Weinberg, QFT Vol II, all of Chapter 22.tom.stoer said:
)The Standard Model Gauge Anomaly Cancellation is a mathematical principle used in particle physics to ensure that the fundamental forces in the universe (strong nuclear force, weak nuclear force, and electromagnetism) are consistent with each other. It states that the symmetries of the Standard Model, which describe the fundamental particles and their interactions, must be preserved in all physical processes.
The Standard Model Gauge Anomaly Cancellation is important because it ensures the consistency and accuracy of the Standard Model, which is the most successful theory in describing the fundamental particles and their interactions. Without it, there would be discrepancies and inconsistencies in the predictions of the Standard Model, making it less reliable as a scientific theory.
Standard Model Gauge Anomaly Cancellation works by requiring that the sum of the charges of all the fundamental particles in a physical process must be zero. This means that the charges of all particles involved in a process must balance out, ensuring that the symmetries of the Standard Model are preserved.
There are some cases where the Standard Model Gauge Anomaly Cancellation does not apply, such as in certain theoretical scenarios involving new, undiscovered particles. In these cases, modifications to the Standard Model may be needed to account for the anomalies.
The implications of Standard Model Gauge Anomaly Cancellation are far-reaching and have significant impacts on our understanding of the fundamental forces and particles in the universe. It allows for the prediction and confirmation of new particles, such as the Higgs boson, and helps to guide future research in particle physics.