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Neutrino oscillation - CP violation obscured by matter effect?

  1. Sep 20, 2012 #1
    In long baseline neutrino oscillation experiments, it is possible to investigate the extent of any CP violation by looking at the difference between the rate of neutrino oscillating vs. anti-neutrinos oscillating, ie. we take [itex]\Delta P = P(\nu_\alpha \rightarrow \nu_\beta) - P(\overline{\nu}_\alpha - \overline{\nu}_\beta)[/itex].

    The neutrinos propagate through the Earth's crust, which introduces a flavour-dependent matter potential which affects the measured parameters (ie. the mixing angles and mass splittings in matter are slightly different to those in vacuum). This much I understand, as I have been able to find an understandable derivation of equations which relate the in-vacuum parameters to the in-matter parameters.

    However, what I do not understand is how the matter effect is able to mimic CP violation and affect the measured [itex]\Delta P[/itex]. Having googled around, the best hint I have found is this difference in Hamiltonian between neutrino and antineutrino:

    [itex]H_\nu = \frac{1}{2p}(UM^{2}U^{\dagger} + diag(a_{cc}, 0, a_{nc}))[/itex]
    [itex]H_{\overline{\nu}} = \frac{1}{2p}(U^{*}M^{2}U^{T} - diag(a_{cc}, 0, a_{nc}))[/itex]

    U = PMNS matrix
    [itex]a_{cc} = 2\sqrt{2}G_fN_ep[/itex]
    [itex]a_{nc} = \sqrt{2}G_fN_np[/itex]
    M^{2} = diag(m_{1}^{2}, m_{2}^{2}, m_{3}^{2}, m_{4}^{2} )
    Gf = Fermi constant
    Ne = electron number density in matter
    Nn = neutron number density in matter
    p = momentum

    The paper I got this from (http://arxiv.org/pdf/hep-ph/9712537v1.pdf) just states this rather than giving an explanation as far as I can tell. So, my question is, can anyone please show me / point me towards a derivation of this?

    Also, this is done for 4 neutrino mass states - does a simpler treatment for just 3 neutrinos exist? Or is four the minimum required for some reason?
  2. jcsd
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