$\Lambda_b \to \Lambda \ell^+ \ell^-$ form factors, differential branching fraction, and angular observables from lattice QCD with relativistic $b$ quarks

TL;DR

This paper presents lattice QCD calculations of form factors for the $to s$ transition in $L$ decays, enabling precise Standard Model predictions for branching fractions and angular observables.

Contribution

It provides the first comprehensive lattice QCD computation of all 10 form factors for $L o L$ transitions with relativistic $b$ quarks, including chiral, continuum, and kinematic extrapolations.

Findings

Predicted differential branching fraction for $L o L o p^+ o ext{pion} o ext{muons}$ decay.

Calculated angular observables consistent with Standard Model expectations.

Enhanced precision in $L$ decay predictions for testing new physics.

Abstract

Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $\Lambda_b \to \Lambda$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $\Lambda_b \to \Lambda(\to p^+ \pi^-) \mu^+ \mu^-$ differential branching fraction and angular observables in the Standard Model.