Amplification of the scattering cross section due to non-trivial topology of the spacetime

TL;DR

This paper investigates how the topology of extra dimensions in a six-dimensional scalar field model influences scattering cross sections, revealing significant amplification effects due to non-trivial spacetime topology and background gauge fields.

Contribution

It analytically studies the scattering cross section in a six-dimensional model with torus compactification, highlighting the amplification caused by non-trivial topology and background gauge potentials.

Findings

Cross section differs significantly from four-dimensional case below heavy particle threshold.

Analytical structure of the cross section is derived for arbitrary torus radii.

Interaction with background gauge potential further amplifies the cross section.

Abstract

In previous articles it was demonstrated that the total cross section of the scattering of two light particles (zero modes of the Kaluza-Klein tower) in the six-dimensional $\lambda \phi^{4}$ model differs significantly from the cross section of the same process in the conventional $\lambda \phi^{4}$ theory in four space-time dimensions even for the energies below the threshold of the first heavy particle. Here the analytical structure of the cross section in the same model with torus compactification for arbitrary radii of the two-dimensional torus is studied. Further amplification of the total cross section due to interaction of the scalar field with constant background Abelian gauge potential in the space of extra dimensions is shown.