Rare kaon decays from lattice QCD

Abstract

The rare kaon decays, K → π + − and K → πνν, serve as ideal probes for the observation of New Physics (NP) effects. To isolate NP contributions successfully, one needs to control errors for Standard Model prediction from both short-and long-distance contributions. The RBC-UKQCD collaborations have performed a successful exploratory study on the calculation of longdistance contributions to the K L -K S mass difference, and are now developing necessary methods to calculate long-distance contributions to rare kaon decay amplitudes. In this proceeding, we will introduce the phenomenological background for rare kaon decays and describe the lattice methodology to calculate the corresponding decay amplitudes.

Emerging lattice approach to the K-unitarity triangle

“…A variant of this general procedure can be used to compute long-distance contributions to ε and rare Kaon decays mentioned in this work. Work along those lines is in progress [22,33].…”

“…Following Refs. [50,[52][53][54][55], we write: (18)(19)(20)(21)(22)(23)(24)(25)(26). For I = 0 and I = 2 we take µ = 1.531 GeV and µ = 3 GeV, respectively.…”

“…Moreover, it must be stressed that progress towards a precise determination of BR(K + → π + ν ν) is guaranteed by existing and planned experiments and theoretical progress in lattice QCD calculations of such processes (This will be achieved by reduced errors on |V cb | from improved determinations of the B → D form factor (See for instance Ref. [21] where the q 2 dependence of this form factor is calculated) and by a direct calculation of long distance charm contributions to BR(K + → π + ν ν) [22]). Needless to say, improvements on the measurement of ε /ε will require a major experimental effort.…”

Recent progress in applying lattice QCD to kaon physics

“…As flavor changing neutral current processes, these decays are highly suppressed in the Standard Model and thus provide ideal probes for the observation of new physics effects. In this review, I will discuss the lattice QCD calculations of two classes of rare kaon decays: K → πνν and K → π + − [50][51][52][53][54][55][56][57]. The K + → π + νν decay is interesting because it receives the largest contribution from top quark loop and thus theoretically very clean.…”