Crossing Symmetry Violation of Unitarized Pion-Pion Amplitude in the Resonance Region

Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation Theory (ChPT) is crossing symmetric, however the corresponding partial wave amplitudes do not respect exact unitarity relation. There are different approaches to get unitarized partial wave amplitudes from ChPT. Here we consider the inverse amplitude method (IAM) that is often used to fit pion-pion phase shifts to experimental data, by adjusting free parameters. We measure the amount of crossing symmetry violation (CSV) in this case and we show that crossing symmetry is badly violated by the IAM unitarized ChPT amplitude in the resonance region. Important CSV also occurs when all free parameters are set equal to zero.