# Why does the neutrino have a magnetic moment?

1. Mar 16, 2012

### Fastman99

I've read that the neutron has a magnetic moment because it is made of composite particles, namely 1 up and 2 down quarks.

But why does the neutrino, which is electrically neutral and a fundamental particle, have a nonzero (albeit very small) magnetic moment? How is that even possible? Does this have anything to do with electro-weak unification?

2. Mar 16, 2012

### tom.stoer

in the SM the neutrino's magnetic moment should be zero theoretically, but experimentally you can't prove that it's exactly zero, you can only determine a very small upper bound, mainly due to experimental and statistical uncertainties

Last edited: Mar 17, 2012
3. Mar 16, 2012

### geoduck

Quantum fluctuations give the neutrino a non-zero magnetic moment.

Loosely speaking, the neutrino can be a mixture of W+ and e-, and the magnetic field couples to the W+ and e-, and afterwards the W+ and e- combine back to neutrino.

It is like the electron self energy, where instead of photon, you have a W+, and instead of the internal line being the same type of line as the external lines, it's a different fermion.

4. Mar 16, 2012

Staff Emeritus
Well, there's non-zero and there's non-zero. At one loop, the neutrino magnetic moment will be of order:

$$\mu = \frac{1}{16 \pi^2}\frac{m_e m_\nu}{M^2_W} \mu_B = 10^{-19} \mu_B$$

That's a very, very, very small number. I'm also not 100% sure that in the SM this doesn't (at least approximately) cancel at one loop. So it could be a lot smaller.

5. Mar 17, 2012

### tom.stoer

in the SM the neutrino mass is exactly zero! what you are talking about is a minimally extenended standard model with some additional mechanism for neutrino mass generation; so a non-zero magnetic moment is an indicator for physics beyond the SM

6. Mar 17, 2012

Staff Emeritus
Well, we know the neutrino mass is not exactly zero. (And the statement "in the SM the neutrino mass is exactly zero" is somewhat debatable - it's a statement that was repeated a lot more often after the discovery of neutrino oscillations than before. The SM permits (but does not require) a nonzero neutrino Dirac mass.)

Nevertheless, this is still really, really small. If I magnetized a pound of neutrinos, it would have a smaller magnetic moment than about picogram of iron.

7. Mar 17, 2012

### tom.stoer

I agree that b/c of neutrino oscillations we can deduce that the neutrino mass is non-zero.

But a standard Dirac mass term is forbidden in the SM.

There is some additional effect required, e.g.
a) a Higgs-coupling which involves both left- and right-handed neutrinos; but we have neither seen right handed neutrinos, nor does the SM Lagrangian contain a neutrino-Higgs-coupling
b) a see-saw mechanism which generates a Majorana mass; but that requires additional heavy neutrino fields again beyond the SM
c) ...

In any case this requires an extenmsion of the standard model.

8. Mar 17, 2012

### Fastman99

Thank you for all your replies, especially you geoduck I liked your explanation of how at smallest enough time and length scales, the neutrino will spontaneously split apart into a W+ and e-, because the uncertainty in energy becomes very large at very small time and space scales.

From what I gather here, it seems that the neutrino magnetic moment is not fully understood in terms of the SM, but rather a slightly "extended" version of it. I don't understand the SM at all yet, I'm still an undergrad physics major whose just starting to learn about the Dirac equation and QFT, but I think it's a very cool theory so far. It's very pleasing to me haha.

Also, while we are discussing weirdness of neutrinos, can anyone explain why all neutrinos have left-handed spin and all anti-neutrinos have right handed spin?

9. Mar 17, 2012

Because neutrinos only 'feel' the weak interaction, and the weak interaction only touches left-handed particles. To be precise, left-handed as used here refers to chirality, not helicity.

10. Mar 17, 2012

### ParticleGrl

But you can (and we do!) add a higher dimension operator/a majorana mass for the neutrinos.

The standard model is a collection of symmetries and matter fields- if an operator isn't forbidden by the symmetry, there is no reason not to include it. Sure, its non-renormalizable, but ultimately don't we expect the standard model to be effective?

11. Mar 18, 2012

### tom.stoer

Of course you can do that - or many other things - it's not forbidden - but you shouldn't call it standard model ;-)

12. Mar 18, 2012

### ParticleGrl

As I said, the standard model is the collection of symmetries and matter fields. If you don't add a new symmetry group or a new matter field, why isn't it the standard model?

13. Mar 18, 2012

### tom.stoer

for me the standard model is a very specific Lagrangian; afaik the mass term for neutrinos is set to zero; I don't know a 'standard neutrino mass term', only some proposals

14. Mar 18, 2012