Imaginary part of the zero angle light-by-light scattering tensor

TL;DR

This paper derives an explicit, gauge-invariant expression for the zero angle light-by-light scattering tensor involving virtual photons, with applications to particle creation processes and consistency checks.

Contribution

It provides a novel, explicit form of the light-by-light scattering tensor at zero angle, emphasizing gauge invariance and Bose symmetry, with potential applications in particle physics.

Findings

Derived a gauge-invariant expression for the scattering tensor

Connected the tensor to particle creation processes involving virtual photons

Discussed applications and verified the expression's consistency

Abstract

We calculate the bilinear combination of Dirac tensors describing the creation of a pair of charged particle (pi-meson or leptons) by virtual photons integrated on the final particle phase volume. It can be interpreted as an s channel discontinuity of the zero angle light-by-light scattering tensor with both photons off mass shell. The expression of light-by-light scattering tensor is represented in the form where the gauge invariance and the Bose symmetry are explicitly shown. Some applications and the checks are discussed.