Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

TL;DR

This paper calculates two-loop anomalous dimensions for high-dimensional QCD operators and Higgs EFT amplitudes, revealing universal transcendental structures and operator mixing behaviors.

Contribution

It introduces a novel method for computing two-loop form factors of high-dimensional operators up to dimension sixteen in QCD and Higgs EFT.

Findings

Computed two-loop minimal form factors up to dimension sixteen.

Extracted renormalization matrices and analyzed operator mixing.

Identified universal transcendentality structures in finite remainders.

Abstract

We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear also in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process. We first discuss the classification of operators and how to construct a good set of basis using both off-shell field theory method and on-shell form factor formalism. To study loop corrections, we apply efficient unitarity-IBP strategy and compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the UV divergences of form factor results, we extract the renormalization matrices and analyze the operator mixing behavior in detail. The form factors we compute are also equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs EFT. We obtain the analytic finite remainder functions which exhibit several universal transcendentality structures.