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The three-loop form factor in \( \mathcal{N} = {4} \) super Yang-Mills

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Abstract

In this paper we study the Sudakov form factor in \( \mathcal{N} = {4} \) super Yang-Mills theory to the three-loop order. The latter is expressed in terms of planar and non-planar loop integrals. We show that it is possible to choose a representation in which each loop integral has uniform transcendentality. We verify analytically the expected exponentiation of the infrared divergences with the correct values of the three-loop cusp and collinear anomalous dimensions in dimensional regularisation. We find that the form factor in \( \mathcal{N} = {4} \) super Yang-Mills can be related to the leading transcendentality part of the quark and gluon form factors in QCD. We also study the ultraviolet properties of the form factor in D > 4 dimensions, and find unexpected cancellations, resulting in an improved ultraviolet behaviour.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Thomas Gehrmann

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    Thomas Gehrmann, Johannes M. Henn & Tobias Huber

  3. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße15, D-12489, Berlin, Germany

    Johannes M. Henn

  4. Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Johannes M. Henn

  5. Theoretische Physik 1, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Strasse 3, D-57068, Siegen, Germany

    Tobias Huber

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  1. Thomas Gehrmann
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ArXiv ePrint: 1112.4524

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Gehrmann, T., Henn, J.M. & Huber, T. The three-loop form factor in \( \mathcal{N} = {4} \) super Yang-Mills. J. High Energ. Phys. 2012, 101 (2012). https://doi.org/10.1007/JHEP03(2012)101

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