Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints

Abstract

The pion-pion scattering amplitudes provided by second-order chiral perturbation theory are confronted with known rigorous constraints derived from the axioms of quantum field theory. We mainly test constraints restricting the ${\pi }^0$-${\pi }^0$ $S$- and $D$-wave amplitudes in the unphysical interval $0\le s\le 4m_{\pi }^2$. These constraints impose significant lower bounds for a linear combination of coupling constants specifying the second order chiral Lagrangian. The accepted value of this combination is consistent with these bounds. The ${\pi }^0$-${\pi }^0$ $S$- and $D$-waves are strongly correlated by a set of constraints.

Comments: 26 pages using LaTeX and math.sty (appended at the end), 5 figures, 4 .eps files and 1 .ps file, tared, compressed and uuencoded (also available on request if there is a problem from banantha@ulys.unil.ch) Universite de Lausanne, Theory preprint, UNIL-TP-4/94