Pion--pion Scattering at Low Energy
J. Bijnens, G. Colagelo, G. Ecker, J. Gasser and M. Sainio
LU TP 97-14 (submitted to Nuclear Physics B)
Abstract:
We present technical details of the evaluation of the elastic pion-pion
scattering amplitude to two loops in chiral perturbation theory.
In particular, 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 clarity, we discuss these matters both in the
N--component phi^4 theory (in its symmetric phase) and in chiral perturbation
theory. Estimates for the relevant low--energy constants of $O(p^6)$ are
presented. Threshold parameters and phase shifts are then calculated for two
sets of $O(p^4)$ coupling constants and compared with experiment.
We comment on the extraction of threshold parameters from phase shift data.