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Matter Dependence of the Four-Loop Cusp Anomalous Dimension


Henn, J M; Peraro, T; Stahlhofen, M; Wasser, P (2019). Matter Dependence of the Four-Loop Cusp Anomalous Dimension. Physical Review Letters, 122(20):201602.

Abstract

We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop lightlike cusp anomalous dimension in QCD, with nf fermion and ns scalar flavors. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end, we first identify a set of integrals for which the integrands have a d log form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals with a simpler infrared pole structure. In this way, only integrals with ten or fewer propagators are needed for obtaining the cusp anomalous dimension. These integrals are then computed via the method of differential equations through the addition of an auxiliary scale. Combining our result with that of a parallel paper, we obtain the complete nf dependence of the four-loop cusp anomalous dimension in QCD. Finally, using known numerical results for the gluonic contributions, we obtain an improved numerical prediction for the cusp anomalous dimension in N=4 super Yang-Mills theory.

Abstract

We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop lightlike cusp anomalous dimension in QCD, with nf fermion and ns scalar flavors. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end, we first identify a set of integrals for which the integrands have a d log form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals with a simpler infrared pole structure. In this way, only integrals with ten or fewer propagators are needed for obtaining the cusp anomalous dimension. These integrals are then computed via the method of differential equations through the addition of an auxiliary scale. Combining our result with that of a parallel paper, we obtain the complete nf dependence of the four-loop cusp anomalous dimension in QCD. Finally, using known numerical results for the gluonic contributions, we obtain an improved numerical prediction for the cusp anomalous dimension in N=4 super Yang-Mills theory.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > General Physics and Astronomy
Uncontrolled Keywords:General Physics and Astronomy
Language:English
Date:22 May 2019
Deposited On:16 Oct 2019 14:27
Last Modified:29 Jul 2020 11:27
Publisher:American Physical Society
ISSN:0031-9007
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1103/physrevlett.122.201602
Project Information:
  • : FunderH2020
  • : Grant ID725110
  • : Project TitleAMPLITUDES - Novel structures in scattering amplitudes
  • : FunderH2020
  • : Grant ID746223
  • : Project TitleMPAmplitudes - Multi-particle scattering amplitudes for precision collider physics

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