${\Xi }_b\to \Xi$ form factors from lattice QCD and Standard-Model predictions for ${\Xi }_b\to \Xi {\mu }^{+}{\mu }^{-}$ and ${\Xi }_b\to \Xi \gamma$ decays

Abstract

We present the first lattice QCD determination of the ${\Xi }_b\to \Xi$ vector, axial-vector, and tensor form factors, which are relevant for the theory of rare decays including ${\Xi }_b\to \Xi {\ell }^{+}{\ell }^{-}$ and ${\Xi }_b\to \Xi \gamma$. The calculation is performed with 2+1 flavors of domain-wall fermions at three different lattice spacings and pion masses in the range from approximately 430 to 230 MeV. The bottom quark is implemented using an anisotropic clover action. Three-point functions with a wide range of source-sink separations and model averaging are used to extract the ground-state contributions. We fit the dependence of the form factors on the momentum transfer, the pion mass, and the lattice spacing using modified $z$ expansions that account for subthreshold branch cuts, and apply dispersive bounds and asymptotic-behavior constraints to achieve controlled uncertainties in the full semileptonic kinematic region. Using our form factor results, we present Standard-Model predictions for the ${\Xi }_b^{-}\to {\Xi }^{-}\gamma$ and ${\Xi }_b^{-}\to {\Xi }^{-}{\mu }^{+}{\mu }^{-}$ branching fractions and two angular observables.

32 pages, 10 figures. Typos corrected in Eqs. (31), (34), (38)