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

Abstract

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 $M_σ(T,μ) \approx 2 M_π(T,μ)$ is fulfilled. This effect results in a strong enhancement of the cross section for the pion annihilation process $2 π\to 2 γ$ 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.