Weyl Consistency Conditions and γ_{5}

Area of Science:

• Quantum Field Theory
• High Energy Physics
• Theoretical Physics

Background:

• Dimensional regularization introduces ambiguities in calculations involving the gamma-5 matrix.
• These ambiguities affect precise calculations of standard model parameters, such as gauge beta functions.

Purpose of the Study:

• To resolve ambiguities arising from the treatment of gamma-5 in dimensional regularization.
• To establish a scheme-independent method for fixing these ambiguities in field-theoretic calculations.

Main Methods:

• Application of Weyl consistency conditions.
• Derivation of a relation between coefficients in gauge and Yukawa beta functions.

Main Results:

• A scheme-independent relation is established between a term in four-loop gauge beta functions and a corresponding term in three-loop Yukawa beta functions.
• This relation resolves ambiguities related to the treatment of gamma-5.

Conclusions:

• The developed method successfully fixes ambiguities in standard model calculations.
• The approach is extendable to resolve similar ambiguities at higher orders in perturbation theory.