## Thursday, July 1, 2010

### Neutrino Boom II

Looking at the first graphs from the new MiniBooNE slides, we see that the LSND antineutrino result (for a $\textrm{sin}^{2}(2 \theta)$ of $1$ and using the usual analysis) corresponds to a $\Delta m^{2}$ of about $0.06$ $eV^{2}$. This is very large, corresponding to a mass of $0.25$ $eV$. That is about two times the total mass of all six neutrino and antineutrino Koide mass states. The MiniBooNE Neutrino 2010 report focuses on excess event rates for electron antineutrinos, which are in agreement with the LSND results. The MiniBooNE experiment used approximately the same $L/E$ factor (around $1$) but a higher $E$ range. The transition probability for $\overline{\nu}_{\mu}$ $\rightarrow$ $\overline{\nu}_{e}$ supposedly depends on both $\textrm{sin}^{2}(2 \theta)$ and $\textrm{sin}^{2}(\Delta m^{2} L /E)$.

1. Note that although the required mass (in eV) is too large to be obtained as a combination of $\nu$/$\overline{\nu}$ states, it is obtainable from sums of square roots. For example, letting $m_{*}$ be the required mass,

$\sqrt{m_{*}} = \sqrt{m_{3}} + \sqrt{\overline{m}_{2}} + \sqrt{\overline{m}_{3}}$

2. $\sqrt{m_{*}} = 2 \sqrt{\overline{m}_{2}}$

also works all right. At least this would keep the problem in the antineutrino sector. Matti, this would amount to doubling Koide eigenvalues.

3. Zero energy ontology and different p-adic spacetime sheets? But how can time influence on matter? No, on antimatter? And why 4 %? The back of the Big Book is 4% thick = interference?

Gravitation was mentioned, some bending of the spacetime sheets? And dark matter.

Living matter is the clue? Left-and righthanded molecules depend on this (negentropy)?

This was interesting, but I am no expert.

4. Dear Kea,

what is doubled in p-adic framework is $m^2$ scale and thus $\Delta m^2$ scale. From the figure and other similar figtures one indeed sees how $\theta$ very near to $\pi/4$ is consistent with all measurements of neutrino oscillations if one allows mass scale to vary. May be this is consistent with similar scaling for m in Koide formula.

In TGD model for CKM matrix in terms of topological mixing matrices U and D for U and type quarks (sphere, torus, and sphere with two handles characterizing the topology of partonic 2-surface associated with quark) the sum of mass squared for non-mixed quarks is integer if one uses p-adic mass squared scale as unit (and different for different quarks). This integer is not changed in mixing. The additional assumption is that the mixing maximizes entropy defined in terms of mixing probabilities subject to the constraint that the mass square values are integers and their sum is fixed: this says that mixing is as large as possible. This picture applies also to leptonic mixing.