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Based on schematic two-level models extended to $a_1$-meson degrees offreedom, we investigate possible mechanisms of chiral restoration in thevector/axialvector channels in cold nuclear matter. In the first part of thisarticle we employ the massive Yang-Mills framework to construct an effectivechiral Lagrangian based on low-energy mesonic modes at finite density. Thelatter are identified through nuclear collective excitations of `meson'-sobartype such as $\pi\leftrightarrow [\Delta (1232)N^{-1}]\equiv\hat\pi$,$\rho\leftrightarrow [N^* (1520)N^{-1}]\equiv\hat\rho$, etc.. In a mean-fieldtype treatment the in-medium gauge coupling $\hat g$, the (axial-) vector mesonmasses and $\hat f_\pi$ are found to decrease with density indicating theapproach towards chiral restoration in the language of in-medium effectivefields. In the second part of our analysis we evaluate the (first) in-mediumWeinberg sum rule which relates vector and axialvector correlators to the piondecay constant. Using in-medium $\rho$/$a_1$ spectral functions (computed inthe two-level model) also leads to a substantial reduction of the pion decayconstant with increasing density.Comment: 12 pages, 6 figure

physical review. c. nuclear physics/physical review. c, nuclear physics

Schematic model for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mo>−</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>mixing at finite density and in-medium effective Lagrangian

Schematic model forρ−a1mixing at finite density and in-medium effective Lagrangian