Could sea partons be dark?

The model of hadrons involves, besides valence quarks, a somewhat mysterious parton sea. Could the sea consist of partons, which are dark in the TGD sense? This proposal was actually inspired by a model of Kondo effect having strong resemblances with a model of color confinement (see this).

The basic argument in favor of the proposal that at least some quarks are dark, is based on the idea that the phase transition increasing the value of h_eff>h allows to have a converging perturbation expansion: one one half α_s= g²/4πℏ→ g²/4πℏ_eff which is so small that perturbation theory converges. Nature would be theoretician friendly and perform a phase transition guaranteeing preventing the failure of the perturbative approach.

A stronger assumption generalizes Nottale's proposal for gravitational Planck constant and assumes ℏ_eff= g_s²/β₀ , β₀=v₀/c<1 giving α_s → β₀/4π. This would allow a perturbative approach to low energy hadron physics for which ordinary QCD fails.

1. Valence partons cannot be dark but sea partons can

The following argument suggests that valence quarks cannot be dark but sea partons can.

1. It is good to begin with a general objection against the idea that particles could be permanently dark.
   1. The energies of quantum states increase as a function of h_eff/h₀ defining the dimension of extension of rationals. These tend to return back to ordinary states. This can be prevented by a feed of metabolic energy.
   2. The way out of the situation is that the dark particles form bound states and the binding energy compensates for the feed of energy. This would take place in the Galois confinement. This would occur in the formation of Cooper pairs in the transition to superconductivity and in the formation of molecules as a generation of chemical bonds with h_eff>h. This would also take place in the formation of hadrons from partons.
2. It seems that valence quarks of free hadrons cannot be dark. If the valence quarks were dark, the measured spin asymmetries for the cross section would have only shown that the contribution of sea quarks to proton spin is nearly zero, which in fact could make sense. Unfortunately, the assumption that the measured quark distribution functions are determined by sea quarks seems to be inconsistent with the quark model. If only sea quarks contribute always to the lepton-hadron scattering, the deduced distribution functions would satisfy q_i= q^*_i, which is certainly not true.

   Hence it seems that valence quarks must be ordinary but the TGD counterparts of sea partons could be dark and could have large h_eff increasing the size of the corresponding flux tubes. The color MBs of hadrons would be key players in the strong interactions between hadrons.

3. The EMC effect in which the deep inelastic scattering from an atomic nucleus suggests that the quark distribution functions for nucleons inside nuclei differ from those for free nucleons (see this). This looks paradoxical since deep inelastic scattering probes high momentum transfers and short distances. For h_eff>h the situation however changes since quantum scales are scaled up by h_eff/h. If sea partons are dark, the corresponding color magnetic bodies of nucleons are large and could interact with other nucleons of the nucleus so that the dark valence quark distributions could change.
4. Dark quarks and antiquarks at the magnetic body might also provide a solution to the proton spin crisis.

By the above arguments, the valence quarks of free hadrons have h_eff=h but sea quarks can be dark. Could dark valence quarks be created in hadronic scattering?

1. The values of h_eff of free particles tend to decrease spontaneously since energies increase with h_eff. The formation of bound states by Galois confinement prevents this. If not, the analog of metabolic feed increasing the value of h_eff is necessary. It would be also needed to create dark particles, which then form bound states.
2. Could the collision energy liberated in a high energy collision serve as "metabolic" energy generating h_eff>h phases. This could take place in a transition interpreted in QCD as color deconfinement (see this and this).

   The first option is that the phase transition makes valence quarks dark. This could however mean that they decouple from electroweak interactions with leptons. Second option is that the phase transition increases the value of h_eff>h for the dark partons at color MB but leaves valence quarks ordinary.

3. What does one mean with parton sea?

In the TGD framework, one must reconsider the definition of valence quarks and of parton sea.

1. Valence quarks would correspond to the directly observable degrees of freedom whereas parton sea would correspond to degrees of freedom, which are not directly observablee in physics experiments. Usually large transversal momentum transfers are assumed to correspond to short length scales but the EMC effect is in conflict with this assumption. If the unobserved degrees of freedom correspond to h_eff>h phase(s) forced by the requirement of perturbativity, the situation changes and these degrees of freedom can correspond to long length scales.

   The mathematical treatment of the situation requires integration over the unobserved degrees of freedom and would mean a use of a density matrix related to the pairs of systems defined by this division of the degrees of freedom. This would justify the statistical approach used in the perturbative QCD.

   Dark degrees of freedom associated with the color MB, possibly identifiable as parton sea at color MB, are not directly observable. The valence quarks would be described in terms of parton density distributions and quark fragmentation functions. In hadron-hadron scattering at the low energy limit, valence quarks and sea, possibly at color MB, would form a single quantum coherent unit, the hadron. In lepton-hadron scattering, the valence quarks would form the interacting unit. In hadron-hadron scattering also the dark MBs would interact.

2. Color MB could contain besides quark pairs also g>0 gluons contributing to the parton sea. The naive guess is that g=1 gluons are massive and correspond to the p-adic length scale k=113 assignable to nuclei. Muon mass, Λ_QCD, and λ-N mass difference correspond to this mass scale.

   The g>0 many-gluon state must be color singlet, have vanishing spin, and have vanishing U(2)_g or perhaps even SU(3)_g quantum numbers, at least if SU(3)_g is an almost exact symmetry in the gluonic sector. This kind of state can be built from two SU(3)_g gluons as the singlet part of the representation 8_c⊗ 8_g with itself. The state is consistent with Bose-Einstein statistics.

   g>0 gluons could be seen in hadron-hadron interactions. Perhaps as an anomalous production of strange and charmed particles and violation of fermion universality.