# Has the CP violating phase Delta in neutrino oscillation been measured at all?

1. Jun 26, 2012

### Doofy

If I'm not mistaken, measuring the $\delta_{CP}$ from the PMNS matrix may be done by comparing $P(\nu_{\alpha} \rightarrow \nu_{\beta})$ to $P(\overline{\nu_{\alpha}} \rightarrow \overline{\nu_{\beta}})$, where $P(\nu_{\alpha} \rightarrow \nu_{\beta}) - P(\overline{\nu_{\beta}} \rightarrow \overline{\nu_{\alpha}})$ would give a term proportional to $sin\delta_{CP}$.

I've been trawling the net for ages but I've not found anything. Are there any measurements or constraints on what it could be yet?

2. Jun 27, 2012

### Parlyne

The PDG neutrino mixing parameters list has no results for it yet; so, I would guess the answer is that there are not yet any results that particularly constrain it (at least, not without independent determination of other parameters).

Of course, since it's not established whether or not neutrinos are Majorana particles, it may be that we have to worry about three phases, not just one.

3. Jun 27, 2012

### ofirg

There are three phases if neutrinos are majorana particles, but anyway only one is relevant for oscillation probabilities.

Only recently is has been shown (http://arxiv.org/abs/1203.1669) that $\vartheta_{13}\neq$0, a neccesary condition for the cp violation to take place.

$P(\nu_{\alpha} \rightarrow \nu_{\beta}) - P(\overline{\nu_{\beta}} \rightarrow \overline{\nu_{\alpha}})$=0 assumes only CPT symmetry

it is $P(\nu_{\alpha} \rightarrow \nu_{\beta}) - P(\overline{\nu_{\alpha}} \rightarrow \overline{\nu_{\beta}})$ which is $\propto sin\delta_{CP}$