$\Lambda_b \to p l^- \bar{\nu}$ 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 $14 GeV^2 \leq q^2 \leq q^2_{max}$, and obtain the integral $\int_{14 GeV^2}^{q^2_{max}} [d\Gamma/dq^2] dq^2 / |V_{ub}|^2 = 15.3 \pm 4.2 ps^{-1}$. 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.