K to pi pi Amplitudes at Unphysical Kinematics Using Domain Wall Fermions

TL;DR

This paper explores methods to compute K to pi pi decay amplitudes at unphysical kinematics using domain wall fermions, employing chiral perturbation theory and lattice QCD techniques.

Contribution

It introduces a novel approach to extract physical decay amplitudes from unphysical lattice calculations with non-zero pion momentum and partial quenching.

Findings

Preliminary matrix elements calculated on RBC/UKQCD lattices.

Effective mass plots and energy differences extracted.

Method demonstrates potential for future physical amplitude determinations.

Abstract

The use of chiral perturbation theory in extracting physical K to pi pi matrix elements from matrix elements calculated at unphysical kinematics is outlined. In particular, the possibility of utilizing pions with non-zero momentum in the final state, and of using partial quenching is discussed. Preliminary (not physically normalized) Delta I=3/2 (27,1) K to pi pi matrix elements are calculated on the RBC/UKQCD $24^3 \times 64$, $L_s=16$ lattices, using 2+1 dynamical flavors and domain wall fermions, with an inverse lattice spacing of $a^{-1}=1.729(28) GeV$. Effective mass plots are presented for a light sea quark mass of $m_l^{sea}=0.005$, and various valence quark masses. The plateaux are fit and $E_{\pi\pi}-m_K$ is extracted.