$\Lambda_b \to p \ell^- \bar{\nu}_\ell$ and $\Lambda_b \to \Lambda_c \ell^- \bar{\nu}_\ell$ form factors from lattice QCD with relativistic heavy quarks

TL;DR

This paper presents a precise lattice QCD calculation of form factors for Lambda_b decays, enabling improved determinations of CKM matrix elements V_ub and V_cb with quantified uncertainties.

Contribution

The study introduces a novel lattice QCD approach with relativistic heavy-quark actions at physical masses, providing accurate form factors for Lambda_b decays.

Findings

Form factors are computed with 2+1 flavor dynamical fermions.

Predictions for decay rates with 4.4% and 2.2% uncertainties.

Enables precise extraction of CKM elements from experimental data.

Abstract

Measurements of the $\Lambda_b \to p \ell^- \bar{\nu}_\ell$ and $\Lambda_b \to \Lambda_c \ell^- \bar{\nu}_\ell$ decay rates can be used to determine the magnitudes of the CKM matrix elements $V_{ub}$ and $V_{cb}$, provided that the relevant hadronic form factors are known. Here we present a precise calculation of these form factors using lattice QCD with 2+1 flavors of dynamical domain-wall fermions. The $b$ and $c$ quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two different lattice spacings, using gauge-field configurations generated by the RBC and UKQCD collaborations. The $b \to u$ and $b \to c$ currents are renormalized with a mostly nonperturbative method. We extrapolate the form factor results to the physical pion mass and the continuum limit, parametrizing the $q^2$-dependence using $z$-expansions. The form factors are presented in such a way as to enable the correlated propagation of both statistical and systematic uncertainties into derived quantities such as differential decay rates and asymmetries. Using these form factors, we present predictions for the $\Lambda_b \to p \ell^- \bar{\nu}_\ell$ and $\Lambda_b \to \Lambda_c \ell^- \bar{\nu}_\ell$ differential and integrated decay rates. Combined with experimental data, our results enable determinations of $|V_{ub}|$, $|V_{cb}|$, and $|V_{ub}/V_{cb}|$ with theory uncertainties of 4.4%, 2.2%, and 4.9%, respectively.