# How can majorana neutrinos still be CP violating?

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1. Mar 23, 2014

### lizzie96

This question is probably very over-simplistic, however: if neutrinos are majorana particles, which are their own antiparticles, how could they still be CP violating?

I don't understand precisely how this would work, but physicists I have spoken to said that neutrinos being majorana could still be consistent with CP violation.

Thank you for any help!

2. Mar 23, 2014

### ChrisVer

you can always have CP violation if you introduce phase angles in the CKM matrix... how is that connected to the nature of neutrinos?

3. Mar 23, 2014

### Bill_K

There is a mixing matrix, the PMNS matrix, which (Wikipedia) "contains information on the mismatch of quantum states of leptons when they propagate freely and when they take part in the weak interactions". Like the corresponding CKM matrix for quarks, it is a 3x3 unitary matrix. CP-violation results from complex phases of the matrix elements.

The number of independent parameters in the PMNS matrix can be reduced by rephasing the lepton fields

j → exp(iφj) ℓj

with arbitrary φj's, which leaves the charged lepton mass terms invariant. However, due to the Majorana nature of the neutrinos, the rephasing

νj → exp(iψj) νj

is not allowed, since it would not keep the Majorana mass terms invariant.

Consequently, if neutrinos are Majorana, the PMNS matrix can contain more CP-violating phases than the CKM matrix. In general there will be three mixing angles and three phases.

(Remarks largely lifted from this paper.)

4. Mar 23, 2014

### ofirg

It seems that you are thinking intuitivley, if there is no distinct neutrino and anti neutrino , how could there be asymmetry bewteen the two?

Well, for examples , a CP eigenstate ( a state that is its own anti particle) has an eigenvalue. It can be 1 ( cp even) or -1 (cp odd). If this isn't conserved, you have CP violation.

5. Mar 29, 2014

### lizzie96

Thank you, that makes much more sense now! I was thinking about it in the way that ofirg said, without really understanding the reasoning/maths. The paper explains it all very well.