Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors

Area of Science:

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

Background:

• Anomalous dimensions are crucial for understanding particle interactions in Quantum Chromodynamics.
• Previous calculations were limited in loop order and scope.
• The quark and gluon cusp anomalous dimensions are fundamental quantities in perturbative QCD.

Purpose of the Study:

• To analytically compute the complete four-loop quark and gluon cusp anomalous dimensions in massless Quantum Chromodynamics.
• To determine the full matter dependence of quark and gluon collinear anomalous dimensions.
• To advance the precision of theoretical predictions in high-energy particle physics.

Main Methods:

• Analytical calculation from first principles.
• Laurent expansion of four-loop quark and gluon form factors.
• Dimensional regularization parameter analysis.
• Finite field and syzygy techniques for Feynman integral reduction.
• Direct evaluation of basis integrals from parametric representations.

Main Results:

• The complete four-loop quark and gluon cusp anomalous dimensions in massless QCD have been analytically calculated.
• The full matter dependence of quark and gluon collinear anomalous dimensions has been determined.
• A new level of precision in perturbative QCD calculations has been achieved.

Conclusions:

• This work provides essential analytical results for fundamental quantities in QCD.
• The findings contribute to a more precise understanding of particle interactions at high energies.
• The employed methods offer a robust framework for future higher-loop calculations in quantum field theory.