Neutrinos and TGD

In what follows, the problem of missing right-handed neutrinos and the problem created by apparently contradictory findings of Mini-Boone and Micro-Boone about neutrino mixing are discussed. Also the topological model for neutrino and D-quark CKM mixing is briefly considered.

Why only left-handed neutrinos are observed?

A basic theoretical motivation for the sterile neutrinos is the difficulty posed by the fact that the neutrinos behave like massive particles. This is not consistent with their left-handedness, which is an experimental fact.

As a matter of fact, the sterile neutrinos would be analogous to the covariantly constant right-handed neutrinos in TGD if only J(cP₂) would be present.

Remark: As already stated, in the sequel it is assumed that leptons as bound states of 3 antiquarks can be described using spinors of H with chirality opposite to that for quarks. They have colored modes and the action of super-symplectic algebra is assumed to neutralize the color and also give rise to a massless state getting its small mass by p-adic thermodynamics.

How could one understand the fact that only left-handed neutrinos are observed although neutrinos are massive? One can consider two approaches leading to the same conclusion.

Is it possible to have time evolution respecting M⁴ chirality and neutrinos with fixed chirality possible despite their mass?

1. All spinor modes in CP₂ are of the form Φ_L or D(CP₂)Φ_L and therefore generated from left-handed spinors Φ_L.

   If one assumes D(H)Ψ=0, the spinor modes of H are of the form D(M⁴)Ψ_R× Φ_L + Ψ_R× D(CP₂)Φ_L. The modes of form D(M⁴)Ψ_L× Φ_R + Ψ_L× D(CP₂)Φ_R are therefore of the form D(M⁴)Ψ_L× DΦ_L + Ψ_L× D²(CP₂)Φ_L. The mixing of chiralities is unavoidable.

2. However, if one assumes only the condition D²(H)Ψ=0, one can obtain both left- and right-handed modes without mixing of M⁴ chiralities and M⁴ Kähler structure could make the lowest mass second right-handed neutrino (covariantly constant in CP₂) tachyonic. The time evolution generated by the exponent of L₀ would respect M⁴ chirality.

   This does not prevent superpositions of right- and left-handed fermions if their masses are the same. If only charged leptons can satisfy this condition, one can understand why right-handed neutrinos are not observed.

An alternative approach would rely on quantum measurement theory but leads to the same conclusion.

1. Suppose that neutrinos can appear as superpositions of both right- and left-handed components. To detect a right-handed neutrino, one must have a measurement interaction, which entangles both length and right-handed components of the neutrino with the states of the measuring system. Measurement would project out the right-handed neutrino. If only the J(CP₂) form is present, the right-handed neutrino has only gravitational interactions, and this kind of measurement interaction does not seem to be realizable.
2. Putting it more explicitly, the reduction probability should be determined by a matrix element of a neutral (charged) weak current between a massive neutrino (charged lepton) spinor with a massless right-handed neutrino spinor. This matrix element should have the form Ψbar_R OΨ_L, where O transforms like a Dirac operator. If it is proportional to D(H), the matrix element vanishes by the properties of the massless right-handed neutrino.
3. There is however a loophole: the transformation of left- to right-handed neutrinos analogous to the transformation to sterile neutrino in the neutrino beam experiments could demonstrate the existence of ν_R just like it was thought to demonstrate the existence of the inert neutrino in Mini-Boone experiment. Time evolution should thus respect M⁴ chirality.

If J(M⁴) is present, one might understand why right- and left-handed neutrinos have different masses.

1. Also the right-handed neutrino interacts with Kähler gaug potential A(M⁴) and one can consider an entanglement distinguishing between right- and left-handed components and the measurement would project out the right-handed component. How could this proposal fail?

   Could it be that right- and left-handed neutrinos cannot have modes with the same mass so that these superpositions are not possible as mass eigen states? Why charged modes could have the same mass squared but not the neutral ones?

2. The modes with right-handed CP₂ chirality are constructed from the left-handed ones by applying the CP₂ Dirac operator to them and they have the same CP₂ contribution to mass squared. However, for the right-handed modes the J^kl(M⁴)Σ_kl term splits the masses. Could it be that for right- and left-handed charged leptons the same value of mass is possible.

   The presence of J(M⁴) breaks the Poincare symmetry to that for M² which corresponds to a Lagrangian manifold. This suggests that the physical mass is actually M² mass and the QCD picture is consistent with this. Also the p-adic mass calculations strongly support this view. The E² degrees of freedom would be analogous to Kac-Moody vibrational degrees of freedom of string. This would allow right- and left-handed modes to have different values of "cyclotron" quantum numbers n₁ and n₂ analogous to conformal weights. This could allow identical masses for left- and right-handed modes. For a Lagrangian manifold M², one would have n₁=n₂=0, which could correspond to ground states of super-symplectic representation.

3. Why identical masses would be impossible for right- and left-handed neutrinos? Something distinguishing between right- and left-handed neutrinos should explain this. Could the reason be that Z⁰ couples to left-handed neutrinos only? Could the fact that charged leptons and neutrinos correspond to different representations of color group explain why only charged states can have right and left chiralities with the same mass?

   Perhaps it is of interest to notice that the presence of J^kl(M⁴)Σ_kl for right-handed modes makes possible the existence of a mode for which mass can vanish for a suitable selection of B.

Mini-Boone and Micro-Boone anomalies and TGD

After these preliminaries we are ready to tackle the anomalies associated with the neutrino mixing experiments. The incoming beam consists of muonic neutrinos mixing with electron neutrinos. The neutrinos are detected as they transform to electrons by an exchange of W boson with nuclei of the target and the photon shower generated by the electron serves as the experimental signature.

The basic findings are as follows.

1. Mini-Boone collaboration reported 2018 (see this) an anomalously large number of electrons generated in the charged weak interaction assumed to occur between neutrino and a nucleus in the detector. "Anomalous" meant that the fit of the analog of the CKM matrix of neutrinos could not explain the finding. Various explanations including also inert neutrinos were proposed. Muonic inert neutrino would transform to inert neutrino and then to electron neutrino increasing the electro neutrino excess in the beam.
2. The recently published findings of Micro-Boone experiment (see this) studied several channels denoted by 1eNpM\pi where N=0,1 is the number of protons and M=0,1 is the number of pions. Also the channel 1eX, where "X" denotes all possible final states was studied.

   It turned out that the rate for the production of electrons is below or consistent with the predictions for channels 1e1p, 1eNp0\pi and 1eX. Only one channel was an exception and corresponds to 1e0p0\pi.

   If one takes the finding seriously, it seems that a neutrino might be able to transform to an electron by exchanging the W boson with a nucleus or hadron, which does not belong to the target.

In TGD, the only imaginable candidate for this interaction could be charged current interaction with a dark nucleus or with a nucleon with h_eff>h. This could explain the absence of ordinary hadrons in the final state for 1e events.

1. Dark particles are identified as h_eff>h phases of the ordinary matter because they are relatively dark with respect to phases with a different value of h_eff. Dark protons and ions play a key role in the TGD inspired quantum biology (see For a summary of earlier postings (see this) and even in the chemistry of valence bonds (seethis). Dark nuclei play a key role in the model for "cold fusion" (see this) and this) and also in the description of nuclear reactions with nuclear tunnelling interpreted as a formation of dark intermediate state (see this).
2. I have proposed that dark protons are also involved with the lifetime anomaly of the neutron (see this). The explanation relies on the transformation of some protons produced in the decay of neutrons to dark protons so that the measured life time would appear to be longer than real lifetime. In this case, roughly 1 percent of protons from the decay of n had to transform to dark protons.

3. If dark protons have a high enough value of h_eff and weak bosons interacting with them have also the same value of h_eff, their Compton length is scaled up and dark W bosons behave effectively like massless particles below this length scale. The minimum scale seems to be nuclear or atomic scale. This would dramatically enhance the dark rate for ν p→ e+n so that it would have the same order of magnitude as the rates for electromagnetic interactions. Even a small fraction of dark nucleons or nuclei could explain the effect.

CKM mixing as topological mixing and unitary time evolution as a scaling

The scaling generator L₀ describes basically the unitary time evolution between SSFRs (see this) involving also the deterministic time evolutions of space-time surfaces as analogs of Bohr orbits appearing in the superposition defining the zero energy state. How can one understand the neutrino mixing and more generally quark and lepton mixing in this picture?

1. In the TGD framework, quarks are associated with partonic 2-surfaces as boundaries of wormhole contacts, which connect two Minkowskian space-time sheets and have an Euclidean signature of induced metric and light-like projection to M⁴ (see this) and this).

2. For some space-time surfaces in their superposition defining a zero energy state, the topology of the partonic 2-surfaces can change in these time evolutions. The mixing of boundary topologies would explain the mixing of quarks and leptons. The CKM matrix would describe the difference of the mixings for U and D type quarks and for charged and neutral leptons. The topology of a partonic 2-surface is characterized by the genus g as the number of handles attached to a sphere to obtain the topology.

   The 3 lowest genera with g≤ 2 have the special property that they always allow Z₂ as a conformal symmetry. The proposal is that handles behave like particles and thanks to Z₂ symmetry g=2 the handles form a bound state. For g>2 one expects a quasi-continuous spectrum of mass eigenvalues. These states could correspond to so-called unparticles introduced by Howard Georgi (\url{https://cutt.ly/sRZKSFm}).

3. The time evolution operator defined by L₀ induces mixing of the partonic topologies and in a reasonable idealization one can say that L₀ has matrix elements between different genera. The dependence of the time evolution operator on mass squared differences is natural in this framework. In standard description it follows from the approximation of relativistic energies as p₀\simeq p+ m²/2p. Also the model of hadronic CKM relies on mass squared as a basic notion and involves therefore L₀ rather than Hamiltonian.

See the article Neutrinos and TGD.

For a summary of earlier postings see Latest progress in TGD.

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