Subleading Color Corrections at Three Loops to the $\operatorname{tr}(φ^2)$ Three-Point Form Factor in $\mathcal{N} = 4$ Super Yang-Mills Theory

TL;DR

This work addresses subleading-color corrections at three loops to the three-point form factor of the operator $ ext{tr}(oldsymbol{)^2}$ in $ ext{N}=4$ sYM, advancing beyond the planar limit. The authors compute the full-color three-loop contribution by reducing the integrand to five master-integral families using IBP with Blade, solving canonical differential equations, and carefully handling infrared factorization to obtain a finite remainder for the subleading color piece. The resulting finite remainder is compact, expressible as integer linear combinations of generalized polylogarithms of weight six with alphabet $igl\{u,v,w,1-u,1-v,1-wigr brace$ and exhibits a symmetric dependence on $u,v,w$, with a rich but constrained symbol structure. These results provide a crucial data point for extending the amplitude bootstrap beyond leading color and have potential implications for QCD and Higgs phenomenology by informing subleading-color corrections.

Abstract

We compute three-loop corrections to the three-point form factor of the operator $\operatorname{tr}(φ^2)$ in $\mathcal{N} = 4$ Super Yang-Mills theory. In particular, our result is valid beyond the leading-color limit and will consequently be an important input towards extending the amplitude-bootstrap program beyond the leading-color approximation. We find that our analytic formulae are strikingly compact expressions in terms of integer linear combinations of generalized polylogarithms of weight six.

Figures (1)

• Figure 1: The absolute value of the ratio of the corrections of the finite remainder function at L-loops to its 1-loop counterpart in the Euclidean region.