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

摘要

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 themagnitudes of the CKM matrix elements $V_{ub}$ and $V_{cb}$, provided that therelevant hadronic form factors are known. Here we present a precise calculationof these form factors using lattice QCD with 2+1 flavors of dynamicaldomain-wall fermions. The $b$ and $c$ quarks are implemented with relativisticheavy-quark actions, allowing us to work directly at the physical heavy-quarkmasses. The lattice computation is performed for six different pion masses andtwo different lattice spacings, using gauge-field configurations generated bythe RBC and UKQCD collaborations. The $b \to u$ and $b \to c$ currents arerenormalized with a mostly nonperturbative method. We extrapolate the formfactor results to the physical pion mass and the continuum limit, parametrizingthe $q^2$-dependence using $z$-expansions. The form factors are presented insuch a way as to enable the correlated propagation of both statistical andsystematic uncertainties into derived quantities such as differential decayrates 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 withexperimental 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.