Chiral approach to the rho meson in nuclear matter

In this work, the properties of the $\rho$ meson at rest in cold symmetric nuclear matter are studied. We make use of a chiral unitary approach to pion-pion scattering in the vector-isovector channel, calculated from the lowest order Chiral Perturbation Theory ($\chi PT$) lagrangian including explicit resonance fields. Low energy chiral constraints are considered by matching our expressions to those of one loop $\chi PT$. To account for the medium corrections, the $\rho$ couples to $\pi\pi$ pairs which are properly renormalized in the nuclear medium, accounting for both $p-h$ and $\Delta -h$ excitations. The terms where the $\rho$ couples directly to the hadrons in the $p-h$ or $\Delta -h$ excitations are also accounted for. In addition, the $\rho$ is also allowed to couple to $N^{*}(1520)-h$ components.