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.