A Schematic Model for $ρ$-$a_1$ Mixing at Finite Density and In-Medium Effective Lagrangian

Details A Schematic Model for $ρ$-$a_1$ Mixing at Finite Density and In-Medium Effective Lagrangian A Schematic Model for $ρ$-$a_1$ Mixing at Finite Density and In-Medium Effective Lagrangian

1999-12-24

arxiv.org/abs/nucl-th/9912061v2

Phys.Rev. C62 (2000) 015202

Physics

Nuclear Physics

Nuclear Theory

12 pages, 6 figures

Scientific paper

10.1103/PhysRevC.62.015202

Based on schematic two-level models extended to $a_1$-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 $\pi\leftrightarrow [\Delta (1232)N^{-1}]\equiv\hat\pi$, $\rho\leftrightarrow [N^* (1520)N^{-1}]\equiv\hat\rho$, etc.. In a mean-field type treatment the in-medium gauge coupling $\hat g$, the (axial-) vector meson masses and $\hat f_\pi$ are found to decrease with density indicating the approach towards chiral restoration 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 axialvector correlators to the pion decay constant. Using in-medium $\rho$/$a_1$ spectral functions (computed in the two-level model) also leads to a substantial reduction of the pion decay constant with increasing density.

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