TGD diary: How ordinary nuclei can be produced in very high energy collisions of protons?

I learned about a possible solution of a long-standing anomaly related to the proton collisions at very high energies studied at LHC using the ALICE detector. There is a popular article in CERN Courier (see this) telling about the findings published in Nature (see this).

The production of deuterons and antideuterons was studied. A long standing mystery has been why also light nuclei are produced so abundantly. At the huge energies involved the temperature is of order pion mass scale ≈ 100 MeV and is so high so that the nuclei have quite too low binding energy to survive and only nucleons should be produced.
The researchers found evidence that the about 90 per cent of the deuterons were produced by nuclear fusion from the particles emerging from the collision with one of the particles emerging from a decay of a massive short-lived particle, so called Δ resonance, which consist of 3 quarks just like nucleons. Δ decays in a time of order 10^-24 seconds to nucleon and pion. Note that proton Compton time is about 33 times longer than this time.
The studies support the view that decay occurs in the periphery, at sufficient distance from the collision point, where the temperature is lower and the fusion can produce stable deuteron nuclei. The article also mentions that the findings provide support for a model of cosmic ray interactions as cascades.
The proposal is that the d (anti-d) formation is made possible by pion catalysis. The reaction would be π+p+n→ π+d and the final state pion would carry away the 4-momentum. The pion would be produced in the decay of Δ.

These findings are very interesting from the point of view of TGD.

TGD predicts the symmetries of the standard model but since QCD color does not correspond in TGD spin-like quantum number but to partial waves in CP₂, both quarks and leptons move in color partial waves and each color multiplet gives rise to a scaled version of the standard model physics. An infinite hierarchy of standard model physics is predicted. Ordinary hadron physics would correspond to Mersenne prime M₁₀₇ = 2¹⁰⁷-1 and the next one, for which there is evidence from anomalies at LHC, to Mersenne prime M₈₉ with mass scale, which is 512 times higher than for ordinary hadrons (nuclei). For instance, the pion of M₈₉ hadron physics would have mass scale 512× 140 MeV ≈ 70 GeV.
The recent solar model is plagued by anomalies. In the TGD based view of the Sun, solar wind and radiation are produced at the surface layer of the Sun in the transformation of M₈₉ hadrons to ordinary hadrons.
M₈₉ hadrons would decay to ordinary M₁₀₇ hadrons by a process that I call p-adic cooling. The p-adic mass scales would be reduced by powers of 2 (or 2^1/2) and for the first option (107-89)/2=9 steps would be involved (see this). One of the first applications of the p-adic physics was the proposal that p-adic cooling could be involved with very high energy cosmic ray events like Centauros (see this and this).
The emerging ordinary nuclei produced in the p-adic cooling could fuse to heavier ones by what I call dark fusion, which provides a TGD based model for the "cold fusion" to heavier nuclei. Less plausibly, they could be produced in the p-adic cooling directly. These heavier nuclei gradually fall downwards in the gravitational field of the Sun so that the usual layered structure of nuclei is near the surface of the Sun rather than in the core of the Sun.
Quite recently, a direct support from this layered structure emerged from very weird findings related to a Supernova explosion. One cannot even exclude the possibility that the same process could have occurred even in the formation of planets as a surface layer of the Sun exploded (see this, this, this, and this).

Consider now the very energetic proton and heavy ion collisions from the TGD perspective.

The TGD view of generalizes the QCD view of hadron collisions (see this). The interaction region contains the TGD analog of quark gluon plasma in which fermions move as massless particles and obey at the spae-time surfaces induced Dirac equation. In final hadron states the Dirac equation in H= M^4xCP_2 is satisfied. These equations are consistent with each other.
The counterpart of quark gluon plasma corresponds in QCD to the fragmentation of initial state hadrons to quarks but not gluons as elementary particles. In TGD, gluons as all elementary bosons would only exist as fermion-antifermion pairs. Hadronization correspond to the fusion of quarks and antiquarks to form massive hadrons. This picture applies to all particle reactions, also those involving leptons. In fact, weak interactions and color interactions can be seen as aspects of color interactions.
In the TGD Unverse, M₈₉ hadrons could be created in very high energy nuclear and proton collisions in a TGD counterpart of the transition interpreted as a formation of quark gluon plasma. M₈₉ hadrons would have effective Planck constant h_eff/h= 512 and mass scale 512 times higher than for ordinary M₁₀₇ hadrons so that the Compton scales for M₈₉ and M₁₀₇ hadrons would be the same. This would correspond to quantum criticality for M₁₀₇→ M₈₉ phase transition as the TGD counterpart for the QCD transition to quark gluon plasma.
The hadronization would lead to the formation of M₈₉ hadrons rather than only M₁₀₇ hadrons, say M₈₉ pions, whose age would be the same as for ordinary hadrons if it scales like (h_eff/h) × m₁₀₇/m₈₉ =1.
M₈₉ pions would decay by a p-adic cooling to ordinary nucleons. Dark fusion (or ordinary fusion, which in the TGD framework could actually reduce to dark fusion) at a sufficiently large distance from the collision point could produce nuclei.
What would be the value of h_eff/h, if the dark fusion occurs. If it is equal to 512, the Compton lengths of ordinary nuclei would be scaled up by factor 512 and would be of the order of electron Compton length. Could this allow us to understand why the fusion occurs in the periphery with a high probability?
At the temperature T∼ m(π₁₀₇) the thermal energy E_th= T-m(π₈₉) of π₈₉) pions is E-m≈(π₈₉)[1/(1-β_th²)^1/2-1] giving the estimate β_th ∼ m(π₁₀₇)/ m(π₈₉)^1/2≈ 2^-9/2. Could the slow thermal velocity imply that also the decay products of π₈₉ move slowly. Could this increase the rate for the cold fusion proportional to the inverse of the relative velocity?
Note that if Δ has h_eff/h=512, its lifetime is scaled up by this factor and is by a factor ≈ 15 longer than the proton Compton time. What if also the produced pion and the nucleons involved have as h_eff/h=512? Could this increase the cross section for the pion catalyzed fusion to deuteron.
In the TGD based model for the "cold fusion" (see for instance this), the value of h_eff would be of the same order of magnitude since the scale up Compton length of proton would be of the same order of magnitude as electron Compton length. The Δ resonance could be generated at the last step of the p-adic cooling. The question boils down to whether also the ordinary hadrons, rather than only M₈₉ hadrons, can have a large value of h_eff/h and whether the effective scaling of the quantum coherence length in the transversal degrees of freedom can make possible the creation of light nuclei by the TGD dark fusion as the counterpart of "cold fusion". This question is very relevant also for the TGD based solar model.