## Wednesday, June 30, 2010

### Neutrino Boom

New Scientist has stories on both the new MINOS results and the new MiniBooNE antineutrino results.

The MiniBooNE experiment has confirmed old results from the LSND experiment, namely that muon antineutrinos oscillate into electron antineutrinos at a higher rate than expected. Extra sterile neutrinos are often proposed as an explanation for this anomaly, but many other explanations are possible. It is interesting to note that the antineutrino mass triplet has a different ordering of masses to the neutrino triplet. The heaviest antineutrino corresponds to the central eigenvalue of the triplet. This is the heaviest of all neutrino and antineutrino mass states.

1. I looked at slides and tried to understand better what is involved. Some comments.

a) One thing that I learned that two neutrino scenarios for the mixing (no sterile neutrinos) are consistent with data for either neutrinos or antineutrinos but not both. This conforms with the assumption that the mass squared scales differ by two (p-adic length scale hypothesis) so that the expression for the mixing probability a function of neutrino energy, which is of form

P(E) =sin^2(2theta) sin^2(X) , X= k*Delta m^2*L/E), k a numerical constant,

would be modified by the replacement

X-->2*X (Delta m^2-->2*Delta m^2).

as one goes from neutrinos to antineutrinos (or was it vice versa?;-)). The modification depends on energy and thus affects the shape of P as function of E. The variation of theta keeping Delta m^2 fixed affects only the overall scale of P as function of E. This signature might be used to kill the model.

b) If same universal mixing matrices are assumed for neutrinos and antineutrinos (small CP breaking) then only the upper end of the confidence region for which theta is very near to pi/4 is allowed. Nearly this value of theta comes also from atmospheric and solar neutrino experiments for which Delta m^2 scale are totally different. See
<A HREF="http://indico.cern.ch/getFile.py/access?contribId=208&sessionId=3&resId=0&materialId=slides&confId=</A>.
On the other hand, best fits in LSND seem to favor very small values of theta but these are just best fits. Confidence limits allow theta near pi/4.

c) The assumption of a universal mixing matrix plus simultaneous fit to all experiments (that I saw in slides!) favors theta very near to pi/4, the appearance of neutrinos with p-adic mass scales, which can be different for neutrinos and antineutrinos in a similar experimental arrangement. Also the confidence limits for Delta m^2 near pi/4 are consistent p-adic length scale hypothesis (that is the relative variation of Delta m^2 in the confidence range is larger than octave).