Electromagnetic Corrections to K->pi pi II - Dispersive Matching

TL;DR

This paper calculates electromagnetic corrections to K->pi pi decays by matching high and low Q^2 behaviors using operator product expansion and chiral perturbation theory, confirming small shifts in the amplitude.

Contribution

It introduces a dispersive matching method to evaluate electromagnetic corrections across Q^2 regimes in K->pi pi decays.

Findings

Electromagnetic corrections cause a small shift in the delta I - 3/2 amplitude.

The matching of high and low Q^2 regimes is successfully implemented.

Results agree with previous estimates of electromagnetic effects.

Abstract

We express the leading electromagnetic corrections in K-> pi pi amplitudes as integrals over the virtual photon squared-momentum Q^2. The high Q^2 behavior is obtained via the operator product expansion. The low Q^2 behavior is calculated using chiral perturbation theory. We model the intermediate Q^2 region using resonance contributions in order to enforce the matching of these two regimes. The results confirm our previous estimates that the electromagnetic corrections provide a reasonably small shift in the delta I - 3/2 amplitude.