  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 implement the existing constraints from kaon decays, pointing out
the extent to which this hyperon mode can constrain the directions in parameter
space to which the kaons are not sensitive.
