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

Youngman Kim; R. Rapp; G. E. Brown; Mannque Rho

doi:10.1103/PhysRevC.62.015202

paper

A Schematic Model for $ρ$ - $a_{1}$ Mixing at Finite Density and In-Medium Effective Lagrangian

arXiv:nucl-th/9912061 · doi:10.1103/PhysRevC.62.015202

Abstract

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 $π \leftrightarrow [Δ (1232) N^{- 1}] \equiv π^$ , $ρ \leftrightarrow [N^{*} (1520) N^{- 1}] \equiv ρ^$ , etc.. In a mean-field type treatment the in-medium gauge coupling $g^$ , the (axial-) vector meson masses and $f^_{π}$ 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 $ρ$ / $a_{1}$ spectral functions (computed in the two-level model) also leads to a substantial reduction of the pion decay constant with increasing density.

12 pages, 6 figures

References in corpus (1)

Low-Mass Dileptons at the CERN-SpS: Evidence for Chiral Restoration?

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

Abstract

References in corpus (1)

Cited by in corpus (13)

A Schematic Model for $ρ$ - $a_{1}$ Mixing at Finite Density and In-Medium Effective Lagrangian