Indications for M89 hadron physics from cosmic rays

Sabine Hossenfelder has written two excellent blog postings about cosmic rays. The first one is about the GKZ cutoff for cosmic ray energies and second one about possible indications for new physics above 100 TeV. This inspired me to read what I have said about cosmic rays and Mersenne primes- this was around 1996 - immediately after performing for the first time p-adic mass calculations. It was unpleasant to find that some pieces of the text contained a stupid mistake related to the notion of cosmic ray energy. I had forgotten to take into account the fact that the cosmic ray energies are in the rest system of Earth- what a shame! Therefore I did some corrections to the text contained as last section to New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy". I glue here the text in the beginning of this section.The recent version should be free of worst kind of blunders.

TGD suggests the existence of a scaled up copy of hadron physics associated with each Mersenne prime M_n=2ⁿ-1, n prime: M₁₀₇ corresponds to ordinary hadron physics. Also leptohadrons are predicted. Also Gaussian Mersennes (1+i)^k-1, could correspond to hadron physics. Four of them (k=151,157,163,167) are in the biologically interesting length scale range between cell membrane thickness and the size of cell nucleus. Also leptonic counterparts of hadron physics assignable to certain Mersennes are predicted and there is evidence for them.

The scaled up variants of hadron physics corresponding to k<107 are of special interest. k=89 defines the interesting Mersenne prime at LHC, and the near future will probably tell whether the 125 GeV signal corresponds to Higgs or a pion of M₈₉ physics - or perhaps something else. Also cosmic ray spectrum could provide support for M₈₉ hadrons and quite recent cosmic ray observations are claimed to provide support for new physics around 100 TeV. M₈₉ proton would correspond to .5 TeV mass considerably below 100 TeV but this mass scale could correspond to a mass scale of a scaled up copy of a heavy quark of M₁₀₇ hadron physics: a naive scaling of top quark mass by factor 512 would give mass about 87 TeV. Also the lighter hadrons of M₈₉ hadron physics should contribute to cosmic ray spectrum and there are indeed indications for this.

The mechanisms giving rise to ultra high energy cosmic rays are poorly understood. The standard explanation would be acceleration of charged particles in huge magnetic fields. TGD suggests a new mechanism based on the decay cascade of cosmic strings. The basic idea is that cosmic string decays cosmic string → M₂ hadrons k → M₃ hadrons ....→ M₆₁ → M₈₉ → M₁₀₇ hadrons could be a new source of cosmic rays. Also variants of this scenario with decay cascade beginning from larger Mersenne prime can be considered. One expects that the decay cascade leads rapidly to extremely energetic ordinary hadrons, which can collide with ordinary hadrons in atmosphere and create hadrons of scaled variants of ordinary hadron physics. These cosmic ray events could serve as a signature for the existence of these scale up variants of hadron physics.

1. Centauro events and the peculiar events associated with E>10⁵ GeV radiation from Cygnus X-3. E refers to energy in Earth's rest frame and for a collision with proton the cm energy would be E_cm=(2EM)^1/2>10 TeV in good approximation whereas M₈₉ variant of proton would have mass of .5 TeV. These events be understood as being due to the collisions of energetic M₈₉ hadrons with ordinary hadrons (nucleons) in the atmosphere.
   
   
2. The decay π_n→ γγ produces a peak in the spectrum of the cosmic gamma rays at energy m(π_n)/2. These produce peaks in cosmic gamma ray spectrum at energies which depend on the energy of π_n in the rest system of Earth. If the pion is at rest in the cm system of incoming proton and atmospheric proton one can estimate the energy of the peak if the total energy of the shower can be estimated reliably.
   
   
3. The slope in the hadronic cosmic ray spectrum changes at E=3 ×10⁶ GeV. This corresponds to the energy E_cm=2.5 TeV in the cm system of cosmic ray hadron and atmospheric proton. This is not very far from M₈₉ proton mass .5 TeV. The creation of M₈₉ hadrons in atmospheric collisions could explain the change of the slope.
   
   
4. The ultra-higher energy cosmic ray radiation having energies of order 10⁹ GeV in Earth's rest system apparently consisting of protons and nuclei not lighter than Fe might be actually dominated by gamma rays: at these energies γ and p induced showers have same muon content. E=10⁹ GeV corresponds to E_cm=(2Em_p(1/2= 4× 10⁴ GeV. M₈₉ nucleon would correspond to mass scale 512 GeV.
   
   
5. So called GKZ cutoff should take place for cosmic gamma ray spectrum due to the collisions with the cosmic microwave background. This should occur around E=6× 10¹⁰ GeV, which corresponds to E_cm=3.5× 10⁵ GeV. Cosmic ray events above this cutoff are however claimed. There should be some mechanism allowing for ultra high energy cosmic rays to propagate over much longer distances as allowed by the limits. Cosmic rays should be able to propagate without collisions. Many-sheeted space-time suggests manners for how gamma rays could avoid collisions with microwave background. For instance, gamma rays could be dark in TGD sense and therefore have large value of Planck constant. One can even imagine exotic variants of hadrons, which differ from ordinary hadrons in that they do not have quarks and therefore no interactions with the microwave background.
   
   
6. The highest energies of cosmic rays are around E=10¹¹ GeV, which corresponds to E_cm=4× 10⁵ GeV. M₆₁ nucleon and pion correspond to the mass scale of 6× 10⁶ GeV and 8.4× 10⁵ GeV. These events might correspond to the creation of M₆₁ hadrons in atmosphere.
   

The identification of the hadronic space-time sheet as a super-symplectic mini black-hole suggests the science fictive possibility that part of ultra-high energy ∈dexcosmic rays cosmic rays could be also protons which have lost their valence quarks. These particles would have essentially same mass as proton and would behave like mini black-holes consisting of dark matter. They could even give a large contribution to the dark matter. Since electro-weak interactions are absent, the scattering from microwave background is absent, and they could propagate over much longer distances than ordinary particles. An interesting question is whether the ultrahigh energy cosmic rays having energies larger than the GZK cut-off of 5× 10¹⁰ GeV in the rest system of Earth are super-symplectic mini black-holes associated with M₁₀₇ hadron physics or some other copy of hadron physics.