How is it possible a spin-1 particle to ever have a magnetic moment?
Is there any analytical solution to this?
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
8
The W bosons have magnetic moments according to the fact that they have a spin and are charged. Indeed in the standard model there is an interaction term of the form: \begin{equation} \mathcal{L}_{WW\gamma}=-ieF_{\mu \nu} W^{+,\mu} W^{-,\nu} \end{equation} Where $F$ is the Faraday tensor, and $W^+$ and $W^-$ are the fields associated to the bosons. This term can be rewritten as: \begin{equation} -ie \partial_\mu (W^{+,\mu}W^{-,\nu}-W^{-,\mu}W^{+,\nu})A_\nu \end{equation} Which resembles a lot to the corresponding term in QED for fermions : $-\frac{e}{2m}\partial_\mu(\overline{\Psi} \sigma^{\mu \nu} \Psi)A_\nu$. In fact, and according to the article "How Large is the “Natural” Magnetic Moment?" eq. (22), this interaction term leads to: \begin{equation} \mathcal{L}_{WW\gamma}\leadsto-\frac{e}{2m}\partial_i \epsilon^{ijk}\langle f | S_k | i \rangle A_j \end{equation} Which is indeed of the form of a magnetic momentum.
answered Nov 5, 2021 at 11:35
-
$\begingroup$ Lesson learned: As long you have a combination of non-zero charge and non-zero spin you have a magnetic moment. $\endgroup$ Commented Nov 5, 2021 at 19:01
-
$\begingroup$ Nevertheless, neutrinos don't have charge, only spin but still have a magnetic moment. So I guess this rule of thumb is not general. $\endgroup$ Commented Nov 5, 2021 at 19:09
-
$\begingroup$ @Markoul11 Neutrinos don't have magnetic moment per se, there's only one because of the electroweak model allowing a loop W/lepton that can be attached to a photon and an incoming and an outgoing neutrino. $\endgroup$ Commented Nov 6, 2021 at 10:48
-
$\begingroup$ I disagree. Their magnetic moment is analytically proven (2.1 section, [tinyurl.com/hv64n884] and the upper limit of the magnetic moment experimentally defined at $\mu_{\nu}<2 \times 10^{-11} \mu_{B}$. They have so much small tiny magnetic moment because their so tiny mass which is also priori in order a particle to have a magnetic moment. $\endgroup$ Commented Nov 6, 2021 at 12:58
-
$\begingroup$ @Markoul11 see here the answer of Chris. As I said, neutrinos have a magnetic moment only due to loop diagrams, not due to their nature. Since there's no photon/neutrino/antineutrino vertex in the SM, they can't have a "bare" magnetic moment. $\endgroup$ Commented Nov 6, 2021 at 13:11
$\begingroup$
$\endgroup$
1
The definition of the spin is a intrinsic magnetic moment.
-
1$\begingroup$ Correction: For 1/2 spin, not for spin 1. $\endgroup$ Commented Nov 5, 2021 at 9:23