Four-Loop Gauge and Three-Loop Yukawa Beta Functions in a General Renormalizable Theory

Area of Science:

• High-energy physics
• Quantum field theory
• Particle physics

Background:

• Beta functions describe how coupling strengths change with energy scale.
• Calculating these functions is crucial for understanding particle interactions and theory consistency.
• Previous calculations were limited in scope and loop order.

Purpose of the Study:

• To present general four-loop beta functions for gauge and Yukawa couplings.
• To develop a method for determining unknown coefficients in beta function calculations.
• To apply these results to the Standard Model and its extensions.

Main Methods:

• Developing a general ansatz for beta functions.
• Fixing unknown coefficients through direct calculations in simplified models.
• Extending calculations to four loops for gauge couplings and three loops for Yukawa couplings.

Main Results:

• Derived beta functions for gauge and Yukawa couplings in general four-dimensional quantum field theory.
• Provided expressions for four-loop gauge couplings and three-loop Yukawa couplings.
• Applied results to the Standard Model, including extensions with multiple Higgs doublets.

Conclusions:

• The presented method allows for the calculation of beta functions in complex quantum field theories.
• The results are applicable to the Standard Model and provide a basis for further theoretical investigations.
• This work advances the understanding of coupling constant evolution in fundamental physics.