Light-fronts approach to electron-positron pair production in ultrarelativistic heavy-ion collisions

Abstract

We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using lightfront variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic charges of the ions.

Coulomb corrections to thee+e−pair production in ultrarelativistic heavy-ion collisions

“…(1) would lead to the wrong conclusion [1,2,3] that the exact cross section coincides with the Born result. Let us show that, in order to obtain the Coulomb corrections in (1), it is necessary first to take the integral over k using the functions F (∆) with the regularized phase and then remove the regularization.…”

“…As for the higher order terms in (1) (Coulomb corrections), they give the correct result only after the integration over the directions of the positron (electron) momentum. This is due to the fact that the asymptotic form of the wave functions in [1,2,3] corresponds to the problem of scattering, but not to the problem of pair production. If one calculates the cross section integrated over the direction of q, then, due to the completeness relation, it is possible to replace the set of functions containing in asymptotics the converging spherical wave with the set of functions containing the diverging spherical wave.…”

“…Though the existence of the Coulomb corrections is out of doubt, the source of the disagreement between the results was not revealed so far. This question is important from the theoretical point of view, since the approach developed in [1,2,3] is used now in QCD. In the present paper we present the solution of this puzzle.…”

“…Then the expression for the cross section of the e + e − pair production, obtained in [1,2,3], reads…”

“…Using slightly different approaches, the authors of [1,2,3] calculated the cross section of the process exactly in the parameters αZ A,B (Z A,B being the charge numbers of the nuclei A and B, α is the fine-structure constant). In these papers the nuclei were treated as sources of the external field, and the amplitude was calculated at a fixed impact parameter of the nuclei.…”