PION-PION SCATTERING AT LOW-ENERGY

We present technical details of the evaluation of the elastic pi pi sc attering amplitude to two loops in chiral perturbation theory, In part icular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of the relevant Feynman diagrams that can all be expressed in terms of elementary functions, For the sake of cla rity, we discuss these matters both in the N-component phi(4) theory ( in its symmetric phase) and in chiral perturbation theory, Estimates f or the relevant low-energy constants of O(p(6)) are presented, Thresho ld parameters and phase shifts are then calculated for two sets of O(p (4)) coupling constants and compared with experiment, We comment on th e extraction of threshold parameters from phase shift data. (C) 1997 E lsevier Science B.V.