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Realistic Implementation of Massive Yang Mills for rho and a1 Mesons

We revisit the massive Yang-Mills approach to implement axial-/vector mesons into the chiral pion Lagrangian. Employing the non-linear realization of chiral symmetry, we compute vector and axial-vector spectral functions. This includes, for the first time, a resummation of the $ρ$ propagator in the $a_1$ selfenergy while maintaining a partially conserved axial-vector current (PCAC). A realistic $ρ$ propagator, combined with a recent idea of a chirally invariant continuum in the vector and axial-vector channels, turns out be critical to obtain a quantitative description of hadronic $τ$-decay data which has not been achieved before in local-gauge approaches to the chiral lagrangian. The thus obtained model provides a realistic basis to rigorously address the long-standing question of chiral symmetry restoration in the context of dilepton data in heavy-ion collisions.