Infrared structure of $\mathcal{N}$ = 4 SYM and leading transcendentality principle in gauge theory

TL;DR

This paper investigates the infrared properties of $ abla$=4 SYM, exploring soft and collinear structures, their universality, and the principle of maximum transcendentality, revealing new violations at the form factor level.

Contribution

It provides a detailed analysis of the infrared structure of $ abla$=4 SYM, including soft distribution functions and their process independence, and uncovers violations of the maximum transcendentality principle in form factors.

Findings

Soft distribution function is process independent up to third order.

Violation of the maximum transcendentality principle in three-point form factors.

Soft plus virtual cross section factorization confirmed in $ abla$=4 SYM.

Abstract

We present a detailed study on the infrared structure of $\mathcal{N}=4$ SYM and its connection to QCD. Calculation of collinear splitting functions helps to understand the structure and thus one can get infrared safe cross sections. We also demonstrate the factorization property that soft plus virtual part of the cross section satisfies and through factorization, we calculate soft distribution function up to third order in perturbation theory. We show that the soft distribution function is process independent that includes operators as well as external legs. In addition to this we compare our findings against the known results in QCD through principle of maximum transcendentality (PMT). We extend our analysis further for the case of three-point form factors involving stress tensor and find that it violates the PMT while comparing with the corresponding quantity in the standard model, observed for the first time at the level of form factor.