Prospects for a lattice calculation of the rare decay ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$

Abstract

We present a strategy for calculating the rare decay of a ${\Sigma }^{+}(uus)$ baryon to a proton $(uud)$ and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point correlation functions related to the target process. In particular, the four-point function arises from the insertion of incoming and outgoing baryons, together with a weak Hamiltonian mediating the $s\to d$ transition and an electromagnetic current creating the outgoing leptons. As is described in previous work in other contexts, this four-point function has a highly non-trivial relation to the physical observable, due to nucleon and nucleon-pion intermediate states. These lead to growing Euclidean time dependence and, in the case of the nucleon-pion states, to power-like volume effects. We discuss how to treat these issues in the context of the ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$ decay and, in particular, detail the relation between the finite-volume estimator and the physical, complex-valued amplitude. In doing so, we also make connections between various approaches in the literature.

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Cited by in corpus (3)

• $\Delta S=2$ nonleptonic hyperon decays as probes of new physics
• ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$ decays within the standard model and beyond
• Observation of the very rare ${\Sigma }^{+}\to p{\mu }^{+}{\mu }^{-}$ decay