LSND and MiniBooNE are consistent in TGD Universe

MiniBooNE group has published its first findings concerning neutrino oscillations in the mass range studied in LSND experiments. For the results see the press release, the guest posting of Dr. Heather Ray in Cosmic Variance, and the more technical article A Search for Electron Neutrino in Δ m²=1 eV² scale by MiniBooNE group.

1. The motivation for MiniBooNE

Neutrino oscillations are not well-understood. Three experiments LSND, atmospheric neutrinos, and solar neutrinos show oscillations but in widely different mass regions (1 eV² , 3× 10^-3 eV², and 8× 10^-5 eV²). This is the problem.

In TGD framework the explanation would be that neutrinos can appear in several p-adically scaled up variants with different mass scales and therefore different scales for the differences Δ m² for neutrino masses so that one should not try to try to explain the results of these experiments using single neutrino mass scale. TGD is however not main stream physics so that colleagues stubbornly try to put all feet in the same shoe (Dear feet, I am sorry for this: I can assure that I have done my best to tell the colleagues but they do not want to listen;-)).

One can of course understand the stubbornness of colleagues. In single-sheeted space-time where colleagues still prefer to live it is very difficult to imagine that neutrino mass scale would depend on neutrino energy (space-time sheet at which topological condensation occurs using TGD language) since neutrinos interact so extremely weakly with matter. The best known attempt to assign single mass to all neutrinos has been based on the use of so called sterile neutrinos which do not have electro-weak couplings. This approach is an ad hoc trick and rather ugly mathematically.

2. The result of MiniBooNE experiment

The purpose of the MiniBooNE experiment was to check whether LSND result Δ m²=1 eV² is genuine. The group used muon neutrino beam and looked whether the transformations of muonic neutrinos to electron neutrinos occur in the mass squared region considered. No such transitions were found but there was evidence for transformations at low neutrino energies.

What looks first as an overdiplomatic formulation of the result was

MiniBooNE researchers showed conclusively that the LSND results could not be due to simple neutrino oscillation, a phenomenon in which one type of neutrino transforms into another type and back again.

rather than direct refutation of LSND results.

3. LSND and MiniBooNE are consistent in TGD Universe

The habitant of the many-sheeted space-time would not regard the previous statement as a mere diplomatic use of language. It is quite possible that neutrinos studied in MiniBooNE have suffered topological condensation at different space-time sheet than those in LSND if they are in different energy range. To see whether this is the case let us look more carefully the experimental arrangements.

1. In LSND experiment 800 MeV proton beam entering in water target and the muon neutrinos resulted in the decay of produced pions. Muonic neutrinos had energies in 60-200 MeV range. This one can learn from the article Evidence for ν_μ-ν_e oscillations from LSND.

2. In MiniBooNE experiment 8 GeV muon beam entered Beryllium target and muon neutrinos resulted in the decay of resulting pions and kaons. The resulting muonic neutrinos had energies the range 300-1500 GeV to be compared with 60-200 MeV! This is it! This one can learn from the article A Search for Electron Neutrino in Δ m²=1 eV² scale by MiniBooNE group.

Let us try to make this more explicit.

1. Neutrino energy ranges are quite different so that the experiments need not be directly comparable. The mixing obeys the analog of Schrödinger equation for free particle with energy replaced with Δm²/E, where E is neutrino energy. Mixing probability as a function of distance L from the source of muon neutrinos is in 2-component model given by

   P= sin²(θ)sin²(1.27Δm²L/E).

   The characteristic length scale for mixing is L= E/Δm². If L is sufficiently small, the mixing is fifty-fifty already before the muon neutrinos enter the system, where the measurement is carried out and no energy dependent mixing is detected in the length scale resolution used. If L is considerably longer than the size of the measuring system, no mixing is observed either. Therefore the result can be understood if Δm² is much larger or much smaller than E/L, where L is the size of the measuring system and E is the typical neutrino energy.

2. MiniBooNE experiment found evidence for the appearance of electron neutrinos at low neutrino energies (below 500 MeV) which means direct support for the LSND findings and for the dependence of neutron mass scale on its energy relative to the rest system defined by the space-time sheet of laboratory.

3. Uncertainty Principle inspires the guess L_p propto 1/E implying m_p propto E. Here E is the energy of the neutrino with respect to the rest system defined by the space-time sheet of the laboratory. Solar neutrinos indeed have the lowest energy (below 20 MeV) and the lowest value of Δm². However, atmospheric neutrinos have energies starting from few hundreds of MeV and Δm² is by a factor of order 10 higher. This suggests that the the growth of Δm²; with E² is slower than linear. It is perhaps not the energy alone which matters but the space-time sheet at which neutrinos topologically condense. MiniBooNE neutrinos above 500 MeV would topologically could condense at space-time sheets for which the p-adic mass scale is higher than in LSND experiments and one would have Δ m²>> 1 eV² implying maximal mixing in length scale much shorter than the size of experimental apparatus.

4. One could also argue that topological condensation occurs in condensed matter and that no topological condensation occurs for high enough neutrino energies so that neutrinos remain massless. One can even consider the possibility that the p-adic length scale L_p is proportional to E/m₀², where m⁰ is proportional to the mass scale associated with non-relativistic neutrinos. The p-adic mass scale would obey m_p propto m₀²/E so that the characteristic mixing length would be by a factor of order 100 longer in MiniBooNE experiment than in LSND.

To sum up, in TGD Universe LSND and MiniBooNE are consistent and provide additional support for the dependence of neutrino mass scale on neutrino energy.

For more details see the chapter p-Adic Mass Calculations: Elementary Particle Masses of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".