Three-Loop Color-Kinematics Duality: A 24-Dimensional Solution Space Induced by New Generalized Gauge...

Area of Science:

• High-energy physics
• Quantum field theory
• Supersymmetric Yang-Mills theory

Background:

• N=4 super Yang-Mills (SYM) theory is a key model in quantum field theory, offering insights into non-perturbative phenomena.
• Form factors are crucial for calculating scattering amplitudes and understanding particle interactions.
• Color-kinematics duality and on-shell unitarity are powerful tools for simplifying complex calculations in quantum field theory.

Purpose of the Study:

• To compute full-color, three-loop, three-point form factors for the stress-tensor supermultiplet and a specific operator in N=4 SYM theory.
• To explore the implications of color-kinematics duality and on-shell unitarity in these calculations.
• To investigate the structure and properties of these form factors, including potential connections to quantum chromodynamics (QCD).

Main Methods:

• Application of color-kinematics duality to construct integrand results.
• Verification of results using planar and nonplanar unitarity cuts.
• Analysis of loop momentum power counting and diagrammatic symmetries.
• Numerical integration to obtain infrared divergences and planar remainders.

Main Results:

• Obtained full-color three-loop form factors for the stress-tensor supermultiplet and a length-3 half-Bogomol'nyi-Prasad-Sommerfield operator.
• Identified a large number of free parameters (24 for the stress-tensor form factor) due to a new generalized gauge transformation.
• Confirmed results satisfy minimal power counting and diagrammatic symmetries.
• Numerical integration yielded consistent full-color infrared divergences and the known planar remainder.

Conclusions:

• The derived form factors are the N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD.
• These results are expected to provide the maximally transcendental parts of the corresponding QCD amplitudes.
• The presence of numerous free parameters highlights new structural aspects of form factors in N=4 SYM theory.