Search

The Nakanishi perturbative integral representation of the four-dimensional T-matrix is investigated in order to get a workable treatment for scattering states, solutions of the inhomogeneous Bethe-Salpeter Equation, in Minkowski space. The projection onto the null-plane of the four-dimensional inhomogeneous Bethe-Salpeter Equation plays a key role for devising an equation for the Nakanishi weight function (a real function), as in the homogeneous case that corresponds to bound states and it has been already studied within different frameworks. In this paper, the whole formal development is illustrated in detail and applied to a system, composed by two massive scalars interacting through the exchange of a massive scalar. The explicit expression of the scattering integral equations are also obtained in ladder approximation, and, as simple applications of our formalism, some limiting cases, like the zero-energy limit and the Wick-Cutkosky model in the continuum, are presented. [ABSTRACT FROM AUTHOR]

The annihilation of heavy particles close to thermal equilibrium, which plays a prominent role in the chemical equilibration of heavy quarks in the quark-gluon plasma (QGP) as well as in many classic dark matter scenarios, is reexamined. We derive a scattering amplitude that resums near-threshold attractive interaction of the annihilating particles in terms of the nonrelativistic scattering T-matrix and Green's function, thereby capturing the pertinent Sommerfeld enhancement from both nonperturbative scattering state and bound state solutions. The derived formula is of such generality that it applies to arbitrary partial wave processes of two-particle annihilation, and enables us to incorporate finite widths of the annihilating particles. In a screened potential model, the nonperturbative scattering amplitude is computed and the Sommerfeld enhancement is identified for heavy quark-antiquark annihilation in the QGP. [ABSTRACT FROM AUTHOR]