Annihilation Mechanisms of Lepton Pair Production in Relativistic   Nuclear Collisions
  The pion and quark annihilation mechanisms of dilepton production during relativistic nuclear collisions are studied. We focus on the modifications caused by the specific features of in-medium pion and quark states rather than by medium modification of the $\rho $-meson spectral density. The main ingredient emerging in our approach is a form-factor of the multi-pion (multi-quark) system. Replacing the usual delta-function the form-factor plays the role of distribution which, in some sense, "connects" the total 4-momenta of the annihilating and outgoing particles. The difference between the c.m.s. velocities attributed to annihilating and outgoing particles is a particular consequence of this replacement and results in the appearance of a new factor in the formula for the lepton pair production rate. We obtained that the form-factor of the multi-pion (multi-quark) system causes broadening of the rate which is most pronounced for small invariant masses, in particular, we obtain a growth of the rate for the invariant masses below two masses of the annihilating particles. 
Dmitry Anchishkin