The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor

Abstract

We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the ${\epsilon }^{-2}$ pole of the form factor using parametric integrations of finite integrals. We provide uniformly transcendental results for the master integrals through to weight six and confirm a very recent independent analytic result for the full four-loop cusp anomalous dimension of the $\mathcal{N}=4$ model.

13 pages

References in corpus (31)

• Transcendentality and Crossing
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• A novel approach to integration by parts reduction
• Reduze 2 - Distributed Feynman Integral Reduction
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• Color-kinematic Duality for Form Factors
• A quasi-finite basis for multi-loop Feynman integrals
• On hyperlogarithms and Feynman integrals with divergences and many scales
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Matter dependence of the four-loop cusp anomalous dimension
• Feynman integral relations from parametric annihilators
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• The $n_f^2$ contributions to fermionic four-loop form factors
• On the Computation of Form Factors in Massless QCD with Finite Master Integrals
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Master integrals for the four-loop Sudakov form factor
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Soft-gluon effective coupling and cusp anomalous dimension
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Planar master integrals for four-loop form factors
• Constructing multi-loop scattering amplitudes with manifest singularity structure
• The full four-loop cusp anomalous dimension in $\mathcal{N}=4$ super Yang-Mills and QCD
• Modern techniques of multiloop calculations

Cited by in corpus (31)

• Collider Physics at the Precision Frontier
• The Four Loop QCD Rapidity Anomalous Dimension
• Three-loop gluon scattering in QCD and the gluon Regge trajectory
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• Approximate four-loop QCD corrections to the Higgs-boson production cross section
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Full-color three-loop three-point form factors in N=4 SYM
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• The full angle-dependence of the four-loop cusp anomalous dimension in QED
• The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• Anomalous Dimensions from Soft Regge Constants
• Towards massless and massive event shapes in the large-${\beta }_0$ limit
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• Threshold enhanced cross sections for colorless productions
• Three-loop helicity amplitudes for photon+jet production
• Precision QCD phenomenology of exotic spin-2 search at the LHC
• QCD cusp anomalous dimension: current status
• Higgs boson rapidity distribution in bottom annihilation at NNLL and beyond
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• The two-loop Higgs impact factor
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• On-shell Methods for Form Factors in N=4 SYM and Their Applications