Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 305 / 4 / e

The $SU(2{)}_L$ electroweak theta angle can be shifted by an anomalous global rephasing generated by baryon plus lepton number. Because the renormalizable Standard Model has no operator that explicitly breaks this global phase in a way that fixes it, one may choose the rephasing to set ${\theta }_{\mathrm{EW}}=0$ without changing any other physical parameter. The weak theta angle is therefore unobservable in the renormalizable Standard Model; it could enter a physical invariant only after adding suitable explicit violation of baryon plus lepton number.