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

TL;DR

This paper provides the first lattice QCD calculations of $ ext{Xi}_b o ext{Xi}$ form factors, enabling precise Standard-Model predictions for rare $ ext{Xi}_b$ decays involving photons and muons, with controlled uncertainties across the full kinematic range.

Contribution

It introduces the first lattice QCD determination of $ ext{Xi}_b o ext{Xi}$ form factors, incorporating multiple lattice spacings, pion masses, and advanced analysis techniques for reliable predictions.

Findings

First lattice QCD results for $ ext{Xi}_b o ext{Xi}$ form factors.

Predictions for $ ext{Xi}_b o ext{Xi} u^+ u^-$ and $ ext{Xi}_b o ext{Xi} ext{gamma}$ decay rates.

Controlled uncertainties across the full kinematic region.

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.