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) ≈ 2Mπ(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. PACS number(s): 05.70.Jk, 11.30.Rd, 13.40.-f, 14.40.-n, 25.75.-q