The determination of neutrino mass from the beta decay of tritium leads to a tachyonic mass squared [2,3,4,5]. I have considered several alternative explanations for this long standing anomaly. The first class of models relies on the presence of dark neutrino or antineutrino belt around the orbit of Earth. The second class of models relies on the prediction of nuclear string model that the neutral color bonds connecting nucleons to nuclear string can be also charged. This predicts large number of fake nuclei having only apparently the proton and neutron numbers deduced from the mass number.
- 3He nucleus resulting in the decay could be fake (tritium nucleus with one positively charged color bond making it to look like 3He). The idea that slightly smaller mass of the fake 3He might explain the anomaly: it however turned out that the model cannot explain the variation of the anomaly from experiment to experiment.
- Later (yesterday evenening!) I realized that also the initial 3H nucleus could be fake (3He nucleus with one negatively charged color bond). It turned out that fake tritium option has the potential to explain all aspects of the anomaly and also other anomalies related to radioactive and alpha decays of nuclei.
- Just one day ago I still believed on the alternative based on the assumption of dark neutrino or antineutrino belt surrounding Earth's orbit. This model has the potential to explain satisfactorily several aspects of the anomaly but fails in its simplest form to explain the dependence of the anomaly on experiment. Since the fake tritium scenario is based only on the basic assumptions of the nuclear string model and brings in only new values of kinematical parameters it is definitely favored.
In the following I shall describe only the models based on the decay of tritium to fake Helium and the decay of fake tritium to Helium.
1. Fake 3He option
Consider first the fake 3He option. Tritium (pnn) would decay with some rate to a fake 3He, call it 3Hef, which is actually tritium nucleus containing one positively charged color bond and possessing mass slightly different than that of 3He (ppn).
- In this kind of situation the expression for the function K(E,k) differs from K(stand) since the upper bound E0 for the maximal electron energy is modified:
E0 ® E1=M(3H)-M(3Hef)-mm = M(3H)-M(3He)+DM-mm , DM = M(3He)-M(3Hef) .
Depending on whether 3Hef is heavier/lighter than 3He E0 decreases/decreases. From Vb Î [5-100] eV and from the TGD based prediction order m([`(n)]) ~ .27 eV one can conclude that DM should be in the range 5-100 eV.
- In the lowest approximation K(E) can be written as
K(E) = K0(E,E1)q(E1-E) @ (E1-E)q(E1-E).
Here q(x) denotes step function and K0(E,E1) corresponds to the massless antineutrino.
- If the fraction p of the final state nuclei correspond to a fake 3He the function K(E) deduced from data is a linear combination of functions K(E,3He) and K(E,3Hef) and given by
K(E) = (1-p)K(E,3He)+ pK(E,3Hef) @ (1-p)(E0-E)q(E0-E)+ p(E1-E)q(E1-E)
in the approximation mn=0.
For m(3Hef) < m(3He) one has E1 > E0 giving
K(E) = (E0-E)q(E0-E)+ p(E1-E0)q(E1-E)q(E-E0).
K(E,E0) is shifted upwards by a constant term (1-p)DM in the region E0 > E. At E=E0 the derivative of K(E) is infinite which corresponds to the divergence of the derivative of square root function in the simpler parametrization using tachyonic mass. The prediction of the model is the presence of a tail corresponding to the region E0 < E < E1.
- The model does not as such explain the bump near the end point of the spectrum. The decay 3H® 3Hef can be interpreted in terms of an exotic weak decay d® u+W- of the exotic d quark at the end of color bond connecting nucleons inside 3H. The rate for these interactions cannot differ too much from that for ordinary weak interactions and W boson must transform to its ordinary variant before the decay W® e+`n. Either the weak decay at quark level or the phase transition could take place with a considerable rate only for low enough virtual W boson energies, say for energies for which the Compton length of massless W boson correspond to the size scale of color flux tubes predicted to be much longer than nuclear size. Is so the anomaly would be absent for higher energies and a bump would result.
- The value of K(E) at E=E0 is Vb º p(E1-E0). The variation of the fraction p could explain the observed dependence of Vb on experiment as well as its time variation. It is however difficult to understand how p could vary.
2. Fake 3H option
Assume that a fraction p of the tritium nuclei are fake and correspond to 3He nuclei with one negatively charged color bond.
- By repeating the previous calculation exactly the same expression for K(E) in the approximation mn=0 but with the replacement
DM = M(3He)-M(3Hef)® M(3Hf)-M(3H) .
- In this case it is possible to understand the variations in the shape of K(E) if the fraction of 3Hf varies in time and from experiment to experiment. A possible mechanism inducing this variation is a transition inducing the transformation 3Hf® 3H by an exotic weak decay d+p® u+n, where u and d correspond to the quarks at the ends of color flux tubes. This kind of transition could be induced by the absorption of X-rays, say artificial X-rays or X-rays from Sun. The inverse of this process in Sun could generate X rays which induce this process in resonant manner at the surface of Earth.
- The well-known poorly understood X-ray bursts from Sun during solar flares in the wavelength range 1-8 A correspond to energies in the range 1.6-12.4 keV, 3 octaves in good approximation. This radiation could be partly due to transitions between ordinary and exotic states of nuclei rather than brehmstrahlung resulting in the acceleration of charged particles to relativistic energies. The energy range suggests the presence of three p-adic length scales: nuclear string model indeed predicts several p-adic length scales for color bonds corresponding to different mass scales for quarks at the ends of the bonds. This energy range is considerably above the energy range 5-100 eV and suggests the range [4×10-4, 6×10-2] for the values of p. The existence of these excitations would mean a new branch of low energy nuclear physics, which might be dubbed X-ray nuclear physics.
- The approximately 1/2 year period of the temporal variation would naturally correspond to the 1/R2 dependence of the intensity of X-ray radiation from Sun. There is evidence that the period is few hours longer than 1/2 years which supports the view that the origin of periodicity is not purely geometric but relates to the dynamics of X-ray radiation from Sun. Note that for 2 hours one would have DT/T @ 2-11, which defines a fundamental constant in TGD Universe and is also near to the electron proton mass ratio.
- All nuclei could appear as similar anomalous variants. Since both weak and strong decay rates are sensitive to the binding energy, it is possible to test this prediction by finding whether nuclear decay rates show anomalous time variation.
- The model could explain also other anomalies of radioactive reaction rates including the findings of Shnoll  and the unexplained fluctuations in the decay rates of 32Si and 226Ra reported quite recently and correlating with 1/R2, R distance between Earth and Sun. 226Ra decays by alpha emission but the sensitive dependence of alpha decay rate on binding energy means that the temporal variation of the fraction of fake 226Ra isotopes could explain the variation of the decay rates. The intensity of the X-ray radiation from Sun is proportional to 1/R2 so that the correlation of the fluctuation with distance would emerge naturally.
- Also a dip in the decay rates of 54Mn coincident with a peak in proton and X-ray fluxes during solar flare has been observed: the proposal is that neutrino flux from Sun is also enhanced during the solar flare and induces the effect. A peak in X-ray flux is a more natural explanation in TGD framework.
- The model predicts interaction between atomic physics and nuclear physics, which might be of relevance in biology. For instance, the transitions between exotic and ordinary variants of nuclei could yield X-rays inducing atomic transitions or ionization. The wave length range 1-8 Angstroms for anomalous X-rays corresponds to the range Z in the rage [11,30] for ionization energies. The biologically important ions Na+, Mg++, P-, Cl-, K+, Ca++ have Z= (11,15,17,19,20). I have proposed that Na+, Cl-, K+ (fermions) are actually bosonic exotic ions forming Bose-Einstein condensates at magnetic flux tubes (see this). The exchange of W bosons between neutral Ne and A(rgon) atoms (bosons) could yield exotic bosonic variants of Na+ (perhaps even Mg++, which is boson also as ordinary ion) and Cl- ions. Similar exchange between A atoms could yield exotic bosonic variants of Cl- and K+ (and even Ca++, which is also boson as ordinary variant). This transformation might relate to the paradoxical finding that noble gases can act as narcotics. This hypothesis is testable by measuring the nuclear weights of these ions. X-rays from Sun are not present during night time and this could relate to the night-day cycle of living organisms. Note that the nagnetic bodies are of size scale of Earth and even larger so that the exotic ions inside them could be subject to intense X-ray radiation. X-rays could also be dark X-rays with large Planck constant and thus with much lower frequency than ordinary X-rays so that control could be possible.
 S. E. Shnoll et al (1998), Realization of discrete states during fluctuations in macroscopic processes, Uspekhi Fisicheskikh Nauk, Vol. 41, No. 10, pp. 1025-1035.
V. M. Lobashev et al(1996), in Neutrino 96 (Ed. K. Enqvist, K. Huitu, J. Maalampi). World Scientific, Singapore.
 Ch. Weinheimer et al (1993), Phys. Lett. 300B, 210.
 J. I. Collar (1996), Endpoint Structure in Beta Decay from Coherent Weak-Interaction of the Neutrino, hep-ph/9611420. G. J. Stephenson Jr. (1993), Perspectives in Neutrinos, Atomic Physics and Gravitation, ed. J. T. Thanh Van, T. Darmour, E. Hinds and J. Wilkerson (Editions Frontieres, Gif-sur-Yvette), p.31.