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Homework Help: Neutrino mixing

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data
    In some theory the electron neutrinos and the muon neutrinos mix like this:
    [tex]\mathcal{L}_{m} &= -\frac{1}{2}m\left(\overline{ \nu^{C}_{\mu\text{R}} }\nu_{\text{eL}} + \overline{ \nu^{C}_{\text{eR}} }\nu_{\mu\text{L}}\right) + \text{h.c.}[/tex]

    Show that there exists a conserving lepton number in this theory. What are the values for [tex]\nu_{\text{e}}[/tex] and [tex]\nu_{\mu}[/tex]? Are the mass eigenstates Dirac neutrinos or Majorana neutrinos? Does the theory fit with the observational data?

    2. Relevant equations

    [tex]\mathcal{L}_{m} = \dots = -\frac{1}{2}\left(m\overline{ \nu^{C}_{\mu\text{R}} }\nu_{\text{eL}} + m\overline{ \nu^{C}_{\text{eR}} }\nu_{\mu\text{L}}\right) - \frac{1}{2}\left(m\overline{ \nu_{\text{eL}} }\nu_{\mu\text{R}}^{C}+m\overline{ \nu_{\mu\text{L}} }\nu_{\text{eR}}^{C}\right).[/tex] Right?

    3. The attempt at a solution

    Well, I was just thinking that it must be Dirac type mixing, if there exists a conserving lepton number. So the neutrinos are Dirac neutrinos. Right?

    At least, the oscillation fits with the observational data, though in reality there are three types of neutrinos...

    But I do not know how to calculate the lepton number. Maybe using the continuity equation and then constructing the Euler-Lagrange equation, but I do not know the exact procedure.

    Can you help?

  2. jcsd
  3. Feb 17, 2008 #2
  4. Feb 18, 2008 #3


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    Homework Helper

    I think they are Dirac.
    lepton number conservation? is there some kind of a global symmetry somewhere here?
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