Pion-Pion Scattering in the Rho Meson Region

The pion-pion elastic scattering cross-section has a bump around the center-of-mass energy $E= (770 \pm 3)$ MeV, the rho meson region. Chiral Perturbation Theory (ChPT) describes pion-pion scattering well at lower energies but fails to explain this bump. We generalize ChPT by including the rho meson in an Effective Field Theory with a systematic power counting. We have used a realization of chiral $SU(2)_L \times SU(2)_R$ symmetry (``vector realization'') that includes not only massless pseudoscalar mesons (pions) but also scalars that become the longitudinal components of the vector mesons (rhos). We apply the power counting to pion-pion scattering around the bump. In leading order only the P wave with isospin $I=1$ contributes. We have calculated the corresponding phase shifts, which depend on a single parameter. I will present the results of a fitting to data and discuss the extension to higher orders.