Why do we have parity violation?

TL;DR

This paper explores the fundamental reasons behind parity violation in the Standard Model, linking it to gauge invariance, fermion mass protection, and the structure of gauge groups, providing a theoretical derivation of observed parity conservation in electromagnetic and strong interactions.

Contribution

It derives the Standard Model's Weyl fermion representations and explains parity conservation and violation from basic assumptions like mass protection and anomaly cancellation.

Findings

Parity conservation in electromagnetic and strong interactions is explained.

Parity violation in weak interactions is linked to gauge charge dependence on handedness.

The Standard Model gauge group and fermion representations are derived from simple principles.

Abstract

We discuss here two of the questions posed at the beginning of the Bled 1998 workshop: Why is the weak charge dependent on handedness? Why do we have parity violation in the Standard Model? It is argued that the quarks and leptons must be protected from gaining a fundamental mass, very large compared to the electroweak scale, by gauge invariance and hence that their gauge charges must depend on handedness. Furthermore we argue that it is the conservation of parity in the electromagnetic and strong interactions rather than parity violation in the weak interactions that needs an explanation. We derive this parity conservation and indeed the whole system of Weyl fermion representations in the Standard Model from a few simple assumptions: Mass protection, small representations, anomaly cancellation and the Standard Model gauge group $S(U(2)\times U(3))$.