Jiri Hosek

The Meissner effect for the chromoelectric field E⃗a is a property of the non-perturbative QCD vacuum medium assumed to explain the observed confinement of color. The color dielectric function ϵ of such a medium should vanish. By Lorentz invariance ϵμ = 1 i.e., its color magnetic permeability μ should diverge. The assumption based on analogy is well motivated: Ordinary superconductor is the physical medium with μ = 0, confining the opposite magnetic charges (would they exist). For the first successful phenomenological description of both the Meissner effect and superconductivity within Maxwell equations Fritz London guessed two equations for the superconductivity current. We adapt his arguments to QCD and come with two analogous manifestly non-Abelian London-like equations. One equation describes the dual Meissner effect. The analogy is, however, not perfect: We can only speculate that there is some sort of chromo-magnetic superfluidity in QCD phenomena to which the second equation might be ascribed. Moreover, from more advanced Ginzburg-Landau (GL) theory of superconductivity it follows that the Meissner effect is a consequence of spontaneous breaking of the underlying global U(1) symmetry. This is certainly not the case of the dual Meissner effect. Fortunately, the derived London-like equations suggest a strongly color-paramagnetic behavior. We interpret it as a guide to the phenomenological Ginzburg-Landau-like manifestly gauge-invariant low-momentum QCD with the confining vacuum which behaves as a perfect color paramagnet (μ = +∞).

In anomaly free gauged three-flavor SU(3)_f x SU(2)_L x U(1)_Y model of Yanagida with fermion and gauge boson masses described by conveniently chosen elementary scalar Higgs fields the neutrino mass matrix comes out in the seesaw form. Following Yanagida's suggestion we demonstrate that no Higgs fields are needed. Strong flavor gluon interactions themselves, treated in a separable approximation, result in universally split lepton and quark masses calculated in terms of a few parameters. While the realistic splitting of charged lepton and quark masses requires the electroweak and QCD radiative corrections the neutrino seesaw mass matrix comes out exact.

We replace the Higgs sector of the Standard electroweak gauge model of three fermion families by a horizontal non-vector-like gauge SU(3) quantum flavor dynamics with one parameter. With plausible physical assumptions we suggest that the new dynamics generates spontaneously the masses of its eight flavor gluons, of leptons and quarks, and of the intermediate W and Z bosons. Absence of axial anomalies requires neutrino right-handed electroweak singlets and the dynamics then suggests the existence of massive Majorana neutrinos.

We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU(2)_L x U(1)_Y theory. Within this model we demonstrate: (1) Strong Yukawa interactions between massless fermion fields and a massive scalar field carrying the axial charge generate dynamically the fermion and boson proper self-energies, which are ultraviolet-finite and chirally noninvariant. (2) Solutions of the underlying Schwinger-Dyson equations found numerically exhibit a huge amplification of the fermion mass ratios as a response to mild changes of the ratios of the Yukawa couplings. (3) The `would-be' Nambu-Goldstone boson is a composite of both the fermion and scalar fields, and it gives rise to the mass of the axial-vector gauge boson. (4) Spontaneous breakdown of the gauge symmetry further manifests by mass splitting of the complex scalar and by new symmetry-breaking vertices, generated at one loop. In particular, we work out in detail the cubic vertex of the Abelian gauge boson.