QED Radiative Corrections to the Pionium Life Time

TL;DR

This paper calculates the lowest order QED radiative corrections to pionium lifetime and related processes, using scalar QED and effective chiral Lagrangian theory, resulting in a correction of -0.25%.

Contribution

It provides a novel calculation of radiative corrections to pionium lifetime within scalar QED and effective chiral Lagrangian frameworks, clarifying the role of ultraviolet cut-off and Coulomb interactions.

Findings

Radiative correction to pionium lifetime is -0.25%.

Ultraviolet cut-off is set around the rho meson mass.

Coulomb factor should be removed to avoid double counting.

Abstract

The lowest order QED radiative corrections to the cross-section of the recharged process of transition of two charged pions to two neutral ones and to the pionium life time are calculated in frames of scalar QED. It is argued that the ultraviolet cut--off of the loop momentum is to be chosen of order of $\rho$ meson mass. This fact permits to perform the calculation in frames of Effective Chiral Lagrangian theory with vector-meson dominance. The Coulomb factor corresponding to interaction in the initial state, shown, is to be removed to avoid the double counting. Resulting value of the radiative correction to the pionium life time is -0.25%.