K^+ -> pi^+ pi^0 Decays on Finite Volumes and at Next-to-Leading Order in the Chiral Expansion

TL;DR

This paper develops a theoretical framework combining lattice QCD simulations and chiral perturbation theory at next-to-leading order to accurately compute K->pi pi decay amplitudes, accounting for finite-volume effects.

Contribution

It derives expressions for decay matrix elements at NLO in chiral expansion, including finite-volume corrections, for both full and quenched QCD, aiding lattice calculations.

Findings

Derived NLO expressions for <pi pi|O_W|K> matrix elements.

Evaluated one-loop chiral corrections for arbitrary parameters.

Analyzed finite-volume effects in decay amplitude calculations.

Abstract

We present the ingredients necessary for the determination of physical K->pi pi decay amplitudes for Delta I=3/2 transitions, from lattice simulations at unphysical kinematics and the use of chiral perturbation theory at next-to-leading order. In particular we derive the expressions for the matrix elements <pi pi(I=2)|O_W|K>, where O_W is one of the operators appearing in the Delta S=1 weak Hamiltonian, in terms of low-energy constants at next-to-leading order in the chiral expansion. The one-loop chiral corrections are evaluated for arbitrary masses and momenta, both in full QCD and in the quenched approximation. We also investigate the finite-volume effects in this procedure.