Remarks on Compton forward scattering singularity in the NCQED

TL;DR

This paper examines the forward scattering singularity in high-energy Compton scattering within noncommutative QED, proposing cut-offs to manage singularities and suggesting potential observability at future colliders for scales above 1 TeV.

Contribution

It introduces a model for handling forward scattering singularities in NCQED using cut-offs dependent on energy scales, and analyzes their impact on scattering cross sections.

Findings

Cut-offs can suppress NC corrections to negligible levels.

Forward scattering cross section remains larger than backward, aiding observation.

Effects may be detectable at future colliders if NC scale exceeds 1 TeV.

Abstract

We investigate the behaviour of head-to-head high energy Compton scattering in the $\theta$-exact noncommutative (NC) quantum electrodynamics (QED) on the Moyal space (NCQED) in the amid its unresolved forward scattering singularity. We model the effect of the currently unknown resolution to this unavoidable collinear singularity by cut-offs which are functions of the control variable $s/\Lambda_{\rm NC}^2$, and find that such cut-off functions can suppress NC corrections to the inverse Compton scattering to negligible. Discussed cut-offs leave the unpolarised integral cross section of the forward region larger than the backward region all the time, making the former potentially easier to observe. Our estimations indicate that such an effect may be visible in the future collider experiments when the NC scale $\Lambda_{\rm NC}\gtrsim1$ TeV.