# What elementary particles have properties that vary by spin direction?

This table of elementary particles indicates that electron spin = 1/2. My understanding is that electron spin may proceed in two directions which may be denoted by spin sign and that electron spin direction correlates to differences in magnetic interactions. What other elementary particles with nonzero spin have properties that vary by spin direction?

• For the electron , spin 1/2 is the total spin, whereas spin $\pm 1/2$ is the $z$-component of the spin. – flaudemus Mar 2 at 15:17

Your question indicates a lack of understanding of quantum spin; however, don't let that stop you.

Electron (and mus, taus, nus, and all the quarks) have intrinsic spin quantum number $$s=\frac 1 2$$, which means they carry angular momentum:

$$|S| = \hbar \sqrt{s(s+1)} = \frac{\sqrt 3}2\hbar$$

Nothing is spinning, per se. In the Standard Model, these are point particles with intrinsic angular momentum; that is, the angular momentum is a property of the particle.

The spin can point in any direction, the problem is we can't know that direction fully. For spin 1/2, we can know the project of the spin onto an axis, and the projection can be $$\pm \frac 1 2 \hbar$$.

Particles with intrinsic spin also have magnetic moments:

$$\mu = g\vec S$$

where the constant of proptionbality is the aptly named "$$g$$-factor".

The magnetic ($$\vec B$$) interaction has an energy term:

$$H = \vec \mu \cdot \vec B$$

so that the two eigenstates of known projected spin-angular momentum are non-degenerate energy eigenstates too.

This is a more precise phrasing than "[the] electron spin direction correlates to differences in magnetic interactions".

Nevertheless, that does not render moot: "What other elementary particles with nonzero spin have properties that vary by spin direction?"

Here we need to look at the Weak Interaction and consider the spin projection onto to the momentum (aka, helicity):

$$h = \vec S \cdot \hat p$$

For simplicity, I'll consider neutrinos in the massless limit. In that case the helicity is fixed in all reference frames. Positive (negative) helicity is called right (left) handed.

Here is the kicker: neutrinos only interact via the Weak Interaction, and the Weak Interaction only couples to left handed neutrinos and right handed antineutrinos. So that is rather surprising: if you flip the spin direction you turn off the weak force. Of course, there are many subtleties in the weak interaction that I am glossing over).

• A good answer but also might want to include why a half integer spin particle differs from an integer spin particle, or the special case of a zero spin particle. – Triatticus Mar 2 at 19:54

Protons, neutrons, muons and tauons also have spin and a magnetic moment. In the standard model W bosons, having spin 1, are predicted to have a magnetic moment. This remains to confirmed experimentally. All of these have a magnetic field that varies with spin direction, like the electron does.

• @GiorgioP I don't follow your comment. I don't "critique or request clarification". I provide an answer. – my2cts Mar 2 at 19:38
• @GiorgioP I understand and propose to delete the comments. – my2cts Mar 3 at 9:16