Lattice QCD calculation of the two-photon contributions to $K_L \to \mu^+ \mu^-$ and $\pi^0 \to e^+ e^-$ decays

Abstract

The rare second-order weak decay $K_L \to \mu^+\mu^-$ is precisely measured and sensitive to the structure of the weak interactions at short distances. However, these effects are obscured by a large third-order, long-distance contribution to this decay in which the muon pair is created by two photons. We will discuss the prospects for computing this third-order electroweak process using lattice QCD. As a first step in such a calculation a method will be presented for the lattice calculation of the simpler two-photon decay $\pi^0 \to e^+ e^-$.