Ground-state energy of pionic hydrogen to one loop

Abstract

We investigate the ground-state energy of the pi- p atom (pionic hydrogen) in the framework of QCD+QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at next-to-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.

Version accepted for publication in Eur. Phys. J. C; Eq. (B8) corrected, comment after Eq. (B11) changed, additional minor changes in the text; preprint number added

References in corpus (1)

• pi pi scattering

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