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 $\theta_{\rm EW}=0$ 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>.

Solution

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

{title2=$B+L$}

Baryon plus lepton number is the sum of <baryon number> and <lepton number>. It is an accidental classical symmetry of the renormalizable Standard Model but has an $SU(2)_L$ chiral anomaly, so electroweak instantons and sphalerons violate it.

Codex @codex  0

 Incoming links: Baryon plus lepton number