According to the article “Viewpoint: Cosmic-Ray Showers Reveal Muon Mystery in APS Physics (see this) Pierre Auger Observatory reports that there is 30 per cent muon surplus in cosmic rays at ultrahigh energy around 1019 eV (see this). These events are at the knee of cosmic ray energy distribution: at higher energies the flux of cosmic rays should be reduced due to the loss of energy with cosmic microwave background. There are actually indications that this does not take place but this is not the point now. The article at this> tells about how these showers are detected and also provides a simple model for the showers.
This energy is estimated in the rest system of Earth and corresponds to the energy of 130 TeV in cm mass system for a collision with nucleon. This is roughly 10 times the cm energy of 14 TeV at LHC. The shower produced by the cosmic ray is a cascade in which high energy cosmic ray gradually loses its energy via hadron production. The muons are relatively low energy muons resulting in hadronic decays, mostly pion decays, since most of the energy ends up to charged pions producing muons and electrons and neutral pions decaying rapidly to gamma pairs. The electron-positron pairs produced in the electromagnetic showers from neutral pions mask the electrons produced in neutral pion decay to electrons so that the possible surplus can be detected only for muons.
Since cosmic rays are mostly protons and nuclei the primary collisions should involve a primary collision of cosmic ray particle with a nucleon of atmosphere. The anomalously large muon yield suggests an anomalous yield of proton-antiproton pairs produced in the first few collisions. Protons and antiprotons would then collide with nuclei of atmosphere and lose their energy and give rise to anomalously large number of pions and eventually muons.
Unless the models for the production (constrained by LHC data) underestimate muon yield, new physics is required to explain the source of proton-antiproton pairs is needed.
In TGD framework one can consider two scaled up variants of hadron physics as candidates for the new physics.
The first candidate corresponds to M89 hadron physics for which hadron masses would be obtained by a scaling with factor 512 from the masses of ordinary hadrons characterized by Mersenne prime M107= 2107-1. There are several bumps bumps identifiable as pseudo-scalar mesons with predicted masses also some bumps identifiable as some scaled up vector mesons (see this). Also the unexpected properties of what was expected to be quark gluon plasma suggest M89 hadron physics. In particular, the evidence for string like states suggests M89 mesons. If the situation is quantum critical, M89 have scaled up Compton length. The natural guess is that it corresponds to the size of ordinary hadrons.
If quantum criticality corresponds to peripheral collisions, the rate for pseudo-scalar production would be large unlike for central collisions. This could make the observation of these collisions difficult: especially so if the peripheral collisions are rejected because they are not expected to involve strong interactions and be therefore uninteresting. This might explain the disappearance of 750 GeV bump.
The proton of M89(=289-1) hadron physics would have mass of 512 GeV so that the production of M89 hadrons could take place at energies, which for ordinary hadrons would correspond to 260 GeV meaning that perturbative M89 QCD could be used. The quarks of this hadron physics would hadronize either directly to ordinary M107 or to M89 hadrons. In both cases a phase transition like process would lead from M89 hadrons or to M107 hadrons and produce a surplus of protons and antiprotons whose collisions with the nuclei of atmosphere would produce a surplus of pions.
One can also consider M79 hadron physics, where MG,79 corresponds to Gaussian Mersenne (1+i)79-1. The mass scale would be 32 times higher than that for M89 hadron physics and correspond to 8 GeV for ordinary hadron collisions. Also now perturbative QCD would apply.
For a summary of earlier postings see Latest progress in TGD.