# QED-corrected Lellouch-L\"uscher formula for $K \rightarrow \pi\pi$ decay

## TL;DR

This paper advances the theoretical framework for calculating $K
ightarrow \pi\pi$ decay amplitudes by incorporating QED effects into the Lellouch-L"uscher formalism, crucial for precise Standard Model predictions.

## Contribution

It extends the Lellouch-L"uscher formalism to include QED effects, enabling more accurate lattice QCD calculations of charged kaon decay amplitudes.

## Key findings

- Progress in formalism development for QED inclusion
- Framework for relating finite-volume matrix elements to physical amplitudes
- Preparation for precise lattice QCD calculations of $K
ightarrow \pi\pi$ decays

## Abstract

A precise SM prediction for the direct CP violation in the $K \rightarrow \pi\pi$ decay process is of great importance in confronting experiments and constraining new physics. The state-of-art lattice QCD study of this process will soon achieve a precision that QED effects can no longer be neglected. The inclusion of QED in such calculations is planned, and the formalism to relate the finite-volume matrix element obtained from these calculations to the physical amplitude is underway. Here, we report on the progress towards an extension of the Lellouch-L\"uscher formalism in presence of QED, with the goal of enabling the extraction of physical amplitudes for the $K\rightarrow \pi\pi$ process with charged initial and/or final states.