No abstract

Abstract. We investigate the ground-state energy of the π − p atom (pionic hydrogen) in the framework of QCD+QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at nextto-leading order in the low-energy expansion in the framework of the relevant effective field theory. The result provides a relation between the strong energy shift and the pion-nucleon S-wave scattering lengths -evaluated in pure QCD -at next-to-leading order in isospin breaking and in the low-energy expansion. We compare our result with available model calculations.

The renormalized pion-nucleon Lagrangian is calculated to O(p 3 ) in heavy baryon chiral perturbation theory. By suitably chosen transformations of the nucleon field, the Lagrangian is brought to a standard form.

The elastic πN scattering amplitude in the isospin limit is calculated in the framework of heavy baryon chiral perturbation theory, up to the third order. Threshold parameters like scattering lengths, volumes, effective ranges, etc. are compared with data. All relevant low energy constants are fixed from the available pion-nucleon data. A clear improvement in the description of data is observed, when going from the first two orders in the chiral expansion to the third one. The importance of even higher orders is suggested by the results.