Could lepto-hadrons correspond to dark matter?

It has been proposed that the particles produced in CDF anomaly might be decay products of dark matter particles. In TGD framework leptohadron hypothesis explains successfully the basic quantitative and qualitative factors about CDF anomaly and relates it to a bundle of other anomalies (as previous postings should demonstrate). The question is whether there are compelling reasons for identifying leptohadrons as dark matter in TGD sense.

Consider first the experimental side. The proposed identification of cosmic strings (in TGD sense) as the ultimate source of both visible and dark matter does not exclude the possibility that a considerable portion of topologically condensed cosmic strings have decayed to some light particles. In particular, this could be the situation in the galactic nuclei.

The idea that lepto-hadrons might have something to do with the dark matter has popped up now and then during the last decade but for some reason I have not taken it seriously. Situation changed towards the end of the year 2003. There exist now detailed maps of the dark matter in the center of galaxy and it has been found that the density of dark matter correlates strongly with the intensity of monochromatic photons with energy equal to the rest mass of electron.

The only explanation for the radiation is that some yet unidentified particle of mass very nearly equal to 2m_e decays to an electron positron pair. Electron and positron are almost at rest and this implies a high rate for the annihilation to a pair of gamma rays. A natural identification for the particle in question would be as a lepto-pion (or rather, electro-pion). By their low mass lepto-pions, just like ordinary pions, would be produced in high abundance, in lepto-hadronic strong reactions and therefore the intensity of the monochromatic photons resulting in their decays would serve as a measure for the density of the lepto-hadronic matter. Also the presence of lepto-pionic condensates can be considered.

These findings force to take seriously the identification of the dark matter as lepto-hadrons. This is however not the only possibility. The TGD based model for tetra-neutrons is based on the hypothesis that mesons made of scaled down versions of quarks corresponding to Mersenne prime M₁₂₇ (ordinary quarks correspond to k=107) and having masses around one MeV could correspond to the color electric flux tubes binding the neutrons to form a tetra-neutron. The same force would be also relevant for the understanding of alpha particles. Of course, also now the identification as dark matter in tGD sense can be considered. One implication would be that strong interactions would become weak in higher orders and guarantee the convergence of perturbative QCD type theory.

There are also good theoretical arguments for why lepto-hadrons and also exotic quarks should be dark matter in the sense of having a non-standard value of Planck constant.

1. Since particles with different Planck constant correspond to different pages of the book like structure defining the generalization of the imbedding space, the decays of intermediate gauge bosons to colored excitations of leptons would not occur and would thus not contribute to their decay widths.

2. In the case of electro-pions the large value of the coupling parameter Z₁Z₂a_em > 1 combined with the hypothesis that a phase transition increasing Planck constant occurs as perturbative QFT like description fails would predict that electro-pions represent dark matter. Indeed, the power series expansion of the exp(iS) term might well fail to converge in this case since S is proportional to Z₁Z₂α_em. For t-pion production one has Z₁=-Z₂=1 and in this case one can consider also the possibility that t-pions are not dark in the sense of having large Planck constant. Contrary to the original expectations darkness does not affect the lowest order prediction for the production cross section of lepto-pion.

For details and background see the updated chapter Recent Status of Leptohadron Hypothesis of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy", and the article New evidence for colored leptons.

P.S. CDF anomaly was quite a nice birthday gift and the successful explanation of the anomaly eventually led to a Christmas gift from Finnish colleagues. Thank you very much. The gift was a message telling that I cannot anymore use the computer of Helsinki University for my homepage (this has been the only support that I have obtained from Helsinki University for years). Thank you again and Good Christmas!