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

TL;DR

This paper analyzes $oldsymbol{ ext{Sigma}^+ o p\, ext{lepton}^+ ext{lepton}^-}$ decays within and beyond the Standard Model, using recent experimental data to refine predictions and explore potential new physics effects through effective operators.

Contribution

It provides updated estimates for decay rates and asymmetries, resolves ambiguities in Standard Model predictions, and constrains new physics operators using hyperon and kaon decay data.

Findings

Standard Model prediction has a fourfold ambiguity.

New measurements help reduce long-distance uncertainties.

Constraints on new physics operators are derived from decay data.

Abstract

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.