Delta I=3/2, K to Pi Pi Decays with Light, Non-Zero Momentum Pions

TL;DR

This study calculates Delta I=3/2, K to Pi Pi decay matrix elements on quenched lattice QCD with light pions and non-zero momentum, using twisted boundary conditions to approach on-shell decay conditions.

Contribution

It introduces a lattice QCD calculation of K to Pi Pi decay matrix elements with light, non-zero momentum pions using twisted boundary conditions and quenched approximation.

Findings

Matrix elements have 3-4% error at zero and Pi/L momentum.

Errors increase to 7% at sqrt(2)*Pi/L momentum.

Errors reach 15% at sqrt(3)*Pi/L momentum.

Abstract

Delta I=3/2, K to Pi Pi matrix elements are calculated on 68 configurations of quenched 24^3 x 64 lattices using the DBW2 action, and domain wall fermions with L_s=16. The lattice spacing is a^(-1)=1.3 GeV, corresponding to a physical volume of (3.6 fm)^3, which allows us to simulate a pion mass of m_Pi=227.6(6) MeV and a kaon mass of m_K=564(2) MeV. Twisted boundary conditions are used to give the two pions momentum. One twist corresponds to a pion momentum of p=Pi/L=170 MeV, which represents a decay that is nearly on-shell. Results for time separations of 20, 24, 28, and 32 between the kaon and the two pions are computed and an error weighted average is performed to reduced the error. The matrix elements are then found to have errors of order 3-4% for momentum 0 and Pi/L, 7% for momentum sqrt(2)*Pi/L, and 15% for momentum sqrt(3)*Pi/L.