all scales*]{} involved in the process. There are a vast variety of such formulations in the literature and a direct comparison with them is not our aim here. As an indication of the subtlety involved in the problem, let us take an exemplary case discussed by us[@BR:PR], i.e., the effective chiral Lagrangian in the mean field that can be recast in Landau Fermi-liquid theory for nuclear matter. There the scaling $\Phi (n)$ for $n\approx n_0$ (where $n_0$ is the nuclear matter density) can be related to the Landau parameter $\tilde{F}_1$ [^8] as[^9] \_1 -\_1\^3(1-1/)\[LandauF\] where $\tilde{F}_1^\pi$ is the contribution to the Landau parameter from the pion exchange which is completely fixed by chiral dynamics. One can get $\tilde{F}_1$ from the anomalous gyromagnetic ratio of the proton $ \delta g_l$ measured experimentally by using the Migdal formula that relates the two quantities [@Migdal]. Using (\[LandauF\]), one finds [@Friman-Rho] (n\_0)0.78.\[Phivalue\] In HLS$_\infty$ theory, the Landau parameter $F_1$ must be receiving contributions from all of the $V_\infty$ in the $\omega$ channel. However assuming that the lowest $\omega$ dominates, we can interpret (\[Phivalue\]) as m\_(n\_0)/m\_0.78. While this is valid only near the nuclear matter density for the “$\omega$" meson in the average sense, it 