A Schematic Model for ρ-a1 Mixing at Finite Density and In-Medium Effective Lagrangian

Based on schematic two-level models extended to a1-meson degrees of freedom, we investigate possible mechanisms of chiral restoration in the vector/axialvector channels in cold nuclear matter. In the first part of this article we employ the massive Yang-Mills framework to construct an effective chiral Lagrangian based on low-energy mesonic modes at finite density. The latter are identified through nuclear collective excitations of ‘meson’-sobar type such as π ↔ [∆(1232)N−1] ≡ π̂, ρ ↔ [N∗(1520)N−1] ≡ ρ̂, etc.. In a mean-field type treatment the in-medium gauge coupling ĝ, the (axial-) vector meson masses and f̂π are found to decrease with density indicating the approach towards chiral restoration phase in the language of in-medium effective fields. In the second part of our analysis, we evaluate the (first) in-medium Weinberg sum rule which relates vector and axial-vector correlators to the pion decay constant. Using inmedium ρ/a1 spectral functions (computed in the two-level model) also leads to a substantial reduction of the pion decay constant with increasing density.