CP violation in $\Sigma^+\to p\ell^+\ell^-$ within the standard model and beyond

The LHCb collaboration has recently observed the rare hyperon decay $\Sigma^+\to p\mu^+\mu^-$. It can also measure the corresponding antihyperon channel with comparable precision and is thus in a position to extract information on $CP$ violation in this mode. Interestingly, the long-distance contributions that dominate it within the standard model provide large absorptive phases that could drive substantial $CP$ violation through interference with potential new-physics contributions. Here we explore this possibility, finding that the decay rate asymmetry is currently allowed to be as high as tens of percent, which can be probed by LHCb in the near future. We additionally consider the same with regard to the dielectron mode $\Sigma^+\to pe^+e^-$ as well as the related radiative one $\Sigma^+\to p\gamma$.