Lepton pair production in heavy-ion collisions in perturbation theory

We derive the first terms in the amplitude of lepton pair production in the Coulomb fields of two relativistic heavy ions. Using the Sudakov technique, which simplifies the calculations in momentum space for the processes at high energies, we get compact analytical expressions for the differential cross section of the process under consideration in the lowest order in the fine-structure constant (Born approximation) valid for any momentum transfer and in a wide kinematic region for produced particles. Exploiting the same technique, we consider the next terms of the perturbation series (up to the fourth order in the fine-structure constant) and investigate their energy dependence and limiting cases. It has been shown that taking into account all relevant terms in the corresponding order, one obtains expressions that are gauge invariant and finite. We estimate the contribution of the Coulomb corrections to the total cross section and discuss the cancellations of the different terms in the total cross section.