Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles

Abstract

We compute the fermionic contributions to the cusp anomalous dimension in QCD at four loops as an expansion for small cusp angle. As a byproduct we also obtain the respective terms of the four-loop HQET wave function anomalous dimension. Our new results at small angles provide stringent tests of a recent conjecture for the exact angle dependence of the matter terms in the four-loop cusp anomalous dimension. We find that the conjecture does not hold for two of the seven fermionic color structures, but passes all tests for the remaining terms. This provides strong support for the validity of the corresponding conjectured expressions with full angle dependence. Taking the limit of large Minkowskian angle, we extract novel analytic results for certain terms of the light-like cusp anomalous dimension. They agree with the known numerical results. Finally, we study the anti-parallel lines limit of the cusp anomalous dimension. In a conformal theory, the latter is proportional to the static quark-antiquark potential. We use the new four-loop results to determine parts of the conformal anomaly term.

26 pages, 2 figures, 1 table

References in corpus (11)

• FIRE5: a C++ implementation of Feynman Integral REduction
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Fermionic contributions to the three-loop static potential
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The three-loop cusp anomalous dimension in QCD
• Five-loop renormalisation of QCD in covariant gauges
• Four-loop quark form factor with quartic fundamental colour factor
• Analytic three-loop static potential
• On the Casimir scaling violation in the cusp anomalous dimension at small angle

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