K+→π+νν¯ decay amplitude from

Abstract

In Ref. [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the K þ → π þ νν decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The K þ → π þ νν decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required nonperturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of Oð5%Þ in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the K þ → π þ νν decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice (16 3 × 32) and at unphysical pion, kaon and charm quark masses, m π ¼ 420 MeV, m K ¼ 563 MeV and m MS c ð2 GeVÞ ¼ 863 MeV, the techniques presented in this work can readily be applied to a future realistic calculation.

Lattice QCD Inputs for nuclear double beta decay

“…(61) as in Refs. [201,200], it is clear that the correlation function has the asymptotic time dependence Figure 11: Contractions for the π − → π + e − e − transition in Eqs. (62) and (63).…”

Lattice QCD study of the rare kaon decay K+→π+νν¯Christ1, Feng2, Portelli3 et al. 2019Phys. Rev. DSelf Cite220120View full textAdd to dashboardCite

“…Since the LD contributions to K L → π 0 νν decays are negligible, we do not discuss these decays further in this paper. This paper is the latest in a series of lattice QCD studies of the rare kaon decays K → π + − and K → πνν, in which we have developed the theoretical framework and performed exploratory numerical calculations [13][14][15][16][17][18][19][20][21][22][23][24]. Here we focus on the LD contributions to the K + → π + νν decay amplitude.…”

“…For this reason, we computed the amplitude in Refs. [23,24] at a single choice of momenta. The momentum dependence of the decay amplitude was therefore unresolved and is the focus of the study reported here.…”

“…In addition since now, in contrast to the earlier studies in Refs. [23,24], the mass of the kaon is above the two-pion threshold, we are able to study the contribution of the ππ intermediate state to the decay amplitude together with the associated finite-volume effects.…”

Toward a First-Principles Calculation of Electroweak Box Diagrams

“…With lattice QCD simulations having reached an impressive level of precision for tree-level parameters of the electroweak interaction, it becomes timely and important to study higher-order electroweak corrections. The examples of such lattice applications include the QED corrections to hadron masses [8][9][10][11][12][13][14][15] and leptonic decay rates [16][17][18][19] and a series of higher-order electroweak effects, such as K L -K S mass difference [20][21][22], K [23], rare kaon decays [24][25][26][27][28][29] and double beta decays [30][31][32][33][34][35]. As for the γW -box contribution, which is a QED correction to semileptonic decays, it still remains a new horizon for lattice QCD.…”