$\Lambda_c \to \Lambda \ell^+ \nu_\ell$ form factors and decay rates from lattice QCD with physical quark masses

TL;DR

This paper presents the first lattice QCD calculation of form factors for $\Lambda_c o \Lambda \ell^+ u_\ell$ decays using physical quark masses, providing precise decay rate predictions and CKM matrix element determination.

Contribution

The study provides the first lattice QCD computation of $\\Lambda_c o \\Lambda$ decay form factors with physical quark masses, improving precision over previous measurements.

Findings

Predicted decay rates for $\\Lambda_c o \\Lambda e^+ \\nu_e$ and $\\Lambda_c o \\Lambda \\mu^+ \\nu_\\mu$ with uncertainties.

Branching fractions consistent with and twice as precise as recent experimental results.

Determination of $|V_{cs}|$ with reduced uncertainties using lattice form factors and experimental data.

Abstract

The first lattice QCD calculation of the form factors governing $\Lambda_c \to \Lambda \ell^+ \nu_\ell$ decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the $\Lambda_c \to \Lambda e^+ \nu_e$ and $\Lambda_c \to \Lambda \mu^+ \nu_\mu$ decay rates divided by $|V_{cs}|^2$ are $0.2007(71)(74)\:{\rm ps}^{-1}$ and $0.1945(69)(72)\:{\rm ps}^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ from a global fit and the $\Lambda_c$ lifetime from experiments, this translates to branching fractions of $\mathcal{B}(\Lambda_c\to\Lambda e^+\nu_e)=0.0380(19)_{\rm LQCD\:\:}(11)_{\tau_{\Lambda_c}}$ and $\mathcal{B}(\Lambda_c\to\Lambda \mu^+\nu_\mu)=0.0369(19)_{\rm LQCD\:\:}(11)_{\tau_{\Lambda_c}}$. These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives $|V_{cs}|= 0.949(24)_{\rm LQCD\:\:}(14)_{\tau_{\Lambda_c}}(49)_{\mathcal{B}}$.