Abstract. We investigate whether the rho-meson melting scenario is compatible with chiral symmetry restoration utilizing a comprehensive evaluation of the QCD and Weinberg sum rules at finite temperature. As input to this analysis, in-medium vector spectral functions which describe dilepton data from ultra-relativistic heavy-ion collisions are used along with temperature dependent condensates from lattice calculations, when available, or approximated by a hadron resonance gas. The combined deployment of QCD and Weinberg sum rules turns out to be rather stringent in constructing axialvector spectral functions consistent with (partial) chiral restoration.
IntroductionIn the QCD vacuum, chiral symmetry is spontaneously broken by the presence of non-zero quark condensates. Lattice-QCD calculations reveal that this symmetry becomes restored at higher temperatures as the condensates progress through a pseudo-critical region around T pc ≃ 160 MeV [1,2]. A long standing problem in hadronic physics is identifying an experimental signal for this transition. Ideally, this could be achieved by simultaneously measuring the medium modifications of the spectral functions of chiral partners, e.g., vector (ρ) and axialvector (a 1 ) mesons; chiral restoration is then characterized by a degeneracy of the two channel's spectral functions. The vector channel has been extensively explored through dilepton spectra in ultrarelativistic heavy-ion collisions [3,4,5]. Theoretical calculations from hadronic effective theory using microscopic interactions [6] are consistent with the experimental data across a wide range of collision energies. These studies reveal that the ρ-meson resonance "melts" without an appreciable mass shift as the fireball cools through the pseudo-critical region [7]. Experimental access to the axialvector channel (a 1 → πγ) is difficult due to its small branching and large width. Thus establishing this melting as a signal for chiral restoration remains outstanding. A theoretical determination of the axialvector spectral function is therefore needed to provide the necessary connection between the ρ melting and chiral symmetry.