The duality between descriptions of strong interactions as dark weak interactions and color interactions

The assumption of pseudo-neutrons as analogs of p-π^- pairs could provide insights about the values of nuclear binding energy and also the 10 keV energy scale associated with low energy excitations of nuclei required by the proposal for the explanation of the tritium beta decay anomaly.

It is good to start from the problems of existing models.

1. The old-fashioned model of nuclei assumes pion exchanges as the origin of nuclear force. The basic problem of this view is that since gluons have vanishing electroweak quantum numbers and it is difficult to understand why charged pions as mediators of strong interactions could appear.
2. Second problem is that the mass of the pion is about 140 MeV and much larger than the 1 MeV scale of the nuclear excitations. In the harmonic oscillator model this scale is just assumed. Intriguingly, the neutron proton mass difference is also near 1 MeV. Also the electropions, explaining in the TGD framework (see this) the anomalous production of electron-positron pairs in heavy ion collisions discovered already at seventies, have mass very nearly equal to 2m_e= 1 MeV. There is also evidence for muopions and taupions but all this is forgotten since there is no room for these particles in the standard model since their existence would have been observed in weak boson decays. This problem is circumvented if electropions are dark in the TGD sense.

In TGD color is realized as color partial waves in CP₂ degrees of freedom rather than as spin-like quantum numbers and both quarks electrons also allow colored excitations. In particular, leptons allow octet excitations. The anomalous electron-positron pairs would result in the decays of electropions identified as the bound states of colored electron and positron. Also the triplets of color octet leptons allow color singlets analogous to baryons and in the model of nucleus these triplets would occur at vertices from which free edge begins. If this were the case, then colored lepton states could be an essential part of nuclear physics. Note however that one can also consider a model of electropions based on scaled variants of quarks with mass scale defined by the p-adic length scale L(127) of electron.

An attractive proposal is that the pion-like color bonds in nuclei correspond to electropions or their quark-antiquark counterparts and that the mass of the neutral electropion is 1 MeV. In the following I will talk about electronpion also when it consists of quark and antiquark.

1. One can estimate the mass of the charged electropion from the mass of neutral electropion by scaling the mass difference of pion which is Δ m(π)=m(π⁰)- m(π^+/-)= (139.6 -135.0)=4.6 MeV. By scaling this with m(π_L)/m(π)≈; 1/140 one obtains Δ m(π_L)≈; 33 keV, which could correspond to the 10 keV energy scale.
2. Nucleon- flux tube pairings of type n-π_L⁰ and p-π_L^- (pseudo-neutron) and p-π⁰_L and n-π⁺_L (pseudo-proton) pairings are possible. The energy differences between these nucleon-flux tube pairs would naturally correspond to the n-p mass difference of about 1 MeV.

   The first guess is that in nuclear ground states with a minimum energy pseudo neutron p-π_L^- and genuine proton p-π_L⁰ are favored. The excited states with excitation energies in 10 keV scale contain genuine protons p-π_L⁰ and pseudo protons n-π_L^-. Also the excited states n-π_L⁺ can be excited to states n-π_L⁰ with excitation energy in the 10 keV range.

3. Dark W exchanges between nucleons and leptopions would transform the genuine and pseudo variants of nucleons to each other. These transformations involving energy change of order 1 MeV could be behind the excitations of nuclei usually assigned with strong interactions. If W bosons are dark and thus effectively massless in the scale of nuclei these transitions would be fast. This would also concretize the PCAC and CVC inspired idea that somehow strong interactions are dual to weak interactions. What is remarkable is that the value of L_W is not now fixed by the condition L_W= a_W stating that the weak interaction range is at least the Bohr radius of the weak atom! The value of ℏ_eff/ℏ\sim m_W/m_e ≈; 10⁵ would make the leptopions dark with respect to weak interactions.

Tritium beta decay anomaly again

There are several questions to be answered. Does the already proposed mechanism possibly explaining the tritium anomaly have alternatives? What really happens in the tritium beta decay? Can one understand the 10 keV scale in the anomalous tritium beta decay? How can the X-ray flux from the Sun amplify the beta decay anomaly? One can also ask whether the proposed idea about duality between dark weak interactions and strong interactions could allow a concrete quantitative formulation.

1. One should transform π_L^+/- bond to π_L⁰ bond or vice versa by emission of W boson but this changes the charge of H³ unless the W decays to e-ν pair. The exchange of W boson between nucleon and leptopion that is quark/lepton of the corresponding bond involves energy change of about 1 MeV in the process and is considerably larger than 10 keV scale for X rays. A possible mechanism inducing transition between these states would be a variant of beta decay involving a spontaneous beta decay of pseudo-neutron decaying as n-π_L⁰ → p- π_L⁰+ +W^- followed by W^-→ e^- +ν^*.

   In the spontaneous decays of p-π_L⁰ → p-π_L^- + +W⁺ and n-π_L⁺ → n- -π_L⁰ +W⁺ genuine and pseudo proton the scale of energy change is is 10 keV and these transitions could be involved with the tritium beta anomaly.

2. I have already considered a possible mechanism for tritium beta decay involving neutrino atoms and transition n+ν→ p+e. Could one consider alternative mechanisms or at least analogous transitions.

   The spontaneous decay n-π_L⁰ → n- π_L⁺ +W^- is kinematically possible whereas p-π_L^-→ p- π_L⁺ +W^- is not allowed by energy conservation.

   One can imagine also a variant of beta decay involving a spontaneous beta decay of pseudo-neutron decaying as p-π_L⁰ → p-π_L^- +W⁺ and n-π_L⁺ → n-π_L⁰ +W⁺ followed by W⁺→ e⁺ +ν. Now one would however have W⁺ rather than W^- in the final state.

   The energy of W^- and of e^-+ν^* is constrained by the mass difference Δ m(π_L)≈; 33 keV and by energy conservation. The mass difference m(H³)-m(He³) =18 keV is but pseudo neutrons . This beta decay could explain the tritium anomaly instead of n+ν → p+ e^- for the generalized atom.

Why tritium beta anomaly correlates with the X-ray flux from the Sun?

The proposed model of the beta anomaly in terms of a decay p-π_L⁰→ p-π_L^- +W⁺ does not yet explain the correlation of the beta decay anomaly with X ray emission from the Sun. Could X ray absorption with X ray energy equal to the excitation energy induce reverse dark weak transitions p-π_L^- → p-π_L⁰ ? A possible mechanism would be following:

1. The absorption of X-ray by π_L^- (π_L⁺) occurs first and increases the energy of p-π_L^- but does not induce its decay if the energy of X-ray is not much larger than Δ m(π_L). X ray can be also absorbed by n-π_L⁺.
2. After this the exchange of dark W^- between π_L^- and induces the transition p-π_L^-→ n-π_L⁰. In the same way, n-π_L⁺ can be transformed to p-π_L⁰.

See the article About Platonization of Nuclear String Model and of Model of Atoms or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.