Prospects for improved $\Lambda_c$ branching fractions

The experimental uncertainty on the branching fraction $\b(\Lambda_c \to p K^- \pi^+) = (5.0 \pm 1.3)%$ 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 $\Lambda_c$ 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 $\Lambda_c \to \Lambda \ell^+ \nu_\ell$ (the case $\ell = e^+$ is simpler as the mass of the lepton can be neglected). Such a calculation would yield an absolute prediction for the rate for $\Lambda_c \to \Lambda \ell^+ \nu_\ell$. When combined with the $\Lambda_c$ lifetime, it could provide a calibration for an improved set of $\Lambda_c$ branching fractions as long as the accuracy exceeds about 25%.