Derivation of Brown-Rho scaling from scale-chiral perturbation theory

The medium modified hadron properties are studied by using the scale-chiral perturbation theory $\chi$PT$_\sigma$ in which the lightest scalar meson $f_0(500)$ is included as an explicit degree of freedom by regarding it as the Nambu-Goldstone boson of scale symmetry both spontaneously broken and explicitly broken by the QCD trace anomaly. We derive Brown-Rho scaling at the leading order of scale symmetry from $\chi$PT$_\sigma$ and formulate how to make higher-order scale-chiral corrections going beyond the leading order of scale symmetry. By taking into account the intrinsic density dependence given by the dilaton condensate in the "bare" parameters of the Lagrangian, the medium modified hadron properties are investigated. Relying on available experimental information and certain reasonable assumptions, we arrive at the leading order scale symmetric effective theory that can be confronted with nature .