Effective Field Theory Approach to Pionium

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.

Comments: 24 pages, 4 figures, uses feynmf.sty and feynmf.mf, minor corrections in a few formulas, the text and references