2018 Impact factor 4.843
Particles and Fields
Eur. Phys. J. C 26, 13-34 (2002)
DOI: 10.1007/s10052-002-1013-z

Ground-state energy of pionic hydrogen to one loop

J. Gasser1, M.A. Ivanov2, E. Lipartia3, 4, 5, M. Mojzis6, 7 and A. Rusetsky1, 5

1  Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
2  Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
3  Department of Theoretical Physics 2, Lund University, Solvegatan 14A, 22362 Lund, Sweden
4  Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Russia
5  High Energy Physics Institute, Tbilisi State University, University St. 9, 380086 Tbilisi, Georgia
6  Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
7  Department of Theoretical Physics, Comenius University, 28415 Bratislava, Slovakia

(Received: 11 June 2002 / Published online: 9 October 2002)

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.

© Società Italiana di Fisica, Springer-Verlag 2002