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, 51 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)
Abstract
We investigate the ground-state energy of the
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