Two-pion annihilation into e+e− pairs in relativistic non-linear models

We have studied the π+π−→e+e− process in dense and hot nuclear matter using relativistic non-linear models taking into account all scalar-vector coupling terms up to fourth order in the Lagrangian. We have determined the influence of non-linear terms on the cross section and dilepton production rate in both isoscalar and isovector channels. For one of the models considered, we have found an enhancement of the π+π−→ρ→e+e− dilepton production rate in the low invariant mass region as required by the experimental data.