Excess low energy photon pairs from pion annihilation at the chiral phase transition

The photon pair production by pion annihilation in a hot and dense medium at the chiral phase transition is investigated within a chiral quark model. As a direct consequence of this transition the σ meson appears as a bound state in the domain of temperatures and chemical potentials where the condition Mσ(T,μ)≈2 Mπ(T,μ) is fulfilled. This effect results in a strong enhancement of the cross section for the pion annihilation process 2π→2γ compared with the vacuum case. The calculation of the photon pair production rate as function of the invariant mass shows a strong enhancement and narrowing of the σ meson resonance at threshold due to chiral symmetry restoration.