Why do we have parity violation?

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 $S(U(2)\times U(3))$.