Effective Field Theory Approach to Pionium

TL;DR

This paper develops a non-relativistic effective field theory framework to systematically analyze the energy levels and decay width of pionium, connecting low-energy atomic physics with chiral perturbation theory.

Contribution

It introduces a novel EFT approach to pionium, linking atomic observables with chiral Lagrangian parameters at two-loop order.

Findings

Systematic organization of corrections to pionium energy levels and decay width.

Expression of results in terms of a single unknown constant.

Framework facilitates matching to chiral Lagrangian with electromagnetic interactions.

Abstract

The various dynamical scales below the pion mass involved in $\pi^{+}$ $\pi^{-}$ atoms are sequentially integrated out using non-relativistic effective field theory techniques. This allows us to systematically organise the corrections to the energy levels and decay width. We present our results in terms of a single unknown constant which may be obtained by matching to the Chiral Lagrangian with electromagnetic interactions at two loops.