Process 3 -> 3 and crossing symmetry violation

Abstract

Using the Sudakov technique we sum the perturbation series for the process $3\to 3$ and obtain the compact analytical expression for the amplitude of this process, which takes into account all possible Coulomb interactions between colliding particles. Compare it with the amplitude of the lepton pair production in heavy ion collision i.e. in the process $ 2\to 4$, we show that crossing symmetry between this processes holds only if one neglects the interaction of produced pair with ions (i.e. in the approximation $Z_{1,2}\alpha \ll 1$).