Consistency of the chiral pion-pion scattering amplitudes with axiomatic constraints

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 π⁰{{{π}}}⁰S- and D-wave amplitudes in the unphysical interval 0≤s≤4{m}_{{{π}}}²$. These constraints impose significant lower bounds for a linear combination of coupling constants specifying the second-order chiral Lagrangian. The accepted value of this combination is consistent with these bounds. The π^0-{{{π}}}⁰$ S and D waves are strongly correlated by a set of constraints.