_{1}

A chemical non-equilibrium form of the superconductor like potential in the EW theory has been derived. It is obtained from the rate-equation for binding of fermions (quarks) to antifermions (antiquarks) and the spatial correlations for such pairs. In this model, the dimensionless coupling becomes a function of the fermion and antifermion field amplitudes, providing a measure of the matter-antimatter asymmetry from which the ratio between ordinary mass and dark mass is obtained. The dark mass becomes related to the Higgs boson mass and is estimated to about 192 GeV, which could be consistent with a signal observed from the Milky Way.

It is assumed that the Big Bang created equal amounts of matter and antimatter. However, today the Universe consists almost entirely of matter, and what we call ordinary mass is essentially attributed to the effective mass of the valence quarks in protons and neutrons, and to a lesser extent to leptons. As pointed out by Sakharov in 1967 [

As we recently showed in a chemical non-equilibrium derivation [

The chemical off-equilibrium conditions are driven by the approximate rate equation

for “binding” at a distance of e.g. a massless quark of certain flavor and color to its antiquark, y being the field amplitude of such singlet _{0} and

Equation (1) has the solution

where the short-hand notations _{K} and _{0} and

However, to create a point-like Higgs boson or nucleon, the increasing numbers of becoming

This distribution corresponds to the grand partition function (GPF), where the factor _{s}/dt » 0, which like the GPF admits fluctuations. However, in our model the fugacity y/a is driven off chemical equilibrium by Equation (1). The continuum approximation is also key to solve the statistical mechanical problem [

i.e. to describe the dynamics of a system in which the numbers of strongly correlated valence quarks and

The combination of Equation (1) with Equation (3) yields

which has the solutions

Regarding j(t) as a traveling wave that propagates with velocity k according to

we then obtain the potential energy of the system,

This has the same form as the double-well potential in the EW theory in the unitary gauge [

After symmetry breakdown,

where _{H} = 2 ga, and

is the translated solution.

It can thus be concluded that both the Higgs boson mass and the valence quark amplitude,

But if all particles in the infinite lattice of pairs in Equation (3) had a nonzero mass, this would lead to an infinite mass density. The finite Higgs boson mass should therefore correspond to some finite number of massive particles per unit volume. To see how this could occur it is instructive to rewrite

Obviously, the emergence of the finite numbers of the massive valence quarks, and the _{v}(t_{0}) and N_{p}(t_{0}) are the numbers of valence quarks and _{v}(t_{0}) and m_{p}(t_{0}) their effective time dependent masses at time 2t_{0} after Big Bang.

N_{v} = 0 thus corresponds to a Universe void of nucleons (_{v} ¹ 0 to one containing nucleons and valence quarks (

The dimensionless parameter l can thus be interpreted as the ratio between the ordinary mass density, and the density of the sum of ordinary and dark masses. The denominator of g, _{p} = 1), which then annihilates itself. With m_{H} = 125.09 GeV and j_{0} = 174.22 GeV we obtain g =125.09/(125.09 + 223.35) = 0.36 and hence l = 0.13, which agrees reasonably well with the ratio l = 0.156 observed [

But since the quark (and lepton) masses are expected to increase continuously with time, it seems reasonable to assume that the contribution to the observed gravitational effect is due to a time-average of the increasing dark masses. With an observed ratio l = 0.156, this average mass can be estimated to some 85.8% of the value attained at the EW phase transition, l = (125.09)^{2}/(125.09 + 0.858 ´ 223.35)^{2}, which yields a dark mass equal to 0.858 ´ 223.35 = 191.62 GeV. This corresponds approximately to a Higgs boson decaying into two Z bosons and further into two lepton pairs. But 191.62 GeV is also within the limits of the observed excess g-radiation from the Milky Way [

We have derived a chemical non-equilibrium model in which both the ordinary and dark masses emerge. This contrasts to Newton’s view on mass, who regarded mass as a once and for all given primary quality of matter [

This also indicates that the effects on GR and gravitation created by the turmoil from chemical non-equilibrium could be far more important than eventual gravitational quantum effects. Moreover, as a result of the energy increase, the symmetry of the dynamical system is expected to be restored, implying that the decreasing mass of the antiparticles should switch sign [

Identification of dark matter is expected to be of central importance both for astrophysics and the development of particle physics beyond the standard model. Clearly, this is just a semi-classical model based on rather drastic approximations of a delicate cross-disciplinary problem to describe a dynamical system located in the intersection area between point-like particle physics and condensed matter theory. However, the relaxation dynamics after the Big Bang is more complicated than that, because in order to produce valence quarks, the Universe must have evolved under chemical non-equilibrium conditions, a worst-case scenario in statistical physics. Therefore, the continuum approximation of the strong spatial correlations required to obtain a point-like Higgs boson had to be applied prior to the equilibration at the EW phase transition. This was also key to combine Equation (3) with Equation (1) and to solve the underlying chemical non-equilibrium statistical problem.

At a first sight this may look contradictory, because a point-like particle cannot have structure and condensed matter properties, however, in an approximate sense it can. We started out from a discrete infinite lattice [

Without the solution to this chemical non-equilibrium problem, we could not have obtained the actual relaxation dynamics of the quark-antiquark system that cools down, nor the _{0} in the superconductor-like potential have become functions of the quark (fermion) and antiquark (antifermion) amplitudes. The obtained model and its dark mass candidates can hopefully be tested at the CERN Large Hadron Collider (LHC).

In comparison to the QGP energy interval, however, the nonstationary effects become more important and have also been observed [

Confinement has also been invoked by employment of a bilinear contact type

I am grateful to Allan Din for providing interesting literature on these subjects.

Leif Matsson (2017) On Dark Matter Identification. World Journal of Mechanics, 7, 133-141. https://doi.org/10.4236/wjm.2017.74012