A MASTER FORMULA FOR CHIRAL-SYMMETRY BREAKING

We derive a master formula for chiral SU(2) x SU(2) breaking, based on the Veltman-Bell equations and the Peierls-Dyson relation. Our approa ch does not rely on the use of the soft pion limit or an expansion aro und the chiral limit, and yields exact results for on-shell pions. Thr eshold theorems for pi N --> pi N, gamma N --> pi N, pi N --> pi pi N, gamma N --> gamma pi N, gamma N --> pi pi N and pi N --> pi gamma N a re recovered, and corrections to them are given. The reactions pi --> e nu gamma, pi --> e nu e(+)e(-), gamma pi --> gamma pi and gamma gamm a --> pi pi are also discussed. A general formula for pi pi scattering and a new one loop effective action are obtained. The new effective a ction reproduces the KSFR relation, and yields specific estimates for the pion polarisabilities. A detailed comparison with baryon-free chir al perturbation theory to one loop is made. An extension of our effect ive action to two loops is outlined. (C) 1996 Academic Press, Inc.