Momentum-Space Topology of Standard Model

TL;DR

This paper explores the momentum-space topological invariants of the Standard Model, linking them to particle masses, symmetry phases, and chiral anomalies, revealing how topological properties influence fundamental particle behavior.

Contribution

It introduces a topological framework for understanding the Standard Model's phases and mass generation through momentum-space invariants and their relation to anomalies.

Findings

Invariants are continuous functions of hypercharge and weak charge parameters.

Invariants indicate mass protection in the symmetric phase.

Invariants vanish in the broken symmetry phase, correlating with particle mass acquisition.

Abstract

The momentum-space topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetric phase above the electroweak transition (the mass protection). All the invariants become zero in the broken symmetry phase, as a result all the elementary fermions become massive. Relation of the momentum-space invariants to chiral anomaly is also discussed.