Two-Loop Spacelike Splitting Amplitude for N=4 Super-Yang-Mills Theory

TL;DR

This paper analytically computes the two-loop spacelike splitting amplitude in N=4 Super-Yang-Mills theory, revealing factorization violations and their restoration at the squared amplitude level, with implications for QCD.

Contribution

It provides the first explicit two-loop calculation of spacelike splitting amplitudes in N=4 SYM using two methods, and explores factorization properties and their universality.

Findings

Explicit two-loop splitting amplitude derived

Factorization violations identified and analyzed

Conjecture on tripole terms in QCD matching N=4 SYM

Abstract

The study of collinear behavior for gauge theories in the spacelike region is of great phenomenological and theoretical importance. We analytically calculate the two-loop spacelike splitting amplitude for the full color N=4 Super-Yang-Mills theory. The result is derived by two complementary methods starting from the known amplitude: one is based on a discontinuity analysis, while the other one is based on analytic continuation. Our result explicitly shows terms that violate naive factorization. However we show that factorization is restored at the level of color-summed unpolarized squared amplitudes at next-to-next-to-next-to leading order. We conjecture that the two-loop tripole terms in the generalized splitting amplitudes in QCD are identical to what we obtain in N=4 super Yang-Mills theory.