- The key observation was that the X boson (see this, this, this, and previous posting) has just the same mass of 17 MeV as the pion of hadron physics scaled down to nuclear p-adic length scale from hadronic scale (k=107) to nuclear scale (k=113). Recall that p-adic prime is near to 2k, k positive integer with primes preferred and Mersenne primes especially preferred.
- The problem was that I first believed the claim that X cannot be a pseudoscalar but is spin 1 particle. The claim was based on limits on its decay rate to gamma pair. I checked what the rate would be by scaling the decay rate of pion and found that the situation is indeed this. I had however made a stupid calculational blunder - probably under hypnotic suggestion of the X boson article - and only later realized that the decay rate to gamma pairs is below the upper limit. X is k=113 pion!
- The decay rate of k=113 pion to e+e- pairs as predicted by the scaling of the standard model for the decays of ordinary pion assuming that the decay is mediated by creation of virtual gamma pair gave however too slow rate by a factor 1/100. As a matter of fact, also for ordinary pion the predicted rate is somewhat too low already order of magnitude comes out correctly and even leptoquarks have been discussed as an alternative decay mode since decay via axial coupling the intermediate Z boson has quite too low rate.
- It took time to realize that here is the order for as p-adically scaled down variant of weak interactions. Pion couples to the axial current, which couples to Z boson, which decays to e+e- pair. The decay of pion could correspond to the decay to virtual timelike Z boson decaying to e+ee- pair! It turned out that if Z correspond to nuclear p-adic scale k=113 the rate is within the general experimental limits. If it corresponds to k=114 - still nuclear scale but does not correspond correspond to Gaussian Mersenne - a resonance takes place and the rate is in the middle of the interval defining stronger bounds proposed in the article proposing that X boson is prophobic spin 1 boson mediating fifth force. Also the dark variant of M89 weak physics with Z effectively massless within the scaled up Compton length gives a rate within the weak bounds.
- This also leads to a new understanding about semileptonic decays of hadrons since also ordinary mesons could decay to leptons via the same mechanism. p-Adically scaled down or dark weak interaction physics would be realized both in nuclear and hadronic scales! When I started to work with CP2 for about 35 years ago, the frustrating observation was that classical weak boson fields and color gauge fields appear in all scales. This was in complete conflict with standard wisdom. Now it is becoming clear that these physics are there in preferred p-adic scales! Mandelbrot meets particle physics! Weak symmetries predict the decay rate ratios of charged and weak mesons and this together with p-adic scaling of weak boson and pion masses gives a powerful test for the scenario.
- What is also nice that the picture conforms with the number theoretic vision about scattering amplitudes, which suggests that all scattering diagrams understood in topological sense for generalized Feynman diagrams having lines thickened to 4-manifolds should be transformable to tree diagrams and with quantum criticality plus number theoretic vision demanding that the functional integral over WCW gives vanishing loop correction and coupling constant evolution reduces to discrete p-adic coupling constant evolution with piecewise constant coupling constants. Indeed, I ended up with new mechanism of pion decay from the requirement that the diagram in question is tree diagram. The transformation of box diagrams involved with the CP breaking to non-loopy tree diagrams provides a killer test for this vision.
- There is also consistency with M8-M4× CP2 duality in the sense that color group acting in CP2 is replaced with SO(4) group acting in M4× E4. M8 corresponds in twistor approach naturally to the tangent space of M4× CP2 and 4-D momenta are replaced to M8, which naturally lead to M4 momenta and SO(4) quantum numbers as one forms partial wave in E4 degrees of freedom. Some particle physicist might still remember that SO(4) is the symmetry group of low energy hadron physics. One can understand conserved vector current hypothesis (CVC) and partially conserved axial current hypothesis (PCAC) in this framework and scaled variants of weak physics make the picture very concrete.
Event better, also scaled variants of weak physics are showing up. Ordinary k=89 weak physics scaled down to nuclear p-adic scale k=113 or k=114 makes itself visible via X boson decays to e+e- pairs and k=107 in the decays of the ordinary pion. There is also evidence for the Higgs associated with second generation weak bosons assignable to MG,79 as bump at 4 GeV.
Clearly, the fractal TGD Universe is making itself visible in a spectacular manner. Colleagues have no other way than to give up and admit that committees cannot decide about world views. Theoretician could not hope a better prize for the work of almost four decades!
For a summary of earlier postings see Latest progress in TGD.