# The quark and gluon form factors to three loops in QCD through to $\mathcal{O}\left( {{\epsilon^2}} \right)$

Gehrmann, T; Glover, E W N; Huber, T; Ikizlerli, N; Studerus, C (2010). The quark and gluon form factors to three loops in QCD through to $\mathcal{O}\left( {{\epsilon^2}} \right)$. Journal of High Energy Physics, (11):012.

## Abstract

We give explicit formulae for the $\mathcal{O}(\epsilon)$ and $\mathcal{O}\left( {{\epsilon^2}} \right)$ contributions to the unrenormalised three loop QCD corrections to quark and gluon form factors. These contributions have at most transcendentality weight eight. The $\mathcal{O}(\epsilon)$ terms of the three-loop form factors are required for the extraction of the four-loop quark and gluon collinear anomalous dimensions. The $\mathcal{O}\left( {{\epsilon^2}} \right)$ terms represent an irreducible contribution to the finite part of the form factors at four-loops. For the sake of completeness, we also give the contributions to the one and two loop form factors to the same transcendentality weight eight.

## Abstract

We give explicit formulae for the $\mathcal{O}(\epsilon)$ and $\mathcal{O}\left( {{\epsilon^2}} \right)$ contributions to the unrenormalised three loop QCD corrections to quark and gluon form factors. These contributions have at most transcendentality weight eight. The $\mathcal{O}(\epsilon)$ terms of the three-loop form factors are required for the extraction of the four-loop quark and gluon collinear anomalous dimensions. The $\mathcal{O}\left( {{\epsilon^2}} \right)$ terms represent an irreducible contribution to the finite part of the form factors at four-loops. For the sake of completeness, we also give the contributions to the one and two loop form factors to the same transcendentality weight eight.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics Physical Sciences > Nuclear and High Energy Physics English November 2010 04 Jan 2011 16:13 23 Jan 2022 17:44 Springer 1029-8479 Green https://doi.org/10.1007/JHEP11(2010)102 http://arxiv.org/abs/1010.4478