On the Casimir scaling violation in the cusp anomalous dimension at small angle

Abstract

We compute the four-loop $n_f$ contribution proportional to the quartic Casimir of the QCD cusp anomalous dimension as an expansion for small cusp angle $\varphi$. This piece is gauge invariant, violates Casimir scaling, and first appears at four loops. It requires the evaluation of genuine non-planar four-loop Feynman integrals. We present results up to $\mathcal{O}({\varphi }^4)$. One motivation for our calculation is to probe a recent conjecture on the all-order structure of the cusp anomalous dimension. As a byproduct we obtain the four-loop HQET wave function anomalous dimension for this color structure.

arXiv comment13 pages, 2 figures, 1 ancillary file; v2: journal version

References in corpus (20)

• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• FIRE5: a C++ implementation of Feynman Integral REduction
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Group theory factors for Feynman diagrams
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Three-loop static potential
• Static QCD potential at three-loop order
• The three loop on-shell renormalization of QCD and QED
• The three-loop cusp anomalous dimension in QCD
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• The cusp anomalous dimension at three loops and beyond
• Three-loop anomalous dimension of the heavy-light quark current in HQET
• Non-Abelian Dipole Radiation and the Heavy Quark Expansion
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• Analytic three-loop static potential
• Violation of Casimir Scaling for Static QCD Potential at Three-loop Order
• Matching heavy-quark fields in QCD and HQET at three loops
• HQET quark-gluon vertex at one loop

Cited by in corpus (35)

• Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
• The Three-loop Quark Jet Function
• The Four Loop QCD Rapidity Anomalous Dimension
• Four-loop quark form factor with quartic fundamental colour factor
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Lattice continuum-limit study of nucleon quasi-PDFs
• Transverse momentum in double parton scattering: factorisation, evolution and matching
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Small-$x$ phenomenology at the LHC and beyond: HELL 3.0 and the case of the Higgs cross section
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Four-loop cusp anomalous dimension in QED
• Non-abelian infrared divergences on the celestial sphere
• Four-loop wave function renormalization in QCD and QED
• NNLO subtraction for any massless final state: a complete analytic expression
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Wilson loops in terms of color invariants
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Planar master integrals for four-loop form factors
• A matrix model for the latitude Wilson loop in ABJM theory
• The full angle-dependence of the four-loop cusp anomalous dimension in QED
• Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO
• The Holographic Soft $S$-Matrix in QED and Gravity
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters $\hat{q}$
• Four-loop massive cusp anomalous dimension in QCD: a calculation from asymptotics
• Matching the heavy-quark fields in QCD and HQET at four loops
• Four-loop QCD cusp anomalous dimension at small angle
• QCD cusp anomalous dimension: current status
• Four-loop HQET propagators from the DRA method
• Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• On-shell Methods for Form Factors in N=4 SYM and Their Applications