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.

2. Could dark valence partons be created in hadronic collisions?

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.

4. Could dark partons solve the proton spin crisis

The proton spin crisis (this) was discovered in the EMC experiment, which demonstrated that the quark spin in the spin direction of polarized protons was almost the same as in the opposite direction.

4.1 Basic facts about proton spin crisis

In the EMC experiment the contributions of u,d, and s quarks to the proton spin were deduced from the deep inelastic scattering of muons from polarized proton target (\url{https://rb.gy/ktm2tw}). What was measured, were spin asymmetries for cross sections and the conclusions about parton distribution functions (this) were deduced from the experimental data from the muon scattering cross sections using Bjorken sum rule testing QCD and Ellis-Yaffe sum rule assuming vanishing strange quark contribution and testing the spin structure of the proton. Bjorken sum rule was found to be satisfied reasonably well. Ellis-Yaffe sum rules related to the spin structure of the proton were violated.

It was found that the contributions of u quarks were positive and those of s quarks (assuming that they are present) and d quarks negative and the sum almost vanished when the presence of s was assumed. The Gell-Mann quark model predicts that u-quarks contribute spin 2/3 and d-duarks -1/6 units (ℏ) to the proton spin. For the fit allowing besides u, d contributions, also s contributions, the contributions were found to be 0.373, -0.254 and -0.113. The sum was 0.006 and nearly zero. For protons the contribution is roughly one half of Gell-Mann prediction. For d quark the magnitude of the contribution is considerably larger than the Gell-Mann prediction -1/6≈-.16.

The Wikipedia article creates the impression that the proton spin crisis has been solved: the orbital angular momentum would significantly contribute to the spin of the proton. Also sea partons, in particular gluon helicity polarization would contribute to the proton spin. This might well be the case.

4.2 Dark sea partons and proton spin crisis

I have considered possible TGD inspired solutions of the proton spin crisis already earlier. One can however also consider a new version involving dark sea quarks.

1. The possibility that sea partons are dark in the TGD sense, forces us to ask what was really measured in the EMC experiment leading to the discovery of the proton spin crisis. If sea partons are dark, only the quark distribution functions corresponding to quarks with ordinary value of h_eff appearing in the coupling to muon would contribute? This should be the case in all experiments in which incoming particles are leptons.

   Assuming that also valence quarks can be part of time strange, the results of the EMC experiment assume that most of the proton spin could reside at the polarized dark sea. Note however that also orbital angular momentum can explain the finding and in the TGD framework color magnetic flux tubes could carry "stringy" angular momentum.

2. For this option one could identify the measured cross section in terms of scattering from quarks with h_eff=h. It has been proposed that valence quarks are large scale structures (low energy limit) and sea quarks are small scale structures (high energies) inside valence quarks.

   In the TGD framework, this suggests that valence quarks correspond to a larger p-adic prime than sea quarks. This does not imply that valence quarks have large h_eff. Large h_eff for the sea partons would increase their size so that, contrary to the expectations from the Uncertainty Principle, they could contribute to hadron-hadron scattering with large momentum transfer in long length scales.

The idea that the average spin of valence quarks in the baryons vanishes is attractive. What comes to mind is the following idea.

1. >The valence quarks have an ordinary value of h_eff and the perturbation series does not converge. One should have a concrete realization for the transfer of color interactions at the level of valence quark to the level of the sea quarks with large h_eff. If only dark gluons exist, the color interactions take place at the level of the color MB, and one the perturbation theoretic coupling would be α_s= β₀/4π.

   The physical mechanism in question should map valence quarks to dark valence quarks at the MB. Also color confinement could take place at the level of the color MB and induce it at the valence quark level. The ordinary electroweak interactions should take place between valence quarks but also a dark variant of ew interactions between dark quarks is possible and indeed assumed in TGD inspired quantum biology. Could the mechanism be as follows?

2. Consider a free hadron. The color MB contains dark sea quark and antiquark with opposite charges and spins such that dark antiquark combines with a valence quark to form an entangled color singlet meson-like spin singlet.

   The second dark quark with opposite color and electroweak quantum numbers would carry the spin of the valence quark. Quark quantum numbers would be transferred by entanglement to the color MB! Color confinement would take place at the level of MB and induce color confinement at the level of valence quarks.

3. Ordinary electroweak interactions would take place at the level of valence quarks. Electroweak interactions cannot measure color charges so that the color entanglement between valence quark and dark sea quark would be preserved.

   What happens when a quark changes to another quark with different charge in the ordinary electroweak mediated by W boson exchange? Entanglement would be now between different charge states, say between valence u and dark d^*. In the ground states of hadron this cannot be the case. This suggests that the exchange of dark W boson transforms dark d^*u state to u^*u state. Dark W bosons could correspond to a lower mass scale than ordinary gauge bosons.

   What about spontaneous exchange of dark W boson transforming dark u^* u state to d^*u state? This would transform u^* pair to uk ud^*, which is not possible in equilibrium. The emission of ordinary W boson could transform d to d^* and one would have beta decay induced by dark beta decay.

   The more general question is how the physics of ordinary matter can be seen as a shadow dynamics controlled by the dark matter at the magnetic body. The proposed pairing could provide the needed mechanism.

See the article About the TGD based views of family replication phenomenon and color confinement or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.