The experimental uncertainty on the branching fraction B(Λ c → pK − π + ) = (5.0 ± 1.3)% has not decreased since 1998, despite a much larger data sample. Uncertainty in this quantity dominates that in many other quantities, including branching fractions of Λ c to other modes, branching fractions of b-flavored baryons, and fragmentation fractions of charmed and bottom quarks. Here we advocate a lattice QCD calculation of the form factors in Λ c → Λℓ + ν ℓ (the case ℓ = e + is simpler as the mass of the lepton can be neglected). Such a calculation would yield an absolute prediction for the rate for Λ c → Λℓ + ν ℓ . When combined with the Λ c lifetime, it could provide a calibration for an improved set of Λ c branching fractions as long as the accuracy exceeds about 25%.PACS numbers: 14.20.Lq, 14.65.Dw, 13.30.Ce, 12.38.Gc
I INTRODUCTIONDespite the accumulation of a vastly greater sample of charmed particles in e + e − , ep, and hadron-hadron collisions, the most accurately known branching fraction for the decay of the lowest-lying charmed baryon Λ c , B(Λ c → pK − π + ) = (5.0 ± 1.3)%, has remained at the same value since 1998. It was only pinned down to that accuracy thanks to constructive suggestions by Dunietz [1]. This branching fraction sets the scale for a number of other quantities which depend on it. Many other Λ c branching fractions are measured through their ratio to the pK − π + mode [2]. It sets the scale for b-flavored baryon branching fractions, and governs fragmentation fractions of charm and bottom quarks into baryons.In the present paper we advocate improvement of accuracy of the semileptonic branching fraction B(Λ c → Λe + ν e ), whose current value is (2.1 ± 0.6)%, via a lattice QCD calculation of the relevant form factors. Such calculations have been performed for the semileptonic decays of charmed mesons, D → Kℓν ℓ and D → πℓν ℓ [3], which are characterized by two form factors. Although four form factors are relevant to Λ c → Λℓν ℓ in the limit of zero lepton mass, the difficulty of such a calculation is outweighed by its importance. A calculation enabling the prediction of the rate for Λ c → Λe + ν e (and hence its branching fraction, given τ (Λ c ) = 200 ± 6 fs [2]) to an accuracy of better than about 25% would represent an improvement on a wide variety of key quantities.In Section II we review various quantities which could profit from improvement in the accuracy of B(Λ c → Λe + ν e ). We discuss in Section III the present status of understanding of form factors in this decay. The corresponding semileptonic decay Λ b → Λ c e −ν e , to which the Heavy Quark Effective Theory (HQET) can be applied, is treated in Section IV. Some remarks are made in Section V regarding the "calibrating" mode Λ c → pK − π + , while Section V concludes.