Anomaly Cancellation with an Extra Gauge Boson.

Area of Science:

• High Energy Physics
• Theoretical Physics
• Particle Physics

Background:

• The Standard Model (SM) of particle physics describes fundamental particles and forces.
• Extensions to the SM often propose new particles, such as an extra gauge boson.
• Anomaly cancellation is a crucial requirement for the consistency of gauge theories.

Purpose of the Study:

• To find a general solution to the diophantine equations governing anomaly cancellation.
• To investigate the constraints on the couplings of an extra gauge boson in SM extensions.
• To consider a plausible scenario including three right-handed neutrinos.

Main Methods:

• Solving diophantine equations that arise from anomaly cancellation conditions.
• Analyzing the chiral fermion content of the Standard Model plus right-handed neutrinos.
• Applying theoretical constraints from gauge invariance and consistency.

Main Results:

• A general solution to the anomaly cancellation diophantine equations was found.
• The solution is valid for the Standard Model with three right-handed neutrinos.
• This provides a framework for understanding the couplings of new gauge bosons.

Conclusions:

• The study provides a comprehensive solution for anomaly cancellation in a specific class of SM extensions.
• The findings are relevant for phenomenological studies of new physics beyond the Standard Model.
• This work contributes to the theoretical understanding of particle interactions and new gauge bosons.