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

TL;DR

This paper derives the four-loop collinear anomalous dimension in planar ${ m f N}=4$ super-Yang-Mills theory using the principle of maximal transcendentality, matching previous numerical results and providing key quantities for high-energy physics.

Contribution

It introduces a method to extract four-loop anomalous dimensions in super-Yang-Mills theory from QCD data using transcendentality principles, offering precise analytic results.

Findings

Analytic four-loop collinear anomalous dimension obtained

Results agree with previous numerical estimates within 0.2%

Provides values for Regge trajectory and soft anomalous dimensions at four loops

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 ${\cal N}=4$ super-Yang-Mills theory from recent QCD results, obtaining $\hat{\cal G}_{0}^{(4)} = - 300 \zeta_7 - 256 \zeta_2 \zeta_5 - 384 \zeta_3 \zeta_4$. 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.