Dark Matter and Baryons (Surplus Quarks) Generated by Oblique Confinement of Quarks

For surplus quarks (and baryons) to emerge after Big Bang, a nonequilibrium binding and superconductor-like condensation of quark-antiquark pairs must occur before the electroweak (EW) symmetry breakdown (similar for leptons). The formerly unknown dimensionless coupling to the Ginsburg-Landau like potential and the scale parameter in the EW theory then become microscopic functions of the massive quark and antiquark fields, thus defining the matter-antimatter asymmetry and the dark matter content in the Universe at correct orders of magnitude. Thereby also the number of free parameters in the Standard Model is reduced.


Introduction
As shown by Nielsen and Olesen [1], it is easy to construct classical field theories that allow for vortex line solutions with equations of motion equal to those of the Nambu dual string [2]. In brief, they wanted to find a link between the spectrum of the Veneziano model and local field theory in analogy with type II superconductors. 't Hooft [3] and Ezawa and Iwazaki [4] then showed that the QCD vacuum works like a dual type II superconductor with the quark-antiquark ( qq ) pair playing the role of a Cooper pair [5]. The preparation of the QCD vacuum can thus no longer be regarded as just a filling of negative energy states because in addition, quarks must also be confined such that surplus quarks and baryons [6] can emerge after Big Bang. Infinite amounts of free massless quarks and antiquarks were then supposedly equally abundant, which corresponds to a totally empty vacuum with all negative energy states (holes) unfilled, making quantum How to cite this paper: Matsson, L. (2020) Dark Matter and Surplus Quarks (for Baryons) Generated by Oblique Confinement field operators meaningless. A model for transition between the empty and non-empty vacuum states is therefore postulated in terms of classical fields.
Short distance behavior in QCD is usually associated with asymptotic freedom. But since all particles created at Big Bang were massless, infinite amounts of asymptotically free quark-antiquark pair components must then have filled each volume element of the Universe, implying that large numbers of such components from different pairs could have come sufficiently close within a bag-like distance and become strongly bound at zero momentum transfer. High and low energy phenomena could thus have occurred rather independently.
As will be shown, for surplus quarks and baryons to emerge, the negative energy states must be filled in a nonequilibrium manner. This is here formulated as a rate equation for binding of massless quarks to massless antiquarks (holes) are classical fields, which here play the role as densities of massless quarks, antiquarks and qq -pairs of flavor i, and k and k' are temperature dependent association and dissociation constants. The binding of a qq -pair in Equation (1a) is approximately described by a point-like bag [4], and the flavor index i is henceforth suppressed. The colour index was dropped from start because quarks of all colours give the same form of result too.
By insertion of constraints, ( ) where 0 q and 0 q are the initial quark and antiquark fields, and with After integration, Equation (1b) yields are the time dependent quark and antiquark fields, Apart from the surplus quarks q S , which were thus "frozen out" from vacuum, the denominator of ( ) S S NS K g q q q q = + + then contains just the equal numbers of quarks and antiquarks, q NS and K q . As will be further explained here, a similar reasoning should hold for leptons.

Condensation
The condensation of qq -pairs can be approximately described by a geometric series ( ) ( ) ( ) which can also be interpreted as a "partition" function, where ( ) with solution When ( ) t ϕ is interpreted as a travelling wave with k as the traveling wave velocity, Equation (4) becomes which yields a microscopic form of the Ginsburg-Landau (GL) like potential The formerly unknown coupling ( ) ( ) have now become microscopic functions of the massive quark and antiquark fields. However, in quantum field theory, the density of surplus quarks is defined by the square of the surplus quark field where 2ag plays the role of Higgs boson mass m H , which equals approximately the top quark mass   The process can also be followed backwards in time until Big Bang, at which all surplus quarks ( and all masses vanish together with the mass of the Higgs boson, which in this model no longer plays the role of an elementary particle. It essentially consists of qq -pairs, predominantly a massive top qq -pair, which thus plays a more fundamental intermediate role in the generation of mass than the Higgs boson. However, all particle masses are now due to binding energy [10].  (3) and Equation (7).
With a totally empty vacuum at Big Bang, the Standard Model (SM) breaks down together with the quantum fields. The connection between high energy particle physics and cosmology thus goes beyond the SM, and obviously also beyond the Fermi theory.
The emergence of surplus leptons after Big Bang can be described by the nonequilibrium dynamics defined by Equation (1b), Equation (3) and Equation (7), provided that the bags can be replaced by a contact interaction like in the

Matter-Antimatter Asymmetry and Dark Matter
The coupling Regardless of which quark actually contributes, λ could thus give an estimate of the matter-antimatter asymmetry in the Universe. Moreover, since the emergence of surplus quarks q S is a prerequisite for the emergence of nucleons and ordinary matter, Immediately after Big Bang, when The SM prediction that neutrinos were massless was disproved by the neutrino oscillation experiments [16], which showed that also neutrinos have mass and that the neutrino flavour eigenstates do not coincide with the neutrino mass eigenstates. But since the lepton-antilepton asymmetry, like the quark-antiquark asymmetry in g, emerged before mass, and since mass enters equally and simultaneously for all neutrinos and antineutrinos, Equation (10) and Equation (11) should hold also in this case. Given that all heavier dark bound states have de-

Discussion
The suggested model yields a form of oblique quark confinement, by which sur- The formerly unknown coupling λ = g 2 to the GL potential has here become known as an asymmetric function of the quark and antiquark variables, thereby reducing the number of free parameters in the SM and providing a possible tool to determine the matter-antimatter asymmetry and the dark matter content in the Universe. By following the increase of the matter to all matter ratios and the decrease of dark matter after Big Bang, also the increase of dark energy, i.e. of the cosmological constant [18], could be followed.
In the case of neutrinos, however, the problem is more complicated, because the neutrino flavour eigenstates do not coincide with the neutrino mass eigenstates [16] [17]. But since Equation (9) [19] [20]. Soon after Big Bang the top quarks and antiquarks, seem to have been the dominating ordinary and dark mass sources of gravitation, but it is clearly also a question of abundance. Like mass, also gravitation must have been chiefly generated by the gluonic field interactions.
It could be speculated that the dark masses become subjected to the strongest gravitational forces towards the centre of black holes, at which the mass-energy density should increase correspondingly. The dark qq -pairs should then be heated up and disintegrate into infinite amounts of massless dark qq -pair components (similar for leptons), because our model should then work backwards. Such processes could also be responsible for launching of jets from black holes, and the jet particles could then become massive again as described here.
A preliminary version of the model has been presented earlier [ [26]. As Peebles and Ratra put it [18], "It is best to wait and see what the physics of baryogenesis and neutrinos teach us". Hopefully, this model could then fill in some gaps.