Relativistic corrections to the Pionium Lifetime

TL;DR

This paper calculates relativistic corrections to the pionium lifetime using non-relativistic effective field theory, highlighting the importance of precise coupling constants and finding a 4.1% correction.

Contribution

It provides a detailed calculation of relativistic effects on pionium lifetime within an effective field theory framework, improving accuracy over previous non-relativistic estimates.

Findings

Relativistic correction to pionium lifetime is 4.1%.

More accurate decay momentum value is essential for precision.

Coupling constants need refinement for consistency with chiral perturbation theory.

Abstract

Next to leading order contributions to the pionium lifetime are considered within non-relativistic effective field theory. A more precise determination of the coupling constants is then needed in order to be consistent with the relativistic pion-pion scattering amplitude which can be obtained from chiral perturbation theory. The relativistic correction is found to be 4.1% and corresponds simply to a more accurate value for the non-relativistic decay momentum.