  The rare Hyperon decay $\Sigma^+ \to p \ell^+ \ell^-$ is an $s \to d$ flavour
changing neutral current process, which is highly suppressed within the
Standard Model, and is therefore sensitive to new physics. Due to recent
improvements in experimental measurements of this decay, the Standard Model
theory prediction must also be improved in order to identify any new physics in
this channel. We present updates on our progress towards the first exploratory
lattice calculation of the long-distance part of the form factors of this
decay. This pilot calculation is performed on a 340 MeV pion mass ensemble
using domain-wall fermions as part of the RBC-UKQCD collaboration.
