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].(adsbygoogle = window.adsbygoogle || []).push({});

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]

where:

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} )

G_{f}= Fermi constant

N_{e}= electron number density in matter

N_{n}= 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?

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# Neutrino oscillation - CP violation obscured by matter effect?

Can you offer guidance or do you also need help?

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