2015/07/31 by N. H. Christ, Norman H. Christ, X. Feng +5 · 41 citations
Mathematics · Physics and Astronomy · #Amplitude #Hamiltonian (control theory) #High-Energy Particle Collisions Research #Lattice (music) #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Physics beyond the Standard Model #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevd.92.094512
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 92(9) (American Physical Society) · Version published in Phys. Rev. D
openalex publication_date 2015/11/18 · arxiv created 2016/01/28 · arxiv updated 2016/01/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The rare kaon decays K\ensuremath→\ensuremathπ\ensuremathℓ+\ensuremathℓ^\ensuremath- and K\ensuremath→\ensuremathπ\ensuremathν\ensuremathν 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\ensuremath→\ensuremathπ\ensuremathℓ+\ensuremathℓ^\ensuremath- 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 HW 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 HW. 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 K\ensuremath→\ensuremathπ\ensuremathν\ensuremathν decays; these contributions are expected to be at the level of a few percent for K+ decays.