arXiv:hep-ph/0206068·v2·High Energy Physics — Phenomenology
Ground-state energy of pionic hydrogen to one loop
J. Gasser (Bern University)🇨🇭 · M.A. Ivanov (JINR Dubna)🇷🇺 · E. Lipartia (Lund University and JINR Dubna and Tbilisi University)🇸🇪 · M. Mojzis (Massachusetts University and Comenius University)🇺🇸 · A. Rusetsky (Bern University and Tbilisi University)🇨🇭
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.
Comments: 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