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Why does the neutrino have a magnetic moment?

  1. Mar 16, 2012 #1
    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?
     
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  3. Mar 16, 2012 #2

    tom.stoer

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    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
  4. Mar 16, 2012 #3
    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.
     
  5. Mar 16, 2012 #4

    Vanadium 50

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

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

    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.
     
  6. Mar 17, 2012 #5

    tom.stoer

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    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
     
  7. Mar 17, 2012 #6

    Vanadium 50

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    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.
     
  8. Mar 17, 2012 #7

    tom.stoer

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    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.
     
  9. Mar 17, 2012 #8
    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?
     
  10. Mar 17, 2012 #9
    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.
     
  11. Mar 17, 2012 #10
    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?
     
  12. Mar 18, 2012 #11

    tom.stoer

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    Of course you can do that - or many other things - it's not forbidden - but you shouldn't call it standard model ;-)
     
  13. Mar 18, 2012 #12
    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?
     
  14. Mar 18, 2012 #13

    tom.stoer

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    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
     
  15. Mar 18, 2012 #14
    Isn't the simplest modification to add right-handed, sterile neutrinos and then incorporate these into additional Dirac mass terms in the Lagrangian, just as is done for the quarks and charged leptons?
     
  16. Mar 18, 2012 #15
    You can calculate the neutrino magnetic moment and show that it's proportional to the neutrino mass, so if the neutrino mass is zero, then the neutrino has no magnetic moment. I can't really explain in words why the neutrino must have mass to have a non-zero magnetic moment. My best attempt is to say that EM interactions flip the chirality of a particle, so you need right-chiral neutrinos which enter in through mass terms. If the neutrino has mass, a left-handed neutrino has some amplitude to be right-chiral.

    That's all that is meant by extension of the standard model, to give the neutrino a mass term (the neutrino really does have mass, since it has been discovered that they oscillate, and they only oscillate if they have mass) . There are several ways you can give the neutrino mass, with see-saw mechanisms, or just using the standard way leptons are given mass, but also there are questions on whether the neutrino is its own antiparticle (that is, is it a Majorana particle). I think it can be shown that a Majorana neutrino cannot have magnetic moment, even if it has mass. This all assumes the vacuum theory though. If you include temperature/chemical potential effects I don't know how that changes.
     
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