The link between CP violation and neutrino oscillations?

[jeebs]

I'm trying to understand a bit about CP violation and how it relates to neutrino oscillation. I have a book, "Introduction to High Energy Physics" (Donald Perkins) which says that the probability of observing no change in the flavour of a neutrino is equal to that of an antineutrino of the same flavour, ie. [itex]P(\nu_{\alpha} → \nu_{\alpha}) = P(\overline{\nu_{\alpha}} → \overline{\nu_{\alpha}}) [/itex].
However, the probability of seeing a change in flavour of neutrinos is apparently not equal to the probability of seeing the change in antineutrinos, ie. [itex]P(\nu_{\alpha} → \nu_{\beta}) ≠ P(\overline{\nu_{\alpha}} → \overline{\nu_{\beta}}) [/itex]. Also it says that the probability of a neutrino changing flavour is not equal to the probability of the opposite process, ie. [itex]P(\nu_{\alpha} → \nu_{\beta}) ≠ P(\nu_{\beta} → \nu_{\alpha}) [/itex].

The book then says that these relations would be equalities if CP symmetry was obeyed, but the weak interaction can violate it. I have been trawling the net looking for some paper or web page that can explain this but I've not found anything that explains to me why CP violation causes this.

* I am aware that the PMNS matrix has some terms in it that relate to CP violation, and I'd like to understand where they come from (actually, understanding the PMNS matrix is my ultimate goal here) but so far I'm struggling to tie all these things together.
Can anyone help me out here?

 

[Accidently]

The pmns matrix is complex, then when you write down the oscillation transition rate for neutrino and antineutrino, which depends on the real and imaginary part of the pmns matrix elements, you will find the difference.

The key is CP violation vanishes if the pmns matrix is real.