$\Lambda_c \to N$ form factors from lattice QCD and phenomenology of $\Lambda_c \to n \ell^+ \nu_\ell$ and $\Lambda_c \to p \mu^+ \mu^-$ decays

TL;DR

This paper presents lattice QCD calculations of $\Lambda_c o N$ form factors, predicts decay rates for certain $\Lambda_c$ decays, and explores the phenomenology of rare charm decays including potential new physics effects.

Contribution

It provides the first lattice QCD determination of $\Lambda_c o N$ form factors and applies them to predict decay rates and analyze rare decay phenomenology.

Findings

Predicted decay rates for $\Lambda_c o n e^+ u_e$ and $\Lambda_c o n \mu^+ u_$.

Calculated differential branching fraction and asymmetries for $\Lambda_c o p \mu^+ \mu^-$.

Provided form factors extrapolated to physical pion mass and continuum limit.

Abstract

A lattice QCD determination of the $\Lambda_c \to N$ vector, axial vector, and tensor form factors is reported. The calculation was performed with $2+1$ flavors of domain wall fermions at lattice spacings of $a\approx 0.11\:{\rm fm},\:0.085\:{\rm fm}$ and pion masses in the range $230\:{\rm MeV} \lesssim m_\pi \lesssim 350$ MeV. The form factors are extrapolated to the continuum limit and the physical pion mass using modified $z$ expansions. The rates of the charged-current decays $\Lambda_c \to n\, e^+ \nu_e$ and $\Lambda_c \to n\, \mu^+ \nu_\mu$ are predicted to be $\left( 0.405 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$ and $\left( 0.396 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$, respectively. The phenomenology of the rare charm decay $\Lambda_c \to p\, \mu^+ \mu^-$ is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the Standard Model and in an illustrative new-physics scenario.