Abstract
In a previous paper, the present author proposed the infinite sub-layer quark model, in which the proton and the neutron are composed of an infinite number of point-like (structure-less) quarks ?? and anti-quarks at an infinite sub-layer level. The limit particle ?? has all one-half quantum numbers of spin , isospin , third component of isospin , and fractional electric charge , where e is the electron charge. This fermion will behave as if it was lepton, since the baryon number vanishes at an infinite sub-layer level. Thus, this ultimate particle is considered as constituting the non-baryonic cold dark matter. A pair of an infinite number of ?? and quarks would be produced in the first moments after the Big Bang and form the nucleons and remain as the dark matter for all time, stable against decay. It was then shown that is violated in the doublet of ?? and quarks to account for the asymmetry of the number of particles and antiparticles in the present universe. Furthermore, it was shown that the Higgs bosons are composed of ?? and dark matter particles. In this paper, we will show that the Cantor set is constructed from an infinite number of point-like quarks ?? and anti-quarks which constitutes the nucleon and the dark matter. It is also shown that the color charges in quantum chromodynamics (QCD) of ?? and quarks vanish and these limiting particles of dark matter have no color force with the strong interaction and subject only to the weak interaction and gravity.
Highlights
Since the introduction of the parton model (Feynman, 1969; Bjorken & Paschos, 1969), one of the most important problems in high energy physics has been the relationship between an infinite number of partons and the three quarks inside the nucleon
By analyzing deep inelastic electron-proton scattering at high q2, each of the valence quarks will be itself resolved into infinitely many constituents called “partons”
In a previous paper (Sugita, Okamoto, & Sekine, 2008), we proposed the non-baryonic and exotic quark μ∞ as an excellent candidate for non-baryonic cold dark matter to comprise the universe, since they are absolutely stable and the non-baryonic particles with the baryon number 0
Summary
Since the introduction of the parton model (Feynman, 1969; Bjorken & Paschos, 1969), one of the most important problems in high energy physics has been the relationship between an infinite number of partons and the three quarks inside the nucleon. The partons are considered as the quarks, quark and anti-quark sea and gluons (Feynman, 1972). This quark-parton model has been established and has a very strong appeal, we cannot exclude the existence of a further sub-layer quark (Kogut & Susskind, 1974a, 1974b). The anti-particle of u∞ is the d∞ quark, since the baryon number vanishes at N=∞. At N=∞, an infinite number of point-like quarks www.ccsenet.org/apr
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