Prospects for a lattice computation of rare kaon decay amplitudes: $K\to\pi\ell^+\ell^-$ decays

Understand

The rare kaon decays $K\to\pi\ell^+\ell^-$ and $K\to\pi\nu\bar{\nu}$ are flavor changing neutral current (FCNC) processes and hence promising channels with which to probe the limits of the standard model and to look for signs of new physics.

• In this paper we demonstrate the feasibility of lattice calculations of $K\to\pi\ell^+\ell^-$ decay amplitudes for which long-distance contributions are very significant.
• We show that the dominant finite-volume corrections (those decreasing as powers of the volume) are negligibly small and that, in the four-flavor theory, no new ultraviolet divergences appear as the electromagnetic current $J$ and the effective weak Hamiltonian $H_W$ approach each other.
• In addition, we demonstrate that one can remove the unphysical terms which grow exponentially with the range of the integration over the time separation between $J$ and $H_W$.