The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions

Abstract

We present the details of the analytic calculation of the three-loop angle-dependent cusp anomalous dimension in QCD and its supersymmetric extensions, including the maximally supersymmetric $\mathcal{N}=4$ super Yang-Mills theory. The three-loop result in the latter theory is new and confirms a conjecture made in our previous paper. We study various physical limits of the cusp anomalous dimension and discuss its relation to the quark-antiquark potential including the effects of broken conformal symmetry in QCD. We find that the cusp anomalous dimension viewed as a function of the cusp angle and the new effective coupling given by light-like cusp anomalous dimension reveals a remarkable universality property -- it takes the same form in QCD and its supersymmetric extensions, to three loops at least. We exploit this universality property and make use of the known result for the three-loop quark-antiquark potential to predict the special class of nonplanar corrections to the cusp anomalous dimensions at four loops. Finally, we also discuss in detail the computation of all necessary Wilson line integrals up to three loops using the method of leading singularities and differential equations.

63 pages, 14 figures; v2: minor changes, references added; v3: minor changes, eq.(D.7) corrected

References in corpus (13)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithm FIRE -- Feynman Integral REduction
• FIRE5: a C++ implementation of Feynman Integral REduction
• Quark and gluon form factors to three loops
• Feynman Diagrams and Differential Equations
• The all loop AdS4/CFT3 Bethe ansatz
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Iterative structure of finite loop integrals
• Fermionic contributions to the three-loop static potential
• The three-loop cusp anomalous dimension in QCD
• New differential equations for on-shell loop integrals
• Quark-antiquark potential in AdS at one loop
• Dimensional Reduction applied to QCD at three loops

Cited by in corpus (81)

• Large-Momentum Effective Theory
• 50 Years of Quantum Chromodynamics
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Elliptic Feynman integrals and pure functions
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Matter dependence of the four-loop cusp anomalous dimension
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• The Four Loop QCD Rapidity Anomalous Dimension
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Connecting Different TMD Factorization Formalisms in QCD
• Quark--anti-quark potential in N=4 SYM
• Exact Bremsstrahlung and Effective Couplings
• Massive vector form factors to three loops
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Lattice continuum-limit study of nucleon quasi-PDFs
• Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach
• Towards the exact Bremsstrahlung function of ABJM theory
• The Heavy Quark Form Factors at Two Loops
• On the Casimir scaling violation in the cusp anomalous dimension at small angle
• Massive three-loop form factor in the planar limit
• 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
• Soft anomalous dimensions for single-top production at three loops
• Four-loop wave function renormalization in QCD and QED
• Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory
• Soft-gluon effective coupling and cusp anomalous dimension
• Subleading Regge limit from a soft anomalous dimension
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• Relating amplitude and PDF factorisation through Wilson-line geometries
• Massive three-loop form factors: anomaly contribution
• The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy
• Three-loop soft function for heavy-to-light quark decays
• From correlation functions to event shapes in QCD
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• The full angle-dependence of the four-loop cusp anomalous dimension in QED
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• Three-loop cusp anomalous dimension and a conjecture for $n$ loops
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• Heavy quark expansion for heavy-light light-cone operators
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Four-loop massive cusp anomalous dimension in QCD: a calculation from asymptotics
• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• Heavy quark form factors in the large ${\beta }_0$ limit
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• Transverse Momentum-Dependent Heavy-Quark Fragmentation at Next-to-Leading Order
• Emitted Radiation and Geometry
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Matching the heavy-quark fields in QCD and HQET at four loops
• Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications
• QCD cusp anomalous dimension: current status
• Four-loop QCD cusp anomalous dimension at small angle
• Analytic NNLO transverse-momentum-dependent soft function for heavy quark pair hadroproduction at threshold
• Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark
• The Game of Triangles
• Structure constants of twist-two light-ray operators in the triple Regge limit
• Collins-Soper Kernel in the QCD Instanton Vacuum
• Four-dimensional differential equations for the leading divergences of dimensionally-regulated loop integrals
• On Wilson loops for two touching circles with opposite orientation
• Holographic dual of defect CFT with corner contributions
• More on Wilson loops for two touching circles
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Three loop QCD corrections to heavy quark form factors
• Wilson Loops and Integrability
• Non-abelian soft radiation data for a celestial theory
• On the cusp anomalous dimension in the ladder limit of $\mathcal{N}=4$ SYM
• Singlet and non-singlet three-loop massive form factors
• Boomerang webs up to three-loop order