Prospects for improved $\Lambda_c$ branching fractions

TL;DR

This paper discusses the potential for lattice QCD calculations to improve the precision of $\Lambda_c$ branching fraction measurements, which are currently limited by experimental uncertainties and impact many related quantities.

Contribution

It proposes using lattice QCD to calculate form factors for $\Lambda_c o \Lambda \, ext{lepton}^+ \, u_ ext{lepton}$ decays, enabling more accurate branching fraction determinations.

Findings

Current experimental uncertainty on $\Lambda_c$ branching fractions remains high.

Lattice QCD can provide absolute decay rate predictions for $\Lambda_c o \Lambda \, ext{lepton}^+ \, u_ ext{lepton}$.

Improved theoretical predictions could calibrate and refine experimental measurements.

Abstract

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%.