Lattice QCD calculation of form factors for $\Lambda_b \to \Lambda(1520) \ell^+ \ell^-$ decays

TL;DR

This paper reports on a lattice QCD calculation of form factors for the decay bL_b b7 bL(1520) b7 bb b, providing insights into hadronic effects relevant for understanding deviations from the Standard Model in rare baryonic decays.

Contribution

It introduces a novel lattice QCD approach to compute bL_b b7 bL(1520) form factors, including the choice of interpolating fields and extraction methods.

Findings

Preliminary results at pion mass 340 MeV and lattice spacing 0.11 fm.

Use of domain-wall and relativistic heavy-quark actions.

Method for extracting 14 helicity form factors.

Abstract

Experimental results for mesonic $b \to s \mu^+ \mu^-$ decays show a pattern of deviations from Standard-Model predictions, which could be due to new fundamental physics or due to an insufficient understanding of hadronic effects. Additional information on the $b \to s \mu^+ \mu^-$ transition can be obtained from $\Lambda_b$ decays. This was recently done using the process $\Lambda_b \to \Lambda \mu^+ \mu^-$, where the $\Lambda$ is the lightest strange baryon. A further interesting channel is $\Lambda_b \to p^+ K^- \mu^+ \mu^-$, where the $p^+ K^-$ final state receives contributions from multiple higher-mass $\Lambda$ resonances. The narrowest and most prominent of these is the $\Lambda(1520)$, which has $J^P=\frac32^-$. Here we present an ongoing lattice QCD calculation of the relevant $\Lambda_b \to \Lambda(1520)$ form factors. We discuss the choice of interpolating field for the $\Lambda(1520)$, and explain our method for extracting the fourteen $\Lambda_b \to \Lambda(1520)$ helicity form factors from correlation functions that are computed in the $\Lambda(1520)$ rest frame. We present preliminary numerical results at a pion mass of 340 MeV and a lattice spacing of 0.11 fm. This calculation uses a domain-wall action for the $u$, $d$, and $s$ quarks and a relativistic heavy-quark action for the $b$ quark, and is based on gauge-field configurations generated by the RBC and UKQCD Collaborations.