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We investigate whether the soft mode that becomes massless at the QCDcritical point (CP) causes an enhancement of the dilepton production rate (DPR)and the electric conductivity around the CP through the modification of thephoton self-energy. The modification is described by the so-calledAslamazov-Larkin, Maki-Thompson and density of states terms, which have beentaken into account in our previous study on the DPR near thecolor-superconducting phase transition, with a replacement of the diquark modeswith the soft mode of the QCD CP. We show that the coupling of photons with thesoft modes brings about an enhancement of the DPR in the low invariant-massregion and the conductivity near the CP, which would be observable in therelativistic heavy-ion collisions.

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