The Infrared Structure of QCD Amplitudes and $H\to g g$ in FDH and DRED

Abstract

We consider variants of dimensional regularization, including the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED), and present the gluon and quark form factors in the FDH scheme at next-to-next-to-leading order. We also discuss the generalization of the infrared factorization formula to FDH and DRED. This allows us to extract the cusp anomalous dimension as well as the quark and gluon anomalous dimensions at next-to-next-to-leading order in the FDH and DRED scheme, using $\overline{\text{MS}}$ and $\overline{\text{DR}}$ renormalization. To obtain these results we also present the renormalization procedure in these schemes.