UV Divergences of Scattering Amplitudes in D-dimensional Yang-Mills Theories

TL;DR

This paper analyzes one-loop UV divergences in planar gluon scattering amplitudes across various dimensions in Yang-Mills theories, revealing dimension-dependent divergence behaviors and cancellations.

Contribution

It provides a detailed calculation of UV divergences in D-dimensional Yang-Mills theories using Passarino-Veltman reduction and compares results across multiple dimensions and supersymmetric cases.

Findings

UV divergences cancel in D=6 dimensions.

In D=8 and 10, divergences from different loops have the same sign.

Results extend understanding of divergence structure in higher-dimensional gauge theories.

Abstract

We consider UV divergences for the on-shell planar gluon-gluon scattering amplitudes in the gauge theory in arbitrary D-dimensions in the one-loop order. The amplitudes are evaluated using the standard Feynman diagram technique for several choices of external gluon polarizations. Using the Passarino - Veltman reduction, the expansion in terms of the scalar master integrals is constructed and their calculation is performed within dimensional regularization. The resulting expressions are confronted with existing results for various cases, including maximally supersymmetric theories in D=4, 6, 8, and 10 dimensions. One finds that, contrary to the D=4 case, in D=6 one-loop UV divergences cancel, while in D=8 and 10 the contributions of gauge, scalar and fermion loops have the same sign.