Gauge Coupling β Functions to Four-Loop Order in the Standard Model.

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Standard Model

Background:

• The Standard Model describes fundamental particles and forces.
• Gauge couplings determine interaction strengths.
• Calculating beta functions is crucial for understanding renormalization and scale dependence.

Purpose of the Study:

• To compute the beta functions of the three standard model gauge couplings to four-loop order.
• To address the challenges of defining gamma_5 in dimensional regularization at higher loop orders.

Main Methods:

• Modified minimal subtraction scheme (MS-bar) used for renormalization.
• Calculation performed to four-loop order.
• Gamma_5-dependent terms determined by exploiting relations with lower loop order coefficients.

Main Results:

• The beta functions of the three standard model gauge couplings have been computed to four-loop order.
• A method for handling gamma_5-dependent terms in dimensional regularization was successfully applied.

Conclusions:

• The four-loop beta functions provide a more precise understanding of the Standard Model's behavior at high energy scales.
• This work contributes to the ongoing effort to refine theoretical predictions in particle physics.