Dispersive approach to chiral perturbation theory

We generalize the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2→2) scattering of all the pseudoscalar octet mesons (π,K,η). 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.