Enhancement of dilepton production rate and electric conductivity around the QCD critical point

We investigate whether the soft mode that becomes massless at the QCD critical point (CP) causes an enhancement of the dilepton production rate (DPR) and electric conductivity around the CP through modification of the photon self-energy using the two-flavor Nambu-Jona-Lasinio model. The modification is described by the so-called Aslamazov-Larkin, Maki-Thompson, and density of states terms, which have been taken into account in our previous study on the DPR near the color-superconducting phase transition, with a replacement of the diquark modes with the soft mode of the QCD CP. We show that the coupling of photons with the soft modes brings about an enhancement of the DPR in the low-invariant-mass region and the conductivity near the CP, which would be observable in relativistic heavy-ion collisions.