SM additive quantum numbers for leptons and quarks.
The understanding of several cosmological problems that has been obtained from the development of the Generation Model (GM) of particle physics is presented. The GM is presented as a viable simpler alternative to the Standard Model (SM). The GM considers the elementary particles of the SM to be composite particles and this substructure leads to new paradigms for both mass and gravity, which in turn lead to an understanding of several cosmological problems: the matter-antimatter asymmetry of the universe, dark matter and dark energy. The GM provides a unified origin of mass and the composite nature of the leptons and quarks of the GM leads to a solution of the cosmological matter-antimatter asymmetry problem. The GM also provides a new universal quantum theory of gravity in terms of a residual interaction of a strong color-like interaction, analogous to quantum chromodynamics (QCD). This very weak residual interaction has two important properties: antiscreening and finite range, that provide an understanding of dark matter and dark energy, respectively, in the universe.
- generation model
- dark matter
- MOND theory
- dark energy
- big bang
The main purpose of this chapter is to present the contributions to an understanding of several cosmological problems that have been obtained from the development of an alternative to the Standard Model (SM) of particle physics . This alternative model, named the Generation Model (GM) , not only describes all the transition probabilities for interactions involving all the elementary particles of the SM but also provides new paradigms, including the origin of both mass  and gravity .
The GM considers the elementary particles, the six leptons, six quarks and three weak bosons, of the SM to be composite particles. Their constituents are called rishons and antirishons. It will be demonstrated that this substructure leads to new paradigms for both mass and gravity, which in turn lead to an understanding of several cosmological problems: the matter-antimatter asymmetry of the universe, dark matter and dark energy.
It will be shown that the GM provides a unified origin of mass in which the mass of a particle is described in terms of the energy content of its constituents , while in the SM, the elementary leptons, quarks and weak bosons, are described in terms of the Higgs mechanism [6, 7]. It will be demonstrated that the composite nature of the leptons and quarks of the GM leads to a solution of the cosmological matter-antimatter asymmetry problem.
In particular, it will be shown that the GM provides a new universal theory of gravity in terms of a residual interaction of a strong color-like interaction , analogous to quantum chromodynamics (QCD) , the theory of strong interactions, in the SM. This very weak residual interaction has two important properties: asymptotic freedom (antiscreening) [9, 10] and finite range , that provide an understanding of dark matter  and dark energy , respectively, in the universe.
Section 2 discusses the
Section 6 presents a solution to the
Section 10 discusses the possibility that the photon may be considered to be the singlet state of the corresponding QCD color octet binding together the constituents of the leptons and quarks. Finally, Section 11 gives a brief summary and conclusion.
2. Standard model of particle physics
The current formulation of the Standard Model (SM) of particle physics  was essentially finalized in the mid-1970s following the experimental confirmation of the existence of quarks [14, 15]. However, the model is regarded by most physicists as
Because of the incompleteness of the SM, the basic assumptions upon which the SM has been erected have been examined . There are three basic assumptions, which are considered to be
The elementary particles of the SM are six leptons: electron (
Table 1 demonstrates that this classification of the elementary particles in the SM is
A second problem with the SM involves the method it uses to accommodate the universality of the charge-changing (CC) weak interactions, mediated by the
In the SM, the mass eigenstate leptons have weak isospin 1/2, whose third component is related to both charge and lepton number. Restricting the discussion in this chapter to only the first two generations for simplicity means that the two neutrinos interact with their corresponding charged leptons with the full strength of the CC weak interaction and do not interact at all with the other charged lepton. This is guaranteed by the conservation of lepton numbers.
On the other hand the universality of the CC weak interactions in the quark sector is treated differently. It is assumed that the
A third problem with the SM concerns the origin of mass. In the SM, the masses of hadrons arise mainly from the energy content of their constituent quarks and gluons, in agreement with Einstein's conclusion . On the other hand the masses of the elementary particles, the leptons, the quarks and the
There are several problems with the SM’s interpretation of the origin of mass. First, there is no clear evidence for the existence of the hypothetical Higgs field. Second, the model provides no
The assumption that the weak interactions are fundamental interactions arising from a local gauge theory, unlike both the electromagnetic and strong colour interactions, is at variance with the experimental facts: both the
3. Generation model of particle physics
The GM of particle physics [2, 17] overcomes many of the problems inherent in the SM. In the GM the three dubious assumptions of the SM discussed previously are replaced by three different and simpler assumptions. These are (i) the assumption of a
Table 2 shows the additive quantum numbers allotted to both leptons and quarks in the GM. This is a much simpler and unified classification scheme involving only three additive quantum numbers: charge
|− 1||− 1||0||0|
|0||− 1||± 1||± 1|
|− 1||− 1||± 1||± 1|
|0||− 1||0, ± 2||0, ± 2|
|− 1||− 1||0, ± 2||0, ± 2|
The conservation of the generation quantum number in weak interactions was only achieved by making two postulates, which means that the GM differs fundamentally from the SM in two more ways [20, 21]. First the GM postulates that it is the mass eigenstate quarks of the same generation, which form weak isospin doublets: (
The classification scheme given in Table 2 provides a simpler and unified description of leptons and quarks. It also suggests that leptons and quarks are related and in particular allows the development of a composite model of leptons and quarks [4, 22].
The GM assumes that the leptons, quarks and the
The GM has only the charge
4. Composite generation model
Although there is no direct experimental evidence that leptons and quarks have a substructure, there is considerable indirect evidence that leptons and quarks are actually
First, the equal magnitude of the electric charges of the electron and proton, indicates that the charges of the up and down quarks are related to that of the electron.
Second, the leptons and quarks are considered  to form three families or generations, containing particles which have similar properties, except for mass. This feature is analogous to Mendeleev’s periodic table of the elements, based essentially on elements having similar properties, except for mass. The existence of three repeating patterns suggests strongly that the members of each generation are composites, analogous to the elements of the periodic table.
The nonunified classification scheme of the SM provides a major stumbling block for the development of a composite model of leptons and quarks. On the other hand, the unified classification scheme of the GM (Table 2) makes feasible a composite version of the GM (CGM) . Here we shall present the current version .
The composite GM is based on the unified classification scheme and also on 1979 composite models of Harari  and Shupe . The current composite GM was proposed in 2011 and is described in detail in Chapter 1  of the book
Both the models of Harari and Shupe are very similar and treat leptons and quarks as composites of two kinds of spin-1/2 particles, which Harari named “rishons” from the Hebrew word for primary. The CGM adopts this name for the constituents of both leptons and quarks and for consistency the same three additive quantum numbers are assigned to the constituents as were previously allotted in the GM to leptons and quarks (see Table 2).
In the Harari-Shupe Model (HSM), two kinds of rishons labeled
Table 3 shows the proposed HSM structures of the first generation of leptons and quarks. Basically the HSM describes only the charge structure of the first generation of leptons and quarks and does not provide a satisfactory understanding of the second and third generations.
To overcome some of the deficiencies of the simple HSM, the two-rishon model was extended [4, 22], within the framework of the CGM, by the introduction of a
In the CGM, the substructure of the leptons and quarks is described in terms of massless rishons and/or antirishons. Each rishon carries a color charge, red, green or blue, while each antirishon carries an anticolor charge, antired, antigreen or antiblue. The constituents of leptons and quarks are bound together by a strong color-type interaction, corresponding to a local gauged
Table 5 gives the structures of the first generation of leptons and quarks in the CGM. The
|+ 1||+ 1||0|
|− 1||− 1||0|
Each lepton of the first generation is
It should be noted that if each of the three kinds of rishons is
Since the mass of a hadron arises mainly from the energy of its constituents [26–28], the CGM suggests  that the mass of a lepton, quark or weak boson arises from a characteristic energy
The CGM suggests that the mass hierarchy of the three generations arises from the substructures of the leptons and quarks. The mass of each composite particle is expected to be
Qualitatively, for the same generation, one expects that (i) a charged lepton will have a greater mass than the corresponding neutral lepton; (ii) a quark will have a greater mass than the corresponding quark. These are both generally true: (i) the electron has a larger mass than its corresponding neutrino, and (ii) the top quark mass (173 GeV) is > the bottom quark mass (4.2 GeV), the charmed quark mass (1.3 GeV) is > the strange quark mass (95 MeV), although the up quark mass (2 MeV) is < the down quark mass (5 MeV). The first generation quarks seem to present an anomaly since the proton consists of two up quarks and one down quark while the neutron consists of two down quarks and one up quark so that the proton is only stable if the down quark () is more massive than the up quark (). In the CGM, this anomaly is accounted for by the constituents of hadrons being weak-eigenstate quarks rather than mass-eigenstate quarks. The proton is stable since the weak eigenstate quark
6. Matter-antimatter asymmetry problem
According to the prevailing cosmological model  the universe was created in the so-called “Big Bang” from pure energy, and is currently composed of about 5% ordinary matter, 27% dark matter and 68% dark energy. It is generally assumed that the Big Bang and its aftermath produced
An understanding of the matter-antimatter asymmetry requires a precise definition of both matter and antimatter and knowledge of the physical nature of the Big Bang but unfortunately this knowledge is currently far from complete. The prevailing model of the Big Bang is based upon the theory of general relativity : extrapolation of the expansion of the universe backwards in time yields an infinite density and temperature at a finite time in the past (approximately 13.8 billion years ago). Thus the “birth” of the universe seems to be associated with a “singularity”, which not only signals a breakdown of general relativity but also all the laws of physics. This leads to serious impediments to understanding the physical nature of the Big Bang and consequently the development of the matter-antimatter asymmetry in the aftermath of the Big Bang.
Since the physical nature of the Big Bang is still not understood, it is not possible to discuss the matter-antimatter asymmetry problem from the initial singularity. Consequently, the matter-antimatter (i.e. particle-antiparticle) asymmetry problem will be discussed in terms of the observed nature of the universe, ignoring the singularity.
In the SM the universe is made essentially of matter comprising three kinds of elementary particles: electrons, up quarks and down quarks. The matter described by the SM refers to the 5% ordinary matter, which prior to the nucleosynthesis, i.e. the fusion into heavier elements, consisted of about 92% hydrogen atoms and 8% helium atoms , so that the ordinary matter of the universe was, and still is, essentially electrically neutral and colorless.
For many decades now the SM has been unable to provide an acceptable understanding of the matter-antimatter asymmetry problem. The main reason seems to be that the SM assumes that the leptons and quarks are elementary particles. Since this implies no relationship between leptons and quarks, as indicated by the different sets of additive quantum numbers employed by the SM to describe their interactions, this allows the matter/antimatter nature of leptons and quarks to be decided by pure convention. In the SM both leptons and quarks are assumed to be matter particles.
In the SM, neglecting the singularity, it is assumed that the Big Bang initially produces numerous elementary particle-antiparticle pairs such as electron-positron pairs and quark-antiquark pairs by converting energy into mass according to
In the GM, neglecting the singularity, it is expected that the Big Bang would initially produce numerous elementary rishon-antirishon pairs. Then as the universe cooled following an inflationary period, the rishons and antirishons would form leptons, quarks and their antiparticles and eventually atoms of hydrogen, antihydrogen, helium and antihelium. These would later annihilate in pairs until only atoms of hydrogen and helium prevailed.
In order to understand this matter-antimatter asymmetry, it is necessary to define the matter/antimatter nature of composite particles. Historically, the term “particle” defines matter that is naturally occurring, i.e. electrons, protons, hydrogen atoms, etc. This is consistent within the SM in which the electron and the up and down quarks are elementary particles. However, it is not consistent within the GM in which the electron and the up and down quarks are composite particles consisting of elementary particles (rishons) and/or antiparticles (antirishons). In the GM, rishons are considered to be matter (particles) while antirishons are considered to be antimatter (antiparticles), since rishon-antirishon pairs are considered to be created/annihilated in the standard manner, e.g. in the Big Bang.
In the GM the elementary rishons and antirishons have particle number and , respectively. Thus the particle number
The solution of the matter-antimatter asymmetry problem involves the particle number additive quantum number
In the GM the proton is assumed to consist of three weak eigenstate quarks, two up quarks and one down quark, so that the proton has particle number
In the GM the neutron consists of three weak eigenstate quarks, one up quark and two down quarks, so that the neutron also has particle number
Thus the ordinary matter present in the universe, prior to the fusion process into heavier elements, has particle number
Indeed it should be noted that if the Big Bang produced equal numbers of particles and antiparticles so that the initial state of the universe had particle number
To summarize: the ordinary matter present in the universe has an overall particle number of
However, the above does not explain why the present universe consists primarily of hydrogen atoms and not antihydrogen atoms. In the SM this is considered to be the matter-antimatter asymmetry problem, since each of the elementary particles, the electron and both the up and down quarks are defined to be matter (particles). In the GM it has been demonstrated that this is not so: both hydrogen atoms and antihydrogen atoms have
This implies that both hydrogen atoms and antihydrogen atoms should be formed during the aftermath of the Big Bang with about the same probability. In fact, estimates from the cosmic microwave background data suggest  that for every billion hydrogen-antihydrogen pairs there was just one extra hydrogen atom. It is suggested that this extremely small difference, one extra hydrogen atom in 109 hydrogen-antihydrogen pairs, may arise from statistical fluctuations associated with the complex many-body processes involved in the formation of either a hydrogen atom or an antihydrogen atom. The uniformity of the universe , in particular the lack of antihydrogen throughout the universe, indicates that the above statistical fluctuations took place prior to the “inflationary period” [33, 34] associated with the Big Bang scenario.
Let us now consider the nature of gravity within the framework of the GM. It is considered that the rishons of each colorless lepton, e.g. an electron, are very strongly localized since to date there is no direct experimental evidence for any substructure of these particles. It is expected that the product wave function describing the distribution of the constituent rishons is significant for only an extremely small volume of space so that the color fields almost cancel. It should be noted that the color fields would only cancel completely if each of the rishons occupied the same position, but quantum mechanics prevents this. This raises a question:
Between any two colorless leptons (e.g. electrons) there will be a very weak residual interaction, arising from the color interactions acting between the color charges of one lepton and the color charges of the other lepton. There will be a similar residual interaction between any two colorless hadrons such as neutrons and protons, each containing three differently colored quarks.
In two papers [3, 4] it was suggested that this residual interaction, arising from these “interfermion” color interactions, gives rise to the usual gravitational interaction.
The mass of a body of ordinary matter is essentially the total mass of its constituent colorless electrons, neutrons and protons. Each of these three composite particles is in a three-color antisymmetric state so that its behavior with respect to the color interactions is basically the same. This suggests  that the residual color interactions between electrons, neutrons and protons have several properties associated with the usual gravitational interaction: universality, very weak strength and attraction.
In the GM gravity essentially arises from the residual color forces between all electrons, neutrons and protons. This leads  to a
where Newton’s gravitational constant (
The new gravitational interaction of the GM is based upon the residual color interactions acting between electrons, neutrons and protons. The GM assumes that the color interactions acting between rishons have the same characteristics as the color interactions acting between quarks in the SM. These color interactions have two important properties that differ from the Newtonian interaction: (i) asymptotic freedom [9, 10] and (ii) color confinement . These determine the nature of the function
In Sections 8 and 9, we shall indicate how these two additional properties of the interfermion color interactions provide an understanding of dark matter and dark energy, respectively.
8. Galaxy rotation problem and dark matter
For galaxies there is a major gravitational problem , which has been around for about 40 years. It was found that the rotation curves for galaxies disagreed with Newton’s gravitational law for large
The rotation curve for a galaxy is the dependence of the orbital velocity of the visible matter in the galaxy on its radial distance from the center of the galaxy. What the observations showed was that the rotation curves were essentially “flat” at the extremities of the visible matter, i.e. at large distances. This implies gross disagreement with Newton’s universal law of gravitation, which predicts a fall-off as , as in the solar system.
Two solutions, which have been very successful, are first the
It was found that the
Asymptotic freedom is rather a misnomer. A better term is “antiscreening” as used by Wilczek in his 2004 Nobel lecture. The flat galactic rotation curves are described by the property of antiscreening provided by the self-interactions of the hypergluons mediating the residual color interactions. These antiscreening effects lead to an increase in the strength of the residual color interactions so that
In the GM
9. Dark energy
Color confinement is the phenomenon that color charged particles (e.g. quarks in the SM, rishons in the GM) cannot be isolated and consequently form colorless composite particles (e.g. mesons and baryons in the SM and also leptons in the GM). Color confinement leads to another phenomenon analogous to the “hadronization process” , i.e. the formation of hadrons out of quarks and gluons in the SM and implies
In the GM,
The strong color interaction is known to have a finite range of approximately 10− 15 m. Gravity is about 10− 41 times weaker at 10− 15 m  than the strong color interaction. This suggests that the “hadronization process” for gravity occurs at about 1026 m, i.e. roughly ten billion light years.
The new law of gravity implies that gravity ceases to exist for cosmological distances exceeding several billion light years, resulting in less slowing down of galaxies than expected from Newton’s law. This result agrees well with observations [38, 39] of distant Type Ia supernovae, which indicate the onset of an accelerating expansion of the universe at about six billion light years. Thus the new law of gravity suggests that dark energy like dark matter may be understood as an effect arising from the nature of the gravitational interaction.
The nature of the photon within the framework of the GM is worthy of consideration. The photon has several properties that may be accommodated in the GM: (i) massless; (ii) neutral; (iii) colorless; (iv) spin-1; (v)
It is proposed that the photon may be the
In the GM the singlet state is a hypergluon, which is massless, electrically neutral, colorless and has spin-1 and
11. Summary and conclusion
The GM considers that the elementary particles of the SM, the leptons, quarks and weak bosons are all composite particles. This substructure leads to new paradigms for both mass and gravity, which in turn lead to an understanding of several cosmological problems: the matter-antimatter asymmetry of the universe, dark matter and dark energy.
The GM provides a
The GM also provides a new universal quantum theory of gravity. In the GM, gravity is a very weak residual interaction of a strong color-like interaction, which possesses two important properties: antiscreening and finite range that provide an understanding of dark matter and dark energy, respectively, in terms of gravitational effects.
Gottfried K, Weisskopf VF. Concepts of Particle Physics. Vol. 1. New York: Oxford University Press; 1984, 189p
Robson BA. The generation model of particle physics. In: Kennedy E, editor. Particle Physics. Rijeka: InTech; 2012. pp. 1–28
Robson BA. The generation model and the origin of mass. International Journal of Modern Physics E. 2009; 18:1773–1780
Robson BA. A quantum theory of gravity based on a composite model of leptons and quarks. International Journal of Modern Physics E. 2011; 20:733–745
Einstein A. Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig. Annalen der Physik. 1905; 18:639–641
Englert F, Brout R. Broken symmetry and the mass of gauge vector bosons. Physical Review Letters. 1964; 13:321–323
Higgs PW. Broken symmetries and the masses of gauge bosons. Physical Review Letters. 1964; 13:508–509
Halzen F, Martin AD. Quarks and Leptons: An Introductory Course in Modern Particle Physics. New York: Wiley; 1984. 396p
Gross DJ, Wilczek F. Ultraviolet behavior of non-abelian gauge theories. Physical Review Letters. 1973; 30:1343–1346
Politzer HD. Reliable perturbative results for strong interactions. Physical Review Letters. 1973; 30:1346–1349
Lincoln D. Understanding the Universe from Quarks to the Cosmos. Rev. Ed. Singapore: World Scientific; 2012. 567p
Robson BA. The generation model of particle physics and galactic dark matter. International Journal of Modern Physics E. 2013; 22. Article ID 1350067, 11pp.
Robson BA. Dark matter, dark energy and gravity. International Journal of Modern Physics E. 2015; 24. Article ID 1550012, 10pp.
Bloom ED, et al. High-energy inelastic e− pscattering at 60 and 100. Physical Review Letters. 1969; 23:930–934
Breidenbach M, et al. Observed behavior of highly inelastic electron-proton scattering. Physical Review Letters. 1969; 23:935–939
Veltman M. Facts and Mysteries in Elementary Particle Physics. Singapore: World Scientific; 2003. 340p
Robson BA. Progressing beyond the standard model. Advances in High Energy Physics. 2013; 2013. Article ID 341738, 12pp.
Cabibbo N. Unitary symmetry and leptonic decays. Physical Review Letters. 1963; 10:531–533
Aitchison IJR, Hey AJG. Gauge Theories in Particle Physics. Bristol: Hilger; 1982. 341p
Robson BA. A generation model of the fundamental particles. International Journal of Modern Physics E. 2002; 11:555–566
Evans PW, Robson BA. Comparison of quark mixing in the standard and generation models. International Journal of Modern Physics E. 2006; 15:617–625
Robson BA. A generation model of composite leptons and quarks. International Journal of Modern Physics E. 2005; 14:1151–1169
Robson BA. The generation model and the electroweak connection. International Journal of Modern Physics E. 2008; 17:1015–1030
Harari H. A schematic model of quarks and leptons. Physics Letters B. 1979; 86:83–86
Shupe MA. A composite model of leptons and quarks. Physics Letters B. 1979; 86:87–92
Butler F, et al. Hadron mass predictions of the valence approximation to lattice QCD. Physical Review Letters. 1993; 70:2849–2852
Aoki S, et al. Quenched light hadron spectrum. Physical Review Letters. 2000; 84:238–241
Davies CTH, et al. High-precision lattice QCD confronts experiment. Physical Review Letters. 2004; 92. Article ID 022001, 5pp.
Amsler C, et al. Summary tables of particle properties. Physics Letters B. 2008; 667:31–100
Ade PAR, et al. (Planck Collaboration). Planck 2013 results. I. Overview of products and scientific results. Astronomy and Astrophysics. 2014; 571. Article ID A1, 48pp.
Einstein A. The basics of general relativity theory. Annalen der Physik. 1916; 49:769–822
Morris R. Cosmic Questions. New York: Wiley; 1993. 200p
Guth AH. Inflationary universe—a possible solution to the horizon and flatness problems. Physical Review D. 1981; 23:347–356
Linde AD. A new inflationary universe scenario—a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Physics Letters B. 1982; 108:389–393
Milgrom M. A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophysical Journal. 1983; 270:365–370
McGaugh SS, de Blok WJG. Testing the hypothesis of modified dynamics with low surface brightness galaxies and other evidence. Astrophysical Journal. 1998; 499:66–81
Famaey B, McGaugh SS. Modified newtonian dynamics (MOND): Observational phenomenology and relativistic extensions. Living Reviews in Relativity. 2012; 15. Article ID 10, 159pp.
Riess AG, et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astronomical Journal. 1998; 116:1009–1038
Perlmutter S, et al. Measurements of omega and lambda from 42 high-redshift supernovae. Astrophysical Journal. 1999; 517:565–586