Have we already observed the variants of Mk hadron physics for k>107?

TGD also predicts a k>107 hadron physics. Suppose that only Mersenne primes and their Gaussian counterparts correspond to these hadron physics (primes near prime powers two cannot be excluded). For k>107, only the Mersenne prime k=127 associated also with the electron defines a p-adic length scale, which is not super-astronomical. There are several Gaussian primes corresponding to kin {113,151,157,163,167}. k=113 corresponds to the nuclear length scale and kin {151,157,163,167} to 4 miracle length scales in the range 10 nm-2.5 mu, which in the TGD framework would be important for cell nucleus and DNA.

Could all these length scales correspond to scaled copies of hadron physics with k>107?

1. For TGD analog of quark gluon phase quarks are massless in the sense that they satisfy the massless induced Dirac equations at the space-time surface X⁴. In this phase the quarks do not “know” which p-adic length scale they correspond to. In hadronization they become fermions satisfying the Dirac equation either in the embedding space H=M⁴× CP₂ or inside the causal diamond CD= cd× CP₂ serving the role of quantization volume. It is not clear which of these options is correct.
2. In hadronization fundamental quarks transform to color partial waves in CP₂ and correspond to a color multiplet in CP₂. This process occurs also for leptons. Quarks form color triplets and these in turn combine to color singlets. This proves involves formation of tachyonic states reducing the mass scale from the CP₂ scale of fundamental quarks to the mass scale of the physical quarks in hadrons and to the hadronic mass scale.

Hadronization can take place to any color multiplet (quark-like or leptonic) so that a hierarchy of scaled variants of hadron physics is predicted. M₈₉ hadron physics is the hadron physics for this there are indications at LHC and RHIC.

What does this predict? M₈₉ hadrons can decay to ordinary hadrons, say pions. In the same way, dark M₁₀₇ hadrons can decay to pions of M₈₉ hadron physics. The mass of M₈₉ pion is m(π)/8∼ 17.5 MeV. This is precisely the mass of the particle observed and interpreted in terms of new interaction! Also other M₈₉ mesons should be found.

One particular testable signature of the model would be the production of M₁₂₇ pions decaying to gamma pairs with total energy of .14 MeV. Also other M₁₂₇ mesons are produced.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.