Chiral Partners and Their Electromagnetic Radiation (ingredients for a Systematic In-medium Calculation)

It is argued that the chiral partners of the lowest-lying hadrons are hadronic molecules and not three-quark or quark-antiquark states, respectively. As an example the case of a 1 as the chiral partner of the ρ is discussed. Deconfinement — or as a precursor large in-medium widths for hadronic states — is proposed as a natural way to accommodate for the fact that at chiral restoration the respective in-medium spectra of chiral partners must become degenerate. Ingredients for a systematic and self-consistent in-medium calculation are presented with special emphasis on vector-meson dominance which emerges from a recently proposed systematic counting scheme for the mesonic sector including pseudoscalar and vector mesons as active degrees of freedom. 1 Chiral partners Chiral symmetry breaking and its restoration in a strongly interacting medium is one of the key issues of in-medium hadron physics, at least for the states made out of light (u, d, s) quarks (see e.g. the talk of T. Hatsuda in the present proceedings volume). One of the clearest signs that chiral symmetry is indeed spontaneously broken comes from a comparison of the spectra of quark currents related by a chiral transformation, namely the vector–isovector current j µ V = ¯ q τ γ µ q and the axial-vector–isovector current j µ A = ¯ q τ γ 5 γ µ q. 1 If chiral symmetry was realized in the same way as, say, isospin symmetry, then the spectra of the respective current-current correlators would be (approximately) the same. The experimental results for these spectra are shown in Fig. 1. Obviously the spectra are not identical, not even approximately. In particular, the vector spectrum (Fig. 1, left) shows a peak below 1 GeV, the ρ meson, whereas the axial-vector spectrum (Fig. 1, right) does not show any structure below 1 GeV, but instead a broad bump at around 1.2 GeV, the a 1 meson. Since the vector and the axial-vector current are related by a chiral transformation one can call these quark currents chiral partners at the fundamental level. It is suggestive to call ρ and a 1 chiral partners at the hadronic level since they couple to the respective quark currents as seen in Fig. 1. Obviously, due to chiral symmetry breaking the masses of ρ and a 1 are not the same. In the following we shall show strong indications that chiral partners are even different in nature. To …