Analytic Form of Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD

Area of Science:

• High Energy Physics
• Quantum Chromodynamics (QCD)
• Particle Physics

Background:

• Scattering amplitudes are fundamental to understanding particle interactions.
• Calculating higher-order corrections in QCD is essential for precise predictions at particle colliders.
• Previous calculations for five-point amplitudes at two-loop order were limited.

Purpose of the Study:

• To present the analytic form of planar two-loop five-gluon scattering amplitudes in QCD.
• To provide the first analytic results for five-point, two-loop amplitudes relevant for higher-order QCD corrections.
• To enable more precise theoretical predictions at hadron colliders.

Main Methods:

• Reconstruction of analytic expressions from numerical evaluations.
• Exploitation of physical and analytical properties of scattering amplitudes.
• Utilizing a minimal basis of recently classified pentagon functions to simplify computation.

Main Results:

• The complete analytic form of planar two-loop five-gluon scattering amplitudes for all independent helicity configurations.
• These represent the first analytic results for this specific type of amplitude.
• The methodology allows for the computation of next-to-next-to-leading-order QCD corrections.

Conclusions:

• The derived analytic amplitudes are a significant advancement for theoretical particle physics.
• These results pave the way for more accurate predictions of processes at the Large Hadron Collider (LHC).
• The employed techniques offer a path for tackling similarly complex amplitude calculations in the future.