# Is there an operator to measure pre-SSB boson states?

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?

Edit

I'm thinking in terms of the following analogy:

1. 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.
2. 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.
• Apr 22, 2023 at 15:11

It's linear algebra. In terms of the mass eigenstates, $$\gamma , Z^0$$, $$\begin{pmatrix} B^0 \\ W^3 \end{pmatrix} = \begin{pmatrix} \cos \theta_\text{W} & -\sin \theta_\text{W} \\ \sin \theta_\text{W} & \cos \theta_\text{W} \end{pmatrix} \begin{pmatrix} \gamma \\ Z^0 \end{pmatrix} ,$$ so the operators destroying the corresponding states, usable in projectors, are $$B^0= \cos\theta_W ~~ \gamma -\sin\theta_W ~~ Z^0, \\ W^3= \cos\theta_W ~~ Z^0 +\sin\theta_W ~~\gamma,$$ but I am not sure what you expect to learn from them.