Before continuing it is good to summarize the basic differences between TGD and standard model at the level of elementary particle physics. TGD differs from standard model by three basic new elements: p-adic length scale hypothesis predicting a fractal hierarchy of hadron physics and electroweak physics; topological explanation of family replication phenomenon; and TGD view about dark matter.

- p-Adic length scale hypothesis states that Mersenne primes M
_{n}and Gaussian Mersennes M_{G,n}give rise to scaled variants of ordinary hadron and electroweak physics with mass scale proportional to M_{n}^{1/2}= 2^{n/2}.

M_{127}would correspond to electron and possibly also to what I have called lepto-hadron physics. Muon and nuclear physics would correspond to M_{G,113}and τ and hadron physics would correspond to M_{107}. Electroweak gauge bosons would correspond to M_{89}. n_{G}= 73, 47, 29, 19, 11,7,5,3,2 would correspond to Gaussian Mersennes and n= 61,31,19,17,13,7,5,3,2 to ordinary Mersennes. There are four Gaussian Mersennes corresponding to n_{G}∈{151,157,163,167} in biologically relevant length scale range 10 nm-2.5 μm (from cell membrane thickness to nucleus size): this can be said to be a number theoretical miracle.

- The basic assumption is that the family replication phenomenon reduces to the topology of partonic 2-surfaces serving as geometric correlates of particles. Orientable topology is characterized by genus - the number of handles attached to sphere to obtain the topology. 3 lowest genera are assumed to give rise to elementary particles. This would be due to the Z
_{2}global conformal symmetry possible only for g=0,1,2. By this symmetry single handle behaves like particle and two handles like a bound state of 2 particles. Sphere corresponds to a ground state without particles. For the higher genera handles and handle pairs would behave like a many-particle states with mass continuum.

- The model of family replication is based on U(3) as dynamical "generation color" acts as a combinatorial dynamical symmetry assignable to the 3 generations so that fermions correspond to SU(3) multiplet and gauge bosons to U(3) octet with lowest generation associated with U(1). Cartan algebra of U(2) would correspond to two light generations with masses above intermediate boson mass scale.

3 "generation neutral" (g-neutral) weak bosons (Cartan algebra) are assigned with n=89 (ordinary weak bosons), n

_{G}= 79 and n_{G}=73 correspond to mass scales m(79) = 2.6 TeV and m(73) =20.8 TeV. I have earlier assigned third generation with n=61. The reason is that the predicted mass scale is same as for a bump detected at LHC and allowing interpretation as g-neutral weak boson with m(61)=1.3 PeV.

3+3 g-charged weak bosons could correspond to n=61 with m(61)= 1.3 PeV (or n

_{G}=73 boson with m(73) =20.8 TeV) and to n_{G}= 47,29, 19 and n= 31,19. The masses are m(47)= .16 EeV, m(31)=256× m(47)=40 EeV, m(29)=80 EeV, m(19)= 256 EeV, m(17)= .5× 10^{3}EeV, and m(13)= 2× 10^{3}EeV. This corresponds to the upper limit for the energies of cosmic rays detected at ANITA.

In TGD framework the most natural identification of Planck length would be as CP

_{2}length R which is about 10^{3.5}times the Planck length as it is usually identified. Newton's constant would have spectrum and its ordinary value would correspond to G= R^{2}/&bar;_{eff}_{eff}which &bar;_{eff}_{eff}∼ 10^{7}. UHE cosmic rays would allow to get information about physics near Planck length scale in TGD sense!

- TGD predicts also a hierarchy of Planck constants h
_{eff}=n× h_{0}, h=6h_{0}, labelling phases of ordinary matter identified as dark matter. The phases with different values of n are dark matter relative to each other but phase transitions changing the value of n are possible. The hypothesis would realize quantum criticality with long length scale quantum fluctuations and it follows from what I call adelic physics.

n corresponds to the dimension of extension of rationals defining one level in the hierarchy of adelic physics defined by extensions of rationals inducing extensions of p-adic number fields serving as correlates for cognition in TGD inspired theory of consciousness. p-Adic physics would provide extremely simple but information rich cognitive representations of the real number based physics and the understanding of p-adic physics would be easy manner to understand the real physics. This idea was inspired by the amazing success of p-adic mass calculations, which initiated the progress leading to adelic physics.

- According to the article. there are 2 anomalous events detected by ANITA collaboration and 3 such events detected by ICECUBE collaboration. For these events there is cosmic ray shower coming Earth's interior. Standard model does not allow this kind of events since the incoming particle - also neutrino - would dissipate its energy and never reach the detector.

This serves as a motivation for the SUSY inspired model of the article proposing that stau, super-partner of tau lepton, is created and could have so weak interactions with the ordinary matter that it is able to propagate through the Earth. There must be however sufficiently strong interaction to make the detection possible. The mass of stau is restricted to the range .5-1.0 TeV by the constraints posed by LHC data on SUSY.

- The incoming cosmic rays associated with anomalous events have energies around ε
_{cr}=.5× 10^{18}eV. A reasonable assumption is that the rest system of the source is at rest with respect to Earth in an energy resolution, which corresponds to a small energy EeV scale. No astrophysical mechanism producing higher energy cosmic rays about 10^{11}GeV based on standard physic is known, and here the p-adic hierarchy of hadron physics and electroweak physics suggests mechanisms.

_{G,47}=(1+i)

^{47}-1 would correspond to a weak boson mass scale m(47)= 2

^{(89-47)/2}× 80 GeV = .16 EeV. This mass scale is about roughly a factor 1/3 below the energy scale of the incoming cosmic ray. This would require that the temperature of the source is at least 6× m(47) at source if neutrino is produced in the decay of M

_{G,47}W boson. This option does not look attractive to me.

Could cosmic rays be (possibly dark) protons of M_{G,47} hadron physics.

- The scaling of the mass of the ordinary proton about m
_{p}(107)≈ 1 GeV gives m_{p}(47)= 2^{(107-47)/2}GeV ≈ 1 EeV! This is encouraging! Darkness in TGD sense could make for them possible to propagate through matter. In the interactions with matter neutrinos and leptons would be generated.

The article tells that the energy ε

_{cr}of the cosmic ray showers is ε_{cr}∼ .6 EeV, roughly 60 per cent the rest mass of cosmic ray proton. I do not how precise the determination of the energy of the shower is. The production of dark particles during the generation of shower could explain the discrepancy.

- What could one say about the interactions of dark M(47) proton with ordinary matter? Does p(47) transform to ordinary proton in stepwise manner as Mersenne prime is gradually reduced or in single step. What is the rate for the transformation to ordinary proton. The free path should be a considerable fraction of Earth radius by the argument of the article.

The transformation to ordinary proton would generate a shower containing also tau leptons and tau neutrinos coming pion decays producing muons and electrons and their neutrinos. Neutrino oscillations would produce tau neutrinos: standard model predicts flavor ratio about 1:1:1.

- What could happen in the strong interactions of dark proton with nuclei? Suppose that dark proton is relativistic with E
_{p}=x M_{p}= x EeV, x>1, say x∼ 2. The total cm energy E_{cm}in the rest system of ordinary proton is for a relativistic)!) EeV dark proton + ordinary proton about E_{cm}=(3/2)x^{1/2}(m_{p}M_{p}^{1/2}= x^{1/2}× 5 TeV, considerably above the rest energy m_{p}(89)=512 m_{p}=.48 TeV of M_{89}dark proton. The kinetic energy is transformed to rest energy of particles emanating from the collision of dark and ordinary proton.

If the collision takes place with a quark of ordinary proton with mass m

_{q}= 5 MeV, E_{cm}is reduced by a factor of 5^{1/2}10^{-3/2}giving E=x^{1/2}1.3 TeV, which is still above for the threshold for transforming the cosmic ray dark proton to M_{89}dark proton.

This suggests that the interaction produce first dark relativistic M

_{89}protons, which in further interactions transform to ordinary protons producing the shower and neutrinos. I have proposed already more than two decades ago that strange cosmic ray events such as Centauros generate hot spot involving M_{89}hadrons. At LHC quite a number of bumps with masses obtained by scaling from the masses of mesons of ordinary hadron physics are observed. I have proposed that they are associated with quantum critically assignable to a phase transition analogous to the generation of quark gluon plasma, and are dark in TGD sense having h_{eff}/h=512 so that their Compton wavelengths are same as for ordinary hadrons.

- The free path of (possibly) dark M
_{G,47}proton in ordinary matter should be a considerable fraction of the Earth's radius since the process of tau regeneration based on standard physics cannot explain the findings. The interaction with ordinary matter possibly involving the transformation of the dark proton to ordinary one (or vice versa!) must be induced by the presence of ordinary matter rather than being spontaneous.

Also the flux of cosmic ray protons at EeV energies must be high enough. It is known that UHE cosmic rays very probably are not gamma rays. Besides neutrinos dark M

_{G,47}protons would be a natural candidate for them.

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

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