${\Lambda }_b\to p{l}^{-}\bar{\nu }$ form factors from lattice QCD with static b quarks

Abstract

We present a lattice QCD calculation of form factors for the decay ${\Lambda }_b\to p{\mu }^{-}\bar{\nu }$, which is a promising channel for determining the CKM 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 ${\Lambda }_b\to p{\mu }^{-}\bar{\nu }$ differential decay rate in the range $14Ge{V}^2\le q^2\le q_{max}^2$, and obtain the integral ${\int }_{14Ge{V}^2}^{q_{max}^2}[d\Gamma /d{q}^2]d{q}^2/|V_{ub}{|}^2=15.3\pm 4.2p{s}^{-1}$. 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.

Comments: 14 pages, 5 figures