Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors.

Andreas Von Manteuffel,Robert M Schabinger,Erik Panzer

doi:10.1103/physrevlett.124.162001

Andreas Von Manteuffel, Robert M Schabinger + Show 1 more

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https://doi.org/10.1103/physrevlett.124.162001

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Abstract

We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous dimensions. Our approach is to Laurent expand four-loop quark and gluon form factors in the parameter of dimensional regularization. We employ finite field and syzygy techniques to reduce the relevant Feynman integrals to a basis of finite integrals, and subsequently evaluate the basis integrals directly from their standard parametric representations.

Highlights

While we know that the ε−1 poles of quantum chromodynamics (QCD) amplitudes receive color quadrupole corrections at threeloop order and beyond from the soft sector [44,45,46], the four-loop collinear anomalous dimensions have long been of interest in planar N 1⁄4 4 super-Yang-Mills theory [47,48], where the dipole conjecture does appear to hold [49]
Four-loop collinear anomalous dimensions in QCD will not be needed for phenomenological purposes anytime soon, but partial results for the quark case have already appeared [15,18,19,21]
GrL1⁄2k denotes the coefficient of εk in the series GrLðεÞ defined in Eqs. (2.14)–(2.17) of Ref. [71] in terms of the bare form factors. These coefficients can be extracted from the four-loop expansions in our Supplemental Material [70], together with the well-known higher orders in ε of the bare one, two, and three-loop form factors given in Refs. [75,78,79,80] or Ref. [37]

Summary

Introduction

Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. We determine the complete matter dependence of the quark and gluon collinear anomalous dimensions.

Results

Conclusion