Spectral functions in the σ channel near the critical end point

Spectral functions in the σ channel are investigated near the chiral critical end point (CEP), that is, the point where the chiral phase transition ceases to be first ordered in the (μ,T) plane of the QCD phase diagram. At that point the σ meson becomes massless in spite of explicit breaking of the chiral symmetry. It is expected that experimental signatures peculiar to the CEP can be observed through spectral changes in the presence of abnormally light σ mesons. As a candidate, the invariant-mass spectrum for diphoton emission is estimated with the chiral quark model incorporated. The results show the characteristic shape with a peak in the low energy region, which may serve as a signal for the CEP. However, we find that the diphoton multiplicity is highly suppressed by infrared behaviors of the σ meson. Experimentally, in such a low energy region below the threshold of two pions, photons from π0→2γ are major sources of the background for the signal