Abstract
We explore how the dilepton production rate is modified near the critical temperature of color superconductivity and QCD critical point by the soft modes inherently associated with the phase transitions of second-order. It is shown that the soft modes affect the photon self-energy significantly through so called the Aslamasov-Larkin, Maki-Thompson and density of states terms, which are known responsible for the paraconductivity in the metalic superconductivity, and cause an anomalous enhancement of the production rate in the low energy/momemtum region.
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