Measurements and electroweak gauge invariance/transformations

[Michael Price]

TL;DR

Gauge transforms have no effect on measurements, so how can an electroweak SU(2) rotation transform an electron into a neutrino and not be observed?

Most gauge transformations in the standard model are easy to see are measurement invariant. Coordinate transformations, SU(3) quark colours, U(1) phase rotations for charged particles all result in no measurable changes. But how does this work for SU(2) rotations in electroweak theory, where quarks flavours, and electrons and neutrinos, are interchangeable? My guess is that this involves the broken nature of the symmetry and the Higgs field. Is this correct?

 

[HomogenousCow]

In the unitary gauge the Higgs field acquires a VeV only in one of its components and so only one component of the left-handed lepton doublet get a mass term from the Higgs-Lepton Yukawa interaction. So I suppose in arbitrary gauge, we can always diagnolize the mass term and the massive component just gets called an electron by convention.

I suppose you could SU(2) rotate the electron into the neutrino and vice versa even after SSB, but then the Higgs field and all the Gauge fields would all get transformed and the new "neutrino" you end up with will have all the same propeties as the electron.

 

[Michael Price]

In the unitary gauge the Higgs field acquires a VeV only in one of its components and so only one component of the left-handed lepton doublet get a mass term from the Higgs-Lepton Yukawa interaction. So I suppose in arbitrary gauge, we can always diagnolize the mass term and the massive component just gets called an electron by convention.

I suppose you could SU(2) rotate the electron into the neutrino and vice versa even after SSB, but then the Higgs field and all the Gauge fields would all get transformed and the new "neutrino" you end up with will have all the same properties as the electron.

Thanks, that does indeed work. Whatever a particle gets transformed into has the properties of the original particle.