$\Sigma^{+}\to p\ell^{+}\ell^{-}$ decays within the standard model and beyond

Motivated by the LHCb measurement of the hyperon decay mode $\Sigma^+\to p\mu^+\mu^-$ and prospects for improvement, we revisit the estimates for the rate and muon forward-backward asymmetry within the standard model and beyond. The standard model prediction has a fourfold ambiguity, and we suggest ways to resolve it with other measurements, including possible studies of $\Sigma^+\to p e^+e^-$ in the BESIII and LHCb experiments. We use the recent BESIII measurements of $\Sigma^+\to p \gamma$ and $\Sigma^+\to N\pi$ to reduce the uncertainty in the long-distance contribution to $\Sigma^+\to p\mu^+\mu^-$. Beyond the standard model, we consider a general effective Hamiltonian at low energy with ten operators whose Wilson coefficients parametrize the new physics. We derive expressions for the $\Sigma^+\to p\mu^+\mu^-$ rate and the associated muon forward-backward asymmetry in terms of these coefficients. Finally, we present the constraints on these Wilson coefficients that result from both kaon and hyperon decays and emphasize their complementarity.