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 MS‾ and DR‾ renormalization. To obtain these results we also present the renormalization procedure in these schemes.
Highlights
The calculation of cross sections beyond leading order in perturbation theory is of utmost importance to fully exploit the wealth of experimental data provided by particle colliders
Virtual corrections involve the calculation of loop diagrams and only the sum of all contributions leads to finite results
We describe in detail the necessary UV renormalization procedure in the MS and DR renormalization scheme and extract the corresponding two-loop anomalous dimensions
Summary
The calculation of cross sections beyond leading order in perturbation theory is of utmost importance to fully exploit the wealth of experimental data provided by particle colliders. A case of particular interest is the gluon form factor, i.e. the amplitude for the process Higgs to two gluons This process is described by an effective Higgs-gluon–gluon vertex including the effective coupling λ and has not been calculated at the two-loop level in fdh or dred so far. In these schemes there is an additional coupling λ between the Higgs and two -scalars and the renormalization becomes highly non-trivial. [19,20,21], a very simple all-order formula predicting the IR divergences of pure QCD amplitudes in cdr has been proposed An extension of this to the fdh scheme, based on Ref.
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