Abstract
The rare kaon decays and 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 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 and the effective weak Hamiltonian 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 and . We will now proceed to exploratory numerical studies with the aim of motivating further experimental measurements of these decays. Our work extends the earlier study by Isidori et al. [1] which focused largely on the renormalization of ultraviolet divergences. In a companion paper [2] we discuss the evaluation of the long-distance contributions to decays; these contributions are expected to be at the level of a few percent for decays.
4 More- Received 14 August 2015
DOI:https://doi.org/10.1103/PhysRevD.92.094512
© 2015 American Physical Society