0
$\begingroup$

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.
$\endgroup$
1

1 Answer 1

0
$\begingroup$

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.

So the photon is 0.22 B and 0.78 W, if you could measure that.

$\endgroup$
3
  • $\begingroup$ Yes, these are exactly the eigenstates I am talking about. I'm wondering if there theoretically exists a physical observable to measure them. $\endgroup$ Apr 21, 2023 at 21:40
  • $\begingroup$ Perhaps in an early universe simulation comparing multiplicities. But in each energy regime, one of the two bases are promising to be dysfunctional/meaningless... $\endgroup$ Apr 21, 2023 at 21:44
  • $\begingroup$ Perhaps, but I feel the observable should still exist. Could you elaborate on 'comparing multiplicities' a bit, please? $\endgroup$ Apr 21, 2023 at 22:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.