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

Understand

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 .