Eur. Phys. J. A (2006) 27: 231-242
https://doi.org/10.1140/epja/i2006-10004-2

Hadron Physics

Dispersion theory and the low-energy constants for neutral-pion photoproduction

¹ Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia; INFN, Sezione di Pavia, Pavia, Italy
² Institut für Kernphysik, Johannes Gutenberg-Universität, D-55099, Mainz, Germany

^* e-mail: tiator@kph.uni-mainz.de

Received: 26 January 2006
Accepted: 3 March 2006
Published online: 3 April 2006

Abstract

The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t = const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2GeV. For sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables ν and t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysical region provides a unique framework to derive the low-energy constants to any given order as well as an estimate of the higher-order terms by global properties of the absorption spectrum.