are particularly likely to be misidentified as electrons and because they are produced copiously in association with Λ’s due to baryon conservation. In order to take into account the different fake rates of protons and antiprotons compared to kaons and pions, we multiply the number of tracks, which are not positively identified as lepton tracks, by the the fake probabilities weighted by the particle population given by the LUND model [7] for continuum events containing a Λ. We fit the pπ invariant mass distribution to determine the number of fake lepton with real Λ combinations. The results are given in Table I for both right and wrong sign combinations.

The MC was used to estimate the number of real, right and wrong sign Λℓ combinations produced by secondary sources satisfying our selection criteria. To test our MC, we predict the number of wrong sign events both in the signal region and for m_{Λℓ} > 2.3 GeV/c^{2}. When the number of wrong sign, fake lepton events is subtracted from the number of wrong sign events, the MC prediction is in good agreement with the data over the whole mass range. We therefore have confidence in the MC predictions for the right sign secondary sources. The predicted number of events for the electron channel are 10.2 ± 10.2 for B\overline{B} and 21.6 ± 21.6 for c\overline{c}. The large errors account for model uncertainty.

In Figure 2, we show the right sign m_{Λℓ} distribution after Λ sideband subtraction [8]. Agreement between the data and MC is good. However, there is a slight excess of events in the data at low mass. There would be a low mass excess if there are contributions other than Λ_{c}^{+} → Λℓ^{+}ν_{l}. Such decays would have a lower efficiency, and would lead to an underestimation of σ · B. We have made an extensive search for possible decays of the type Λ_{c}^{+} → ΛXe^{+}ν_{e}, where X represents additional decay products. We only search for the lowest lying excited baryons because our efficiency for reconstructing semileptonic decays involving heavier baryons is very small. The decay modes we examine are:

• Λ_{c}^{+} → Λ^{∗}e^{+}ν_{e}, Λ^{∗} → Σ^{0}π^{0} with Σ^{0} → Λγ, where Λ^{∗} = Λ(1405), Λ(1520), Λ(1600), Λ(1670), Λ(1690)

• Λ_{c}^{+} → Σ^{∗}Xe^{+}ν_{e}, Σ^{∗} → Λπ, where Σ^{∗} = Σ^{+}(1385), Σ^{+}(1660), Σ^{0}(1385), Σ^{0}(1660)

• Λ_{c}^{+} → Σ^{0}Xe^{+}ν_{e}, Σ^{0} → Λγ and Λ_{c}^{+} → Λ(ππ)^{0}e^{+}ν_{e}

In addition to the selection criteria previously described, we select photon candidates from showers in the calorimeter that have a minimum energy of 40 MeV, are not matched to a charged-particle track from the drift chamber, and have a lateral energy distribution consistent with that expected for photons. Neutral pion candidates are selected from pairs of photons with at least one photon in the barrel portion of the calorimeter. We also require the two photon mass to be within 3 standard deviations of the known pion mass. All selected candidates are kinematically fitted to the π^{0} mass.

We observe no events of the type Λ_{c}^{+} → ΛXℓ^{+}ν_{l}. The results of all the searches are given in Table II. Combining the results, we find the number of events attributable to Λ_{c}^{+} → ΛXℓ^{+}ν_{l} is less than 15% of the signal events at 90% confidence level.

Our MC simulation found that, for the selection criteria used in this analysis, the efficiency of reconstructing the Ξ_{c}^{0} and Ξ_{c}^{+} modes is about 35% of that for Λ_{c}^{+} → Λℓ^{+}ν_{l}. Using the relative efficiency and measurement of σ · B for the semileptonic decay of Ξ_{c}^{0} and the measured ratio of lifetimes τ(Ξ_{c}^{+})/τ(Ξ_{c}^{0}) [9], we obtain the background given in Table I. (We do not include a contribution from Ω_{c}^{0} semileptonic decays because they have never been observed, and the production cross section for the Ω_{c}^{0} is expected to be small.)

The efficiencies given in Table I are obtained by MC simulation and include B(Λ → pπ). We obtain the yield given in Table I by subtracting the fake contribution and the Ξ_{c}^{0} and Ξ_{c}^{+} feedthrough background from the number of right sign events. The statistical error in the yield is calculated from the number of right sign events. The efficiency-corrected yield and integrated luminosity L are used to obtain the σ · B given in Table I.

As the B\overline{B} and cc̄ backgrounds are small and model dependent, we choose not to subtract them but instead to incorporate them into the systematic error. The largest experimental source of the systematic error in σ · B is the uncertainty in the fake rates (7%). We have investigated model dependence by varying the fragmentation function (5%) and by taking the difference (6%) in calculated efficiencies from the HQET Körner–Krämer (KK) model [3] (which is the efficiency used for the result) and a semileptonic decay model producing Λ’s with no net polarization (model A). An additional systematic error of 7% comes from the possible contribution of Λ_{c}^{+} decays other than Λ_{c}^{+} → Λℓ^{+}ν_{l}.

Our results are :

σ · B(Λ_{c}^{+} → Λe^{+}ν_{e}) = (4.87 ± 0.28 ± 0.69) pb
σ · B(Λ_{c}^{+} → Λμ^{+}ν_{μ}) = (4.43 ± 0.51 ± 0.64) pb.

As the two results are statistically independent, we form the weighted average:

σ · B = (4.77 ± 0.25 ± 0.66) pb.

Our result, which is in agreement with a measurement from ARGUS [10], is the most precise measurement of this quantity to date.

At present, all Λ_{c} branching ratios are normalized to B(Λ_{c} → pKπ), B_{pKπ}, the measurements of which are model dependent and vary by a factor of two [11]. We can determine B_{pKπ} from our measurement of σ · B. As semileptonic decay proceeds only via the emission of a virtual W from the heavy quark, the semileptonic width of all charmed hadrons should be equal. This is well established for the D^{+} and D^{0} [12] where: Γ_{sl}^{D^{+}} = (1.61 ± 0.18) × 10^{11}s^{−1} and Γ_{sl}^{D^{0}} = (1.83 ± 0.29) × 10^{11}s^{−1}. This equality should also hold for the Λ_{c}, assuming no new process gives rise to leptons in baryonic weak decay. Therefore, we can predict the inclusive semileptonic branching ratio, B_{ℓX}, to be:

B_{ℓX} = B(Λ_{c}^{+} → e^{+}X) =< Γ_{sl} > τ_{Λ_{c}} = (3.4 ± 0.4)%

where we have used the weighted average of the semileptonic widths for D^{0} and D^{+} and the average lifetime of Λ_{c} [13]. There exists no theoretical relationship between B(Λ_{c}^{+} → ΛXℓ^{+}ν_{l}) and B_{ℓX}. Also, it is probable that there are semileptonic decays of the Λ_{c} which do not include a Λ, such as Λ_{c}^{+} → Σ^{+}π^{−}ℓ^{+}ν_{l}, Λ_{c}^{+} → pK^{−}ℓ^{+}ν_{l}, as well as Cabibbo suppressed decays like Λ_{c}^{+} → nℓ^{+}ν_{l}. We therefore expect f ≡ \frac{B(Λ_{c}^{+}→Λℓ^{+}ν_{l})}{B_{ℓX}} ≤ 1.

We use the experimentally determined Λ_{c} fragmentation function in the MC simulation. For x_{p} > 0.5 [14], the weighted average of the muon and electron samples is σ · B = (3.38 ± 0.18 ± 0.47) pb. Combining this result with the CLEO measurement of σ(e^{+}e^{−} → Λ_{c}^{+}X) · B(Λ_{c}^{+} → pK^{−}π^{+}) [15] gives R ≡ \frac{σ·B_{pKπ}}{σ·B} = 1.93 ± 0.10 ± 0.33, which is independent of the details of Λ_{c} production. Therefore:

B_{pKπ} = f R B_{ℓX} = f (6.67 ± 0.35 ± 1.35)%

This result does not exclude any of the previous measurements of B_{pKπ} but places a reliable upper bound on this important but poorly determined quantity and thereby provides an absolute scale for all Λ_{c} branching ratios.

In the spectator model the quantity that corresponds to f in the charmed meson sector is Γ(D → (K^{∗} + K)ℓν_{l})/ Γ(D → ℓX) = 0.89 ± 0.12 [16]. Using this value, our result is compatible with the CLEO and ARGUS determination of B_{pKπ} from B decay at the Υ(4S) [11].

In semileptonic baryon decay it is possible to construct six invariant hadronic amplitudes, each of which is a function of q^{2} (the mass squared of the virtual W), from the spins and momenta of the initial and final state baryons. In the framework of HQET, the heavy flavor and spin symmetries imply relations among these amplitudes resulting in only one universal form factor when the final state also includes a heavy quark. If the final state contains only light quarks, as in Λ_{c} decay, then it can be shown that two independent form factors, f_{1} and f_{2}, are required. For any heavy Λ-type baryon decays, HQET predicts G_{A} = −G_{V} [2] [3], where G_{V} is the vector coupling and G_{A} is the axial vector coupling of the hadronic current. The physical consequence is that the daughter baryon will be emitted with 100% negative polarization at q^{2} = 0. The physical observable is the angle, Θ_{Λ}, between the momentum vector of the proton (or pion) in the Λ rest frame and the Λ momentum in the Λ_{c} rest frame. One finds:

\frac{dΓ}{dq^{2}dcosΘ_{Λ}} ∝ 1 + α_{Λ_{c}}α_{Λ}cosΘ_{Λ}

where α_{Λ_{c}} (α_{Λ}) is the decay asymmetry parameter of the Λ_{c} (Λ) and α_{Λ} = 0.64 [12].

The q^{2}-dependence of α_{Λ_{c}} depends on the details of the form factor structure. If the two form factors are assumed to have the same q^{2} dependence, then α_{Λ_{c}} depends only on the ratio of the form factors, r = f_{2}/f_{1}, which is expected to be less than unity. Over most of the q^{2} range α_{Λ_{c}} is less than –0.5 for reasonable values of r and is exactly –1 at q^{2} = 0 for all r [3]. Including terms of order (1/m_{c}) in the HQET expansion leads to a small departure from –1 at q^{2} = 0 [17].

We have shown that the Λℓ^{+} signal events are predominantly Λ_{c}^{+} → Λℓ^{+}ν_{l}. We use only Λe events to measure the asymmetry as the muon sample is very small.

Measuring cos Θ_{Λ} requires knowledge of the Λ_{c} momentum but this is unknown because the neutrino is unobserved. We estimate the direction of the Λ_{c} from the thrust axis of the event. The magnitude of the Λ_{c} momentum is then obtained by solving the equation P⃗_{Λ_{c}}^{2} = (P⃗_{Λ} + P⃗_{e} + P⃗_{ν_{e}})^{2}. The two solutions correspond physically to the undetermined longitudinal momentum of the neutrino. If the direction of the Λ_{c} was known exactly, one of the two solutions would have a value equal to the true magnitude of the Λ_{c} momentum. As the thrust axis is only an approximation to the true Λ_{c} direction, neither solution corresponds to the true Λ_{c} momentum. We therefore determine the best solution by MC simulation. We generate events according to the KK model for five values of r over the theoretically expected range −0.5 < r < 0.5 (-0.97< α_{Λ_{c}} <-0.61). The results of our simulation are:

1. In about half of the events, the thrust axis is not well aligned with the true Λ_{c} direction resulting in two non-physical solutions. In this case the direction of the thrust vector is varied until a physical solution results.

2. There is one physical solution in about 10% of the cases.

3. When there are two physical solutions, the higher (lower) momentum solution systematically over-estimates (under-estimates) the Λ_{c} momentum by similar amounts. In consequence, a measurement of cosΘ_{Λ} which chooses the higher (lower) solution systematically under-estimates (over-estimates) the Λ polarization. We find that the best estimate of the Λ_{c} momentum is obtained from the weighted average of the two solutions, where the weights are given by the measured Λ_{c} fragmentation function [15].

Using this method for estimating the Λ_{c} momentum, the resulting α_{Λ_{c}} is consistent with the input value. The resolution in cosΘ_{Λ} is 0.2, independent of the original number of the solutions for the Λ_{c} momentum, so we separate the data into four cosΘ_{Λ} bins.

We calculate the Λ_{c} momentum for the data exactly as for the MC. We determine the yield in each cosΘ_{Λ} bin by fitting the pπ invariant mass spectra shown in Figure 3. We compute the fake lepton background as a function of cosΘ_{Λ} using the same procedure described above and subtract the fake background from each bin.

The efficiency as a function of cosΘ_{Λ} is flat except for a small decrease towards cosΘ_{Λ} = +1. This bin corresponds to a backward soft pion which is difficult to detect in the drift chamber. We use the KK model with r = −0.25 to calculate the efficiency in each cosΘ_{Λ} bin. The efficiency corrected cosΘ_{Λ} distribution is shown in Figure 4. We find α_{Λ_{c}} = −0.89_{−0.11}^{+0.17} _{−0.05}^{+0.09}, where the first error is the error returned from the fit and the second error is the systematic error.

We have examined five sources of systematic error in the determination of α_{Λ_{c}}: the effect of using the thrust axis as the Λ_{c} direction, modelling of the detector efficiency as a function of cosΘ_{Λ}, model dependence, the fitting method, and the presence of Ξ_{c}^{0}, Ξ_{c}^{+}, and Ω_{c}^{0} decays or decays other than Λ_{c}^{+} → Λℓ^{+}ν_{l}. We discuss each of these sources below.

We do not find any evidence in the MC for a shift between the input and reconstructed values of α_{Λ_{c}} for the KK model using five different values of r. Therefore we do not assign a systematic error due to the methods of estimating the Λ_{c} momentum.

To allow for errors in efficiency modelling as a function of cosΘ_{Λ}, we repeat our analysis by varying the efficiency according to our understanding of the detector performance. We ascribe a systematic error of -0.04 from this source.

To estimate the KK model dependence, we repeat the analysis using the efficiency computed for five values of r satisfying -0.5< r <0.5. The spread in values of α_{Λ_{c}} is described by a systematic error of (_{+0.01}^{−0.03}). In order to determine the overall model dependence of our result, we repeat the analysis using model A. We find a result which is larger by 0.17 and take half of this difference as the systematic error arising from this source.

We treat the final two systematic errors simultaneously. To allow for the presence of Ξ_{c}^{0}, Ξ_{c}^{+}, and Ω_{c}^{0} decays and Λ_{c}^{+} decays other than Λ_{c}^{+} → Λℓ^{+}ν_{l} in the asymmetry distribution, we add various polynomial background functions to the fit. The area of the polynomial is constrained to that expected from this work and reference [9]. Following this procedure the result of the fit does not change so we do not ascribe a systematic error to this source. The result varies by 0.01 using different fitting methods. This variation is taken as the systematic error.

Our result is consistent with the HQET KK model. The average value of the efficiency corrected q^{2} distribution of the data is 0.7 (GeV/c)^{2}. Since we expect α_{Λ_{c}} to decrease as a function of q^{2} as q^{2} → 0, our result implies that α_{Λ_{c}} is close to –1 at q^{2} = 0 in agreement with the prediction of HQET.

We have measured the cross section times branching ratio for the semileptonic decay modes of the Λ_{c} that include a Λ. We find σ(e^{+}e^{−} → Λ_{c}^{+}X) · B(Λ_{c}^{+} → Λe^{+}ν_{e}) = 4.87 ± 0.28±0.69 pb and σ(e^{+}e^{−} → Λ_{c}^{+}X)·B(Λ_{c}^{+} → Λμ^{+}ν_{μ}) = 4.43±0.51±0.64 pb. The combined result is σ(e^{+}e^{−} → Λ_{c}^{+}X) · B(Λ_{c}^{+} → Λℓ^{+}ν_{l}) = 4.77 ± 0.25 ± 0.66 pb. Our result is the most precise measurement of this quantity to date. We find the number of events attributable to decays of the type Λ_{c}^{+} → ΛXℓ^{+}ν_{l} is less than 15% of the signal events at 90% confidence level. Combining our result for σ · B with the charm semileptonic width and the lifetime of the Λ_{c} gives B(Λ_{c}^{+} → pK^{−}π^{+}) = f · (6.67 ± 0.35 ± 1.35)%, where f represents the unknown fraction of Λ_{c}^{+} → Λℓ^{+}ν_{l} to the total semileptonic rate.

A large negative polarization of the Λ in the decay Λ_{c}^{+} → Λe^{+}ν_{e} of α_{Λ_{c}} = −0.89_{−0.11}^{+0.17} _{−0.05}^{+0.09} has been observed. This is the first observation of parity violation in a semileptonic charmed baryon decay. The sign of this polarization arises from the fact that the hadronic current is V-A. Our result is consistent with the prediction of the HQET KK model. Assuming factorization, one can relate α_{Λ_{c}} for Λ_{c}^{+} → Λe^{+}ν_{e} at q^{2} = m_{π}^{2} to α_{Λ_{c}} in the decay Λ_{c} → Λπ determined by CLEO [18] and ARGUS [19]. Our findings are consistent with the factorization ansatz.

We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. This work was supported by the National Science Foundation, the U.S. Dept. of Energy, the Heisenberg Foundation, the SSC Fellowship program of TNRLC, and the A.P. Sloan Foundation.

REFERENCES

[1] N. Isgur and M.B. Wise, Phys. Rev D42 (1990) 2388.

[2] F. Hussain, J.G. Körner, M. Krämer and G. Thompson, Z. Phys. C51 (1991) 321. T. Mannel, F. Roberts and Z. Ryzak, Nucl. Phys B 355 (1992) 38.

[3] J.G.Körner and M.Krämer, Phys. Lett. B275 (1992) 495.

[4] Y. Kubota et al., Nucl. Instrum. Methods A320 (1992) 66.

[5] Throughout this paper charge conjugate modes are implicitly included.

[6] G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41 (1978) 1581.

[7] The version JETSET 6.3 of the LUND Monte Carlo is used.

[8] The Λ signal region is defined as 1.1128< m_{Λ} <1.1188 GeV/c^{2}. The Λ sideband regions are 1.1070< m_{Λ} <1.1100 GeV/c^{2} and 1.1220< m_{Λ} <1.1250 GeV/c^{2}.

[9] H.Albrecht et al. (ARGUS), Phys. Lett. B303 (1993) 368.

H.Cheung (E687), FERMILAB-conf-93/164-E,1993. S.Barlag et al. (NA32), Phys. Lett. B233 (1989) 522 and Phys. Lett. B236 (1990) 495. ARGUS reports: B(Ξ_{c}^{0} → Ξ^{−}e^{+}ν_{e}) · σ(e^{+}e^{−} → Ξ_{c}^{0}X) = 0.74 ± 0.24 ± 0.09pb. We use weighted average lifetime ratio R=\frac{τ(Ξ_{c}^{+})}{τ(Ξ_{c}^{0})}=3.28 ± 0.84 from E687 and NA32 to estimate the B(Ξ_{c}^{+} → Ξ^{0}e^{+}ν_{e}) · σ(e^{+}e^{−} → Ξ_{c}^{+}X)

[10] H.Albrecht et al., Phys. Lett. B269 (1991) 234.

[11] G. Abrams et al. (MARK II), Phys. Rev. Lett. 44 (1980) 10. M. Aguilar-Benitez et al. (LEBC-EHS) Z. Phys. C40, 321 (1988). H. Albrecht et al. (ARGUS) Phys. Lett. B207 (1988) 109. G. Crawford et al. (CLEO) Phys. Rev D45 (1992) 752.

[12] Particle Data Group, Phys. Rev. Lett. 45 (1992) 1.

[13] John Cumulat, Proceeding of DPF’92 V1, 197, Fermilab (1992).

[14] Here x_{p} = p/p_{max} where p_{max} = \sqrt{E_{beam}^{2} − m_{Λ_{c}}^{2}}.

[15] P.Avery et al. (CLEO), Phys. Rev. D43 (1991) 3599.

[16] A.Bean et al. (CLEO), Phys. Lett. B317 (1993) 647.

[17] G.-L.Lin and T.Mannel, CERN-TH 7086/93 (1993).

[18] P.Avery et al. (CLEO), Phys. Rev. Lett. 65 (1990) 2842.

[19] H.Albrecht et al. (ARGUS), Phys. Lett. B274 (1992) 239.

TABLES

TABLE I. Signals and backgrounds

mode  electrons  muons
N_{Λℓ^{+}} (right)  510 ± 25  110 ± 11
fakes (right)  83 ± 25  13 ± 4
Ξ_{c} feeddown  77 ± 24  19 ± 6
corrected yield  350 ± 25 ± 28  78 ± 11 ± 7
efficiency (all x_{p}) (%)  4.44 ± 0.07  1.09 ± 0.04
σ · B(Λ_{c} → Λℓ^{+}ν_{l})  4.87 ± 0.28 ± 0.69pb  4.43 ± 0.51 ± 0.64pb
N_{Λℓ^{−}} (wrong)  109 ± 14  7 ± 5
fakes (wrong)  90 ± 27  21 ± 6

TABLE II. Upper limits for decays of the type Λ_{c}^{+} → ΛXℓν_{l}

modes  events  efficiency^{∗}  upper limit^{∗} at 90% CL
Σ^{0} → Λγ  0.0 ± 8.9  0.46  6.6%
Σ^{+}(1385) → Λπ^{+}  0.0 ± 0.1  0.7  0.09%
Σ^{+}(1660) → Λπ^{+}  0.0 ± 0.1  0.7  0.09%
Σ^{0}(1385) → Λπ^{0}  0.0 ± 0.1  0.3  0.1%
Σ^{0}(1660) → Λπ^{0}  0.0 ± 0.5  0.3  0.5%
(Λπ^{+}π^{−})_{nr}ℓ^{+}ν_{l}  3.2± 3.8  0.5  3.6%
(Λπ^{+}π^{−})_{1520}ℓ^{+}ν_{l}  0.4± 6.8  0.5  4.5%

∗ The efficiencies and upper limits given are relative to that for Λ_{c}^{+} → Λℓν_{l}.

FIGURES

FIG. 1. The pπ invariant mass for right sign and wrong sign combinations satisfying the cuts described in the text; (a) Right sign electrons, (b) Right sign muons, (c)Wrong sign electrons, (d)Wrong sign muons.

FIG. 2. Invariant Λe^{+} mass for right sign combinations. The points with error bars are data after subtraction of the contribution of fake lambdas estimated using the pπ invariant mass sidebands. The dashed line shows the sum of the backgrounds described in the text. The dotted line shows the Monte Carlo prediction for Λ_{c}^{+} → Λe^{+}ν_{l} normalized to the data after subtraction of the backgrounds. The solid line shows the sum of the Monte Carlo prediction and the backgrounds.

FIG. 3. The pπ invariant mass for values of cosΘ_{Λ}. (a) −1.0 ≤ cos Θ_{Λ} < −0.5,

(b) −0.5 ≤ cos Θ_{Λ} < 0.0, (c) 0.0 ≤ cos Θ_{Λ} < 0.5, (d) 0.5 ≤ cos Θ_{Λ} ≤ 1.0.

FIG. 4. dN/dcosΘ_{Λ} with efficiency correction and background subtraction.

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