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Chiral approach to the rho meson in nuclear matter

In this work, the properties of the $ρ$ 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 ($χPT$) lagrangian including explicit resonance fields. Low energy chiral constraints are considered by matching our expressions to those of one loop $χPT$. To account for the medium corrections, the $ρ$ couples to $ππ$ pairs which are properly renormalized in the nuclear medium, accounting for both $p-h$ and $Δ-h$ excitations. The terms where the $ρ$ couples directly to the hadrons in the $p-h$ or $Δ-h$ excitations are also accounted for. In addition, the $ρ$ is also allowed to couple to $N^{*}(1520)-h$ components.