The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension

Abstract

We use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar $\mathcal{N}=4$ super-Yang-Mills theory from recent QCD results, obtaining ${\hat{\mathcal{G}}}_0^{(4)}=-300{\zeta }_7-256{\zeta }_2{\zeta }_5-384{\zeta }_3{\zeta }_4$. This value agrees with a previous numerical result to within 0.2 percent. It also provides the Regge trajectory, threshold soft anomalous dimension and rapidity anomalous dimension through four loops.

12 pages, no figures. v2, references added

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• The Four Loop QCD Rapidity Anomalous Dimension
• Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Subleading Regge limit from a soft anomalous dimension
• Relating amplitude and PDF factorisation through Wilson-line geometries
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Form factors with two operator insertions and the principle of maximal transcendentality
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Maximal transcendental weight contribution of scattering amplitudes
• Two-loop amplitudes for di-Higgs and di-pseudo-Higgs productions through quark annihilation in QCD
• Deciphering the Maximal Transcendentality Principle via Bootstrap