Why the $a_1$ meson might be a difficult messenger for the restoration of chiral symmetry

We perform a theoretical analysis of the $a_1$ resonance mass spectrum in ultra-relativistic heavy ion collisions within a hadron/string transport approach. Predictions for the $a_1$ yield and its mass distribution are given for the GSI-FAIR and the critRHIC energy regime. The potential of the $a_1$ meson as a signal for chiral symmetry restoration is explored. In view of the latest discussion, we investigate the decay channel $a_1\to \gamma \pi$ in detail and find a strong bias towards low $a_1$ masses. This apparent mass shift of the $a_1$ if observed in the $\gamma \pi$ channel might render a possible mass shift due to chiral symmetry restoration very difficult to disentangle from the decay kinematics.