Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude.

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Particle Physics

Background:

• The computation of multi-leg scattering amplitudes is crucial for precision predictions in quantum chromodynamics (QCD).
• Two-loop amplitudes are essential for achieving higher precision beyond next-to-leading order in perturbative QCD.
• The all-plus helicity configuration in five-gluon scattering presents unique challenges due to its non-trivial structure.

Purpose of the Study:

• To compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration.
• To obtain an analytic expression for this amplitude in the physical scattering region.
• To provide a foundation for precision calculations in high-energy particle collisions.

Main Methods:

• Calculation of master integrals for all external leg permutations.
• Verification of the amplitude's divergence structure.
• Extraction of the finite hard function.
• Analysis of factorization properties in the collinear limit.

Main Results:

• The full-color two-loop five-gluon amplitude for the all-plus helicity configuration has been computed.
• The result is fully analytic and valid in the physical scattering region.
• The amplitude is expressed in a compact form involving logarithms, dilogarithms, and rational functions.

Conclusions:

• The computed amplitude provides a significant step towards higher-precision predictions in QCD.
• The analytic result facilitates further theoretical studies and phenomenological applications.
• The methods employed are applicable to other challenging scattering amplitude calculations.