I have been developing a model of hadrons based on the idea that hadrons involve both ordinary quarks and their dark counterparts (see this).
The basic idea is that Nature is theoretician friendly: when the perturbation series fails to converge, a phase transition increasing the value of h_{eff}=nh_{0} takes place and reduces the value of gauge coupling strength proportional to 1/ℏ_{eff}. The color of the ordinary quarks q_{o} ("o" for "ordinary") must be neutralized by color entangling them with corresponding dark antiquarks q_{d}^{c} ("d" for "dark") at color magnetic body (MB) to form a color singlet (color for them is screened) . After that one adds to color MB dark variants q_{d} of quarks. This mechanism would actually apply quite generally to all elementary particles.
It came as a surprise that this principle actually realizes holography, which is a basic principle of TGD and implied by general coordinate invariance. The good news is that there is actually experimental evidence for this holography.
Theoretician friendly character of Nature implies holography
The two key ideas behind the proposal deserve restating.
 Nature is theoretician friendly and guarantees the convergence of perturbation theory by h→ h_{eff} phase transition. The simple and perturbatively convergent dynamics at the level of MBs for the dark images X_{d} of the particles induces the dynamic of particles X_{o} by stable color quantum entanglement. The MB of the dark particle would be the boss and the dynamics of the ordinary particle would be shadow dynamics in accordance with the general vision about induction as the basic dynamical principle of TGD.
One open question is whether the ordinary matter follows the dynamics of dark particles instantaneously or whether the time scales of the dynamics of dark matter and ordinary matter can be different in which case only the asymptotic states would realize the proposed correspondence between X_{d} and X_{o}.
 It took some time to realize that the map of X_{o} to X_{d} based on colored entanglement is nothing but a concrete actualization of the quantal version of the TGD based holography. In the classical realization of this holography, the 3D boundary of the spacetime surface determines the spacetime surface (tangent space data are not needed). In quantum realization, the states X_{o} are analogous to states at the 3D boundary of spacetime surface and states X_{d} to those in its interior. Instead of strings in the interior AdS_{5} as in AdS/CFT correspondence, one has monopole flux tubes, indeed string like objects) in the interior of spacetime carrying state X_{d} and X_{o}^{c} determine the dark state.
 In the classical holography, 3D surfaces carry holographic data fixing the 4D complement of 4surface (see this and this). Also 2D string world sheets are involved and 1D surfaces as orbits of boundaries of string world sheets at the lightlike orbits of partonic 2surfaces fix the interiors of string world sheets. An additional condition could be that the string world sheets are surfaces in H^{3} ⊂ M^{4}⊂ M^{8}. The pair of dark sea quarks and leptons would be delocalized at string worlds sheets associated with the color magnetic flux tubes. This is in accordance with the hadronic string model, which was one of the original motivations for TGD.
Experimental support for the holography and for proton as an analog of blackhole
There is experimental evidence for the analogy of protons with a blackhole (see this) found from deep inelastic electronproton scattering (DIS). The report (see this) of the research group led by theorists Krzysztof Kutak and Martin Hentschinski, published in European Physical Journal C, provides evidence for the claim that portions of proton's interior exhibit maximal quantum entanglement between constituents of photon.
The following statement of the report gives a rough idea of what is claimed.
"If a photon is 'short' enough to fit inside a proton, it begins to 'resolve' features of its internal structure. The proton may decay into particles as a result of colliding with this type of photon. We've demonstrated that the two scenarios are intertwined. The number of particles originating from the unobserved section of the proton is determined by the number of particles seen in the observed part of the proton if the photon observes the interior part of the proton and it decays into a number of particles, say three."
The abstract of (see this) gives a technical summary of the article.
"We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low x and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low x, which we obtain from an unintegrated gluon distribution subject to nexttoleading order Balitsky–Fadin–Kuraev–Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both nexttonexttoleading order and nexttonexttoleading with small x resummation, where the latter provides an acceptable description of data."
The following is my rough view of what the article says.
 Deep inelastic scattering (DIS) is described in terms of photon exchange with momentum q a large value of q^{2}=Q^{2}. The parton distribution functions at the low x limit, where x= X^{2}/2p• q, (p denotes proton momentum). This limit corresponds to the perturbative high energy limit at which α_{s}<< 1 is true. The theoretical proposal is that DIS would only probe the parts of the proton wave function, which give rise to entanglement entropy. This entanglement characterizes correlation between the two parts of the system.
 By theoretical arguments authors end up with a proposal that DIS at low x limit probes a maximally entangled state and a relation between parton number and final state hadron multiplicity. A more precise statement is that the partonic entropy S(x,Q^{2}) coincides with the entropy S(h) of the final state hadrons in DIS. This means that parton and hadron pictures are dual. Mathematically this corresponds to the simple fact that entanglement entropies obtained by tracing over either entangled system are identical.
 More concretely, the partonic entropy is given by S(x,Q^{2})=ln(≤n(ln(1/x,Q^{2})≥), where ≤n(ln(1/x,Q^{2})≥ is the average number of partons with longitudinal momentum fraction x. S(x,Q^{2}) is deducible from the measured parton distribution functions. Also S(h) is deducible from experimental data.
 The unseen parts of the proton are probed by virtual photons inducing a large enough momentum transfer Q^{2}. In standard quantum theory this corresponds by Uncertainty Principle to short distances. In TGD, large h_{eff} means that the size of the color MB of protons is scaled up by h_{eff}/h so that distances can be rather large as in the case of EMC effect.
 Low x large Q^{2} limit would more or less correspond to the dark part of proton for which h_{eff} is larger and α_{s} ∝ 1/ℏ_{eff} small. This suggests that the situation would be described in terms of dark scattering. This might hold true quite generally if the dynamics of the color magnetic MB dictates the dynamics of ordinary quarks.
 The portions of proton would correspond to ordinary and dark parts of the proton. The maximal entanglement would correspond to the color entanglement between ordinary and dark quarks/partons. The counterpart of the blackhole entropy would be the entanglement entropy obtained when one integrates over the invisible dark degrees of freedom, which might, but need not, correspond to the parton sea. The integration over the dark degrees of freedom justifies the statistical approach of QCD used to describe hadrons.
 The equality of partonic and hadronic entropies states simply the fact that the integration over partonic degrees of freedom (ordinary quarks) gives the same density matrix as the integration over hadronic degrees of freedom. Dark degrees of freedom would correspond to hadronic ones and ordinary degrees of freedom to partonic ones.

See the article What it means if a Higgslike particle decaying to eμ pairs exists? or the chapter with the same title.
For a summary of earlier postings see Latest progress in TGD.
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