Is the magnetic moment of a particle an intrinsic property or is there a formula to find it? What is its source?

Is there a formula or a general explanation that can account for the $\mu$ of known particles: electrons, protons, neutrons and neutrinos?

I searched the web and found different values for the neutrino, ranging from 10^-10 to 10^-19, how is such great discrepancy possible? Can we use the formula given for neutrinos (see here) for any other particle?

Can you briefly explain the genesis/rationale of that formula: $$3eG_Fm_\nu /8\pi^2 \sqrt{2}$$ and how it applies to other particles?They say in that article that its value is proportional to the mass of the neutrino, why so? In what way ismass related to it?

## Best Answer

The

spinof a particle is an intrinsic property. From experiments we can infer that a particle with the spin $\mathbf{s}$ has a magnetic spin moment $\mathbf{\mu_s} = g_s\cdot\mathbf{s}$. For electrons the so-calledLandÃ© factor$g_S$ is roughly 2.If the particle also has an angular momentum $\mathbf{l}$, however it also carries a magnetic momentum $\mathbf{\mu_l}$ due to its angular momentum, much like in classical electrodynamics. So in total you have $\mathbf{\mu}=\mathbf{\mu_s}+\mathbf{\mu_l}$.

Hence, the source of the magnetic momentum of a particle are both its spin and its angular momentum. But the calculation of the LandÃ© factor differs in classical quantum mechanics and in quantum electrodynamics, which is by far the more accurate theory.