A common statement is that post-SSB electroweak gauge bosons are linear combinations of pre-SSB gauge bosons.
It is also usually stated that pre-SSB bosons can also be thought of as linear combinations of post-SSB bosons - it's just a choice of basis, after all.
However, with a choice of basis, there usually comes an operator corresponding to an observable which allows us to measure the eigenstates corresponding to the chosen basis . The eigenvectors of such operator will correspond to the basis states.
If there was a quantum operator / observable whose eigenvectors correpond to the 'pure' pre-SSB boson states (B, W1, W2, W3), we would be able to 'detect' pre-SSB bosons in post-SSB environment - i.e. measure whether the photon 'chooses' to be a 'B' or a 'W' at any given interaction.
So: does such an operator / observable exist? Can it be constructed? Or does it even make sense?
I'm thinking in terms of the following analogy:
- A photon is usually emitted in a superposition of spin left / spin right states. Upon 'arrival' however we can always measure it to be either one or the other.
- A photon is emitted in superposition of B / W states. Upon 'arrival' we should somehow be able to measure if it is one or the other.