Soft theorem to three loops in QCD and N = 4 super Yang-Mills theory

• Published in: The journal of high energy physics Vol. 2024; no. 1; p. 131
• Main Authors: Chen, Wen, Luo, Ming-xing, Yang, Tong-Zhi, Zhu, Hua Xing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 23.01.2024; Springer Nature B.V
• Subjects: Boundary conditions; Classical and Quantum Gravitation; Elementary Particles; Gauge theory; Integrals; Partons; Physics; Physics and Astronomy; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering amplitude; String Theory; Theorems; Yang-Mills theory; Effective Field Theories of QCD; Higher-Order Perturbative Calculations
• ISSN: 1029-8479
• DOI: 10.1007/JHEP01(2024)131

A bstract The soft theorem states that scattering amplitude in gauge theory with a soft gauge-boson emission can be factorized into a hard scattering amplitude and a soft factor. In this paper, we present calculations of the soft factor for processes involving two hard colored partons, up to three loops in QCD. To accomplish this, we developed a systematic method for recursively calculating relevant Feynman integrals using the Feynman-Parameter representation. Our results constitute an important ingredient for the subtraction of infrared singularities at N 4 LO in perturbative QCD. Using the principle of leading transcendentality between QCD and N = 4 super Yang-Mills theory, we determine the soft factor in the latter case to three loops with full-color dependence. As a by-product, we also obtain the finite constant f 2 3 in the Bern-Dixon-Smirnov ansatz analytically, which was previously known numerically only.