Towards a lattice determination of the form factors of the rare Hyperon decay $\Sigma^+ \to p \ell^+ \ell^-$

TL;DR

This paper explores lattice QCD techniques to compute form factors of the rare Hyperon decay $\, ext{Sigma}^+ o p \, ext{l}^+ ext{l}^-$, aiming to provide Standard Model predictions and investigate new physics signals.

Contribution

It introduces an exploratory lattice QCD study of the decay, including new methods for sampling and generalizations of the summed method for complex correlation functions.

Findings

Preliminary results for the decay form factors.

Assessment of source-sink sampling applicability.

Generalization of the summed method for 3- and 4-point functions.

Abstract

The rare Hyperon decay $\Sigma^+ \to p \ell^+ \ell^-$ is an $s \to d$ flavour changing neutral current, and is therefore suppressed in within the Standard Model, making it an excellent probe for new physics. The process is dominated by long distance processes and therefore lattice QCD is the only existing technique to obtain a first principles Standard Model theoretical prediction. We present our work on an unphysical exploratory study of the rare Hyperon decay on the lattice, including an investigation into the applicability of source-sink sampling for this decay, and we show a generalisation of the summed method for arbitrary 3-point functions and 4-point functions. In addition we show preliminary results for a computation of the $s \to u$ semileptonic Hyperon decays.