## Sunday, June 20, 2010

### MINOS Neutrinos

As reported by Philip and many others, the MINOS experiment has been releasing results at Neutrino 2010. They claim a $2$ sigma observation of a difference between (electron, muon) $\Delta m^2$ for neutrinos and antineutrinos. That is,
neutrinos have $\Delta m^2 = 2.35 \times 10^{-3} \pm 0.11$ $eV^2$
antineutrinos have $\Delta m^2 = 3.35 \times 10^{-3} \pm 0.45$ $eV^2$
with
neutrino parameter $\textrm{sin}^2 (2 \theta) > 0.91$
antineutrino parameter $\textrm{sin}^2 (\overline{2 \theta}) = 0.86 \pm 0.12$
where $\theta$ is the $2 \times 2$ matrix phase for two neutrino mixing. But the plot shows that one should not be too enthusiastic yet about such a radical result. The data points are for antineutrinos and the dashed line is the neutrino result. Given that such a result could demolish almost everything that has been written about quantum gravity, we live in interesting times.

1. Carl, you first ...

2. p-Adic length scale hypothesis and CP breaking provide a simple explanaton once again. There is already old evidence that neutrinos can appear in several p-adic length scales.

Suppose that the p-adic mass squared scales of neutrinos and and antineutrinos differ by 2 (p =about 2^k by p-adic length scale hypothesis). This means k(nubar)= k(nu)+1.

This allows same mixing matrices but the scale of delta m^2 is two time larger for neutrinos than for antineutrinos. The experimenteres talk about 40 percent not far from 50 per cent.

See my blog posting.

3. Matti, the team agrees with you that this is a real result ... as you will soon see ...

4. I hope you are right Kea, different masses for particles and their anti-particles would upset all conventional theories and bring on a new revolution in particle physics. Even Matti would get a good shout.

5. Dammit, where is Carl! This cannot wait ...

Recall that Carl uses an angle of $2/9 + \pi / 12$ for the neutrino mass matrix. Now Carl has observed (in a private email exchange) that an angle of $\delta =$ $2/9 - \pi / 12$ gives an alternative set of three masses, and these happen to be

$0.0006$, $0.0582$ and $0.0012$ eV

using the eigenvalue formula
$\sqrt{m_i} = 1 + \sqrt{2} \textrm{cos}(\theta)$
for $\theta = \delta + \omega$, with $\omega$ a cubed root. The first two of these masses give a $\Delta m^2$ of $0.0034$ $eV^2$, in perfect agreement with the MINOS results. (The neutrino masses give the other value, $0.0024$, because this value was originally used to fit the masses).

6. Now reported at Physics World.

7. I love it when data meets theoretical predictions.

Khawar Nehal
http://atrc.net.pk

8. Yes, Khawar, this result was essentially predicted in Carl's Koide Hadrons paper. This paper does not mention antineutrinos, but it does make a mention of possible phases equal to $n \pi /12$ for mass triplets, and of course it discusses the neutrinos.