We generalize the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the ($2\to 2$) scattering of all the pseudoscalar octet mesons $(\pi ,K,\eta )$. We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented.

• Received 26 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.116016