Λb→pℓ−ν¯ℓform factors from lattice QCD with staticbquarks

Abstract

We present a lattice QCD calculation of form factors for the decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$, which is a promising channel for determining the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$ at the Large Hadron Collider. In this initial study we work in the limit of static $b$ quarks, where the number of independent form factors reduces to two. We use dynamical domain-wall fermions for the light quarks, and perform the calculation at two different lattice spacings and at multiple values of the light-quark masses in a single large volume. Using our form factor results, we calculate the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ differential decay rate in the range $14\text{ }\text{ }{\mathrm{GeV}}^{2}\ensuremath{\le}{q}^{2}\ensuremath{\le}{q}_{\mathrm{max}}^{2}$, and obtain the integral ${\ensuremath{\int}}_{14\text{ }{\mathrm{GeV}}^{2}}^{{q}_{\mathrm{max}}^{2}}[\mathrm{d}\ensuremath{\Gamma}/\mathrm{d}{q}^{2}]\mathrm{d}{q}^{2}/|{V}_{ub}{|}^{2}=15.3\ifmmode\pm\else\textpm\fi{}4.2\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$. Combined with future experimental data, this will give a novel determination of $|{V}_{ub}|$ with about 15% theoretical uncertainty. The uncertainty is dominated by the use of the static approximation for the $b$ quark, and can be reduced further by performing the lattice calculation with a more sophisticated heavy-quark action.