2.0 THE FRACEP MODEL OF ELEMENTARY PARTICLES

2.1 The FRACEP Fundamental Particles and Primary Groupings

The FRACEP Model is a different picture of what is perceived today as the fundamental building blocks of nature. It looks inside the smallest known SM particles and proposes a composite structure. The philosophy of the FRACEP is that, in its most fundamental state, matter in the universe is polarized into only two types of particles that have energy potentials that are interpreted as mass.

One particle has positive mass (G0p). The second particle has equal but opposite (i.e., negative/minus) mass (G0m). Like masses attract and unlike masses repel. These two FRACEP fundamental particles clump into stable primary groupings, using bindings analogous to the covalent chemical bond, to produce charge, spin and momentum effects (Table 3).

TABLE 3. This shows the characteristics of the fundamental particles and primary
groupings of the FRACEP Model mentioned above are shown including: particle name;
mass (in units of MeV/c²); spin; and em-charge (q_e, in units of the electron charge). The
configuration of the primary groupings is discussed below. Note that 1Mev/c²~ 4.65x10^-34gm.

The masses of G0p and the groupings in Table 3 were determined empirically based on several assumptions.

1) The electron is composed of three composite components, each containing three types of primary groupings (i.e., e^- = 3(SGp + QGp + GXp).

2) The spin carrier has a mass part and a spin part (i.e., SGp = S0p + MSp where S0p carries the spin and some mass and MSp carries the bulk of the mass but no spin).

3) The charge carrier has a mass part and a charge part (i.e., QGp = Q0p + MQp where Q0p carries charge and some mass and MQp carries bulk of the mass but no charge).

4) The anti-electron, or positron, is defined as e⁺ = 3(SGm + QGm + GXp).

5) The electron-neutrino is defined as n_e- = SGp with the anti-electron-neutrino as n_e- = SGm.

6) The mass difference between particles and anti-particles is less than the experimental measurement uncertainty.

The determined values for the masses, using GXp = G22p, satisfy the observed data in the SM (i.e., n_e- < 15x10^-6 MeV/c² and e- = 0.5109989 + 4.0x10^-8 MeV/c²).

Unlike the SM that assumes em-charge, spin and total rest mass are intrinsic properties, the FRACEP treats these properties as components of the compound particles that exhibit the appropriate characteristics because of the symmetry in their fractal-based structure.

The charge effect is captured in a linear chain of pairs of G0p for negative charge or G0m for positive charge. The G0p’s or G0m’s are joined by a stable double bond (i.e., - G0p = G0p -) to produce a two-bond system that oscillates. Each chain has 4¹⁹ pairs of elements.

Q0p = 2G0p ^. 4¹⁹ ..... and ..... Q0m = 2G0m ^. 4¹⁹.

Two chains are needed for each basic charge carrying structure ^{[Ref. 20]} (Figure 1a).

Figure 1. This shows the structure of the primary groupings that are used to build the
intermediate building blocks: a) a single em-charge carrying chain contains a total of 4¹⁹
elements; b) the spin carrying group is a 16 level recursive structure with the 1st level shown;
c) the zero level general momentum carrier; d) the level 1 general momentum carrier.

The spin effect is captured in a fractal structure based on a 5-element group where each element, in the lowest order, is a pair of G0p or G0m particles joined by a single bond that rotates about each other (i.e., = G0p - G0p = ) to produce a four-bond system. The full spin effect has 16 levels of the recursive structures S0p for positive spin or S0m for negative spin.

S0p = level 16 = 5 ^. level 15 = 5^{2 .} level 14 = ... = 5^{16 .} 2G0p

and

S0m = 5^{16 .} 2G0m.

Each of the pairs of G0p or G0m shown in Figure 1b contributes to the total spin effect ^{[Ref. 21]}.

The bulk of the rest mass is captured in the momentum carriers. The general momentum carrier is a fractal structure based on a 6-element ring of G0p or G0m particles with an additional 3 particles bound to give a 3-bond system. Like the spin effect grouping, the general momentum carrier is a recursive structure (GXp = G0p ^. 9^x and GXm = G0m ^. 9^x ) (Figure 1 c, d). The specific momentum carriers for the spin effect and charge effect are:

MSp = 4G16p ..... and ..... MSm = 4G16m

MQp = G19p + 2 G13p + 48R13p + 121R16p

and

MQm = G19m + 2 G13m + 48R13m + 121R16m

2.2 The FRACEP Intermediate Building Blocks of Nature

The bulk of all matter that we see in our every-day lives (as well as, in the multitude of particles observed in experiments - both particle and anti-particle) is based on the positive mass, G0p. For convenience, this matter will be referred to as the Bright Universe (BU). The FRACEP, however, also allows for a set of particles based on the negative mass, G0m. This matter will be referred to as the Dark Universe (DU).

Using the fundamental particles and the primary groupings in Table 3, a second tier of groupings, referred to as the intermediate building blocks, is constructed (Table 4) for both the bright and dark universes. It is out of these building blocks that all of the SM fundamental particles are constructed.

The BU spin carrier (SGp) (including both the spin effect group and the spin specific momentum carrier), is stable - with only positive mass components (Figure 2a). The BU anti-spin carrier (SGm) is unstable because the S0m (which replaces the S0p in Figure 2) is composed of negative mass components which repel the positive mass momentum carrier (MSp). Thus, any BU particle with an SGm component is unstable. Similarly, the DU spin carrier (SDm) will be stable, while its anti-spin carrier (SDp) will be unstable. Finally, SGp will repel SDm.

The BU charge carrier, QGp (including both the charge effect group and the charge specific momentum carrier), is stable - with only positive mass components. The BU anti-charge carrier, QGm, is unstable because the Q0m is composed of negative mass components which repel the positive mass momentum carrier, MQp. Thus any BU particle with a QGm component is unstable. Similarly, the DU charge carrier, QDm will be stable, while its anti-charge carrier, QDp will be unstable.

Recall that in the universe we see (the BU), positive charge repels positive charge. Negative charge repels negative charge. And positive charge attracts negative charge. However, in the FRACEP, the BU negative charge carriers (QGp) will repel the DU positive charge carriers (QDm) in local proximity because of the unlike masses. But the QGp and QDm will attract each other because of the unlike em-charge. The strength of the competing effects will be discussed in Part 2^{[Ref. 19]}.

In the construction of the composite fermions and bosons, several stable momentum carrying groups are used (their mass is in parentheses): G13p (4.384550939508x10^-10 MeV/c²), G16p (3.196337634901 x10^-7 MeV/c²), G19p (2.330130135843 x10^-4 MeV/c²), G22p (0.169866486903 MeV/c²), G24p (13.75918543914 MeV/c²), and G26p (1114.494020570 MeV/c²).

Figure 2.This shows the structure of the intermediate building blocks:
a) the spin carrier showing the spin group plus the momentum part; b) the
em-charge carrier showing the two charge chains plus the momentum part

2.3 The Composition of the FRACEP Composite Fermions

The FRACEP constructs all of the SM fermions and bosons from the intermediate building blocks in Table 4. Only the BU fermions will be considered here. The BU bosons will be discussed in Part 5 ^{[Ref. 22]}.

The FRACEP particles are grouped into three categories: the primary composite, the secondary composite particles, and the heavy composite particles (Table 5). The categories are based on FRACEP composite mass (Table 6) and number of decay paths.

Note that the SM predicts that the particle and its anti-particle have equal masses, but the FRACEP predicts a small mass difference due to the negative mass components in the composite structure. In every case the charge and spin predicted by FRACEP agrees with the SM. Note that the word "predicts" with respect to the FRACEP indicates a heuristic, as opposed to theoretical, concept.

TABLE 4. This shows the composition of the intermediate building blocks of the FRACEP
Model including: particle name; component composition; mass (m, in units of MeV/c²);
spin (s); and em-charge (qe, in units of the electron charge). Recall the mass of G0m = -G0p.

The primary composite group contains the lightest and only stable particles in the SM fermion collection; and includes: the electron-neutrino (n_e-), the muon-neutrino (n_m-), the electron (e^-) and their respective anti-particles. The anti-particles are not stable because of their negative mass components. The secondary composite particles and anti-particles are unstable groupings based on, and decaying to, the primary composite particles. They are distinguished by their single decay path. The up-quark is assumed to be stable only within the potential well of a nucleon such as a proton. This group includes: the up-quark (u⁺), the down-quark (d^-), and the mu (m^-) and their respective anti-particles.

TABLE 5. This shows the composition of the composite fermions. The fermions all have spin = ½.
By the FRACEP, they are composed of three parts. One part is the base to which the other components
are bound. The second part has the spin and charge carrying components. The third part has the
momentum carrying groups. The base and the momentum carriers are zero-spin and
zero-charge. The table presents the particle symbol and the
three grouping types. One possible configuration for the components is shown in the appendix.

The heavy composite particles are unstable groupings based on, and decaying to, the primary composite particles, and the secondary composite particles. They generally have more than one decay path, and often decay through intermediary mesons (the two-quark bound states discussed above). This group includes the tau-neutrino (n_t-), the tau (t^-), the charm-quark (c⁺), the strange-quark (s^-), the top-quark (t⁺), the bottom-quark (b^-) and their respective antiparticles. The term "decay path" indicates that the necessary components are present; but, no mathematical proof of that decay sequence is available at this time.

TABLE 6. This shows the masses of the FRACEP composite fermions. It is compared
to the SM measured fermion masses. The table includes the particle symbol, em-charge
(q_e = electric charge in units of 1e), the FRACEP mass (sum of base, spin and charge
components and momentum carriers - the core mass does not include the momentum
carriers), difference between the FRACEP and the SM observed mass, the FRACEP
difference between the particle and its respective anti-particle, and the SM measurement
bounds - this includes upper bound for the neutrino family, (measurement error for
the electron family) or measurement range for the quarks. All masses are given in units MeV/c².

The SM treats the fermions and bosons as fundamental particles (single wave form representation in the quantum mechanical theory, with intrinsic properties of em-charge, spin and rest mass) despite considerable evidence to the contrary. The preon theory that is being developed introduces internal components to these particles, representing them with multiple wave forms in a quantum mechanical treatment, but, does not clearly identify a minimum set of "true" fundamental particles.

The new FRACEP Model presented in this paper demonstrates the possibility of a minimum set of truly fundamental particles that can be used to construct all of the fermions and anti-fermions as composite particles. It shows that the composite fermions match the Standard Model observations for basic characteristics of em-charge, spin, mass and decay path. (The representation of the bosons is presented separately ^{[Ref. 22]}).

The FRACEP is based on the positive mass and negative mass pair of particles that form the fundamental set. By defining each particle of the pair with zero spin and zero em-charge, and, with equal but opposite mass, the FRACEP presents a framework for building the composite intermediate building blocks that are used to make up the composite fermions, where the em-charge, spin and rest mass are components in the compound structure.

The concept of negative mass presents some interesting possibilities. For every particle in the Bright Universe (BU) that we see, there is the possibility of a truly opposite particle (in spin, charge and mass). It is possible that these Dark Universe (DU) particles do exist and represent the dark matter and energy that seem to be affecting the behavior of our observable universe. (Because BU and DU particle repel each other, the expansion of our universe as evidenced by the observed galaxy behavior would be expected.)

The FRACEP presented in this work does not include a mathematical framework, but, it is anticipated, based on the current state of development that several things will be established. First, a mass vs. charge relation will be developed that allows the theoretical prediction of the observed fermion masses. Second, an energy potential will be developed that demonstrates a relation between interactions at the quantum scales with that at the macro scales of gravity. Third, a physical explanation of the electric charge effect will be shown. Fourth, a physical explanation of the spin effect will be shown. It is anticipated that ultimately a mathematical framework will be developed. As with any new conceptual model, there is much to resolve before any chance of validation against reality can be made. However, the feasibility of a specific minimum set (opposite pair) of fundamental particles to explain the internal structure of the fermions has been shown here.

4.0 REFERENCES
¹ S.N. Kramer, Sumerian Mythology, University of Pennsylvania Press, Phila. PA (1972); S.H. Hooke, Middle Eastern Mythology, Penguin Books, NY (1963); A. Birrell, Chinese Mythology, The Johns Hopkins University Press, Baltimore, MD (1993); E.A. Wallis Budge, Legends of the Egyptian Gods, Dover Publications, Inc., Minneola, NY (1994); T. Bulfinch, Bullfinch's Mythology, Avenel Books, NY (1978).

² J.N. Lockyer, The Dawn of Astronomy, a Study of Temple Worship and Mythology of the Ancient Egyptians, Cassell and Company, Limited, London (1894).

³ H.P. Yoke, Li, Qi and Shu, An Introduction to Science and Civilization in China, Hong Kong University Press, Hong Kong (1985)

⁴ H.M. Leicester, The Historical Background of Chemistry, John Wiley & Sons, Ltd., NY (1956).

⁵ W.B. Jensen, ed., Mendeleev on the Periodic Law, Selected Writings, 1869-1905, University of Cincinnati, Cincinnati, OH (2002).

⁶ M.H. Shamos, ed., Great Experiments in Physics, Dover Publications, Inc. New York, NY (1987).

⁷ I. Newton, Philosophiae Naturalis Principia Mathematica (1686), Principia,University of California Press, London, England (1999).

⁸ J.C. Maxwell, A Treatise on Electricity and Magnetism, Vol. I & II, 3rd ed. (1891), Dover Pub. Inc., Mineola, NY (1954).

⁹ M. Jammer, The Conceptual Development Of Quantum Mechanics, McGraw-Hill Book Company, NY (1966): L.I. Schiff, Quantum Mechanics, 3rd ed., McGraw-Hill Book Company, NY (1968).

¹⁰ A. Einstein, The Meaning Of Relativity, PrincetonUniversity Press, Princeton, NJ (1922).

¹¹ B. Povh, K. Rith, C. Scholz, F. Zetsche, Particles and Nuclei, 2nd ed., Springer, NY (1999).

¹² G. Kane, "The Dawn of Physics Beyond the Standard Model", Scientific American, June 2003, p68; S. Weinberg, "A Unified Physics by 2050?", Scientific American, December 1999, p. 68.

¹³ Sources for fundamental particle properties: "Particle Data Book" (www-pdg.lbl.gov); Physics Today, August 2003, pBG6-16; Physics Today, August 2004, p26.

¹⁴ J.A. Peacock, Cosmological Physics, Cambridge Univ. Press, Cambridge (1999) p. 252; B. Schwarzchild, "New Result Contradicts Troubling Old Evidence of Neutrino Oscillation at Small Distances", Physics Today, June 2007, p18; E. Waxman, "Neutrino Astrophysics: A New Tool for Explaining the Universe", Science, 5 Jan. 2007 Vol 315, p63; T. Siegfried, "Neutrino Study Finds Four's a Crowd", Science, 27 Apr 2007, Vol 316, p539; Elgaroy et al., Phys. Rev. Lett., 89, 061301, 2002.

¹⁵ A.H. Guth, The Inflationary Universe, Perseus Books, Reading MA (1997), p. 122

¹⁶ Sources for composite particle properties: Ref. 11, chapters 14-15.

¹⁷ L.A. D'Souza and C.S. Kalman, Preons: Models of Leptons, Quarks and Gauge Bosons as Composite Objects, World Scientific Pub. Co., Pte. Ldt., Singapore (1992)

¹⁸ J.A. Giannini, The FRACEP Model, Part 1b: What Is the Size of the Composite Particles?, part 2 of this book.

¹⁹ J.A. Giannini, The FRACEP Model, Part 2: Why Is There No Evidence Of Internal Structure In Electrons?, in progress

²⁰ J.A. Giannini, The FRACEP Model, Part 3: What Is the Charge Effect?, in progress

²¹ J.A. Giannini, The FRACEP Model, Part 4: What Is the Spin Effect?, in progress

²² J.A. Giannini, The FRACEP Model, Part 5: What Is the Structure Of The Bosons And Field Mechanisms?, in progress

5.0 APPENDIX
A POTENTIAL CONFIGURATION FOR THE FRACEP COMPOSITE FERMIONS

This appendix shows one possible configuration for the composite fermions. It is not necessarily the only configuration. The particles are grouped by their decay characteristics. Section A includes the primary composite particles. Section B includes the secondary composites. Section C includes the heavy composites. It is not intended that these configurations should be interpreted as "the only correct configuration". It is only one possible configuration for the components.

A. The Primary Composite Fermions are stable.

A.1. The FRACEP Electron-Neutrino (n_e- ) is considered stable (Figure A1.a). Scattering can cause it to pick up additional components that allow it to appear to oscillate with other neutrino types as is observed in the SM. Note that the minus sign for the particle in this case indicated the association of n_e- with e^- (i.e., the em-charge is zero). The anti-electron-neutrino (n_e+) replaces SGp with SGm, and would not be stable because of the negative mass component, SGm. (The lines represent free bonds).

A.2. The FRACEP Muon-Neutrino (n_m-) (Figure A1.b), is not considered stable, but possibly appears to oscillate with other neutrino types as in the SM. The anti-muon-neutrino (n_m+) replaces SGp with SGm in the n_m-. The anti-muon neutrino is unstable.

A.3. The FRACEP Electron (e^-) (Figure A1.c) is stable (as it is in the SM). The particle (e^-) has a negative em-charge, and the anti-particle (e⁺) has a positive charge. The anti-electron (positron, e⁺) replaces ne- with n_e+ and QGp with QGm in the electron. The anti-electron is unstable.

Figure A1. This shows the three primary composite fermions of the FRACEP:
a) electron neutrino, n_e- ; b) muon neutrino, n_m- ; c) electron, e^-

B. The Secondary Composite Fermions have a single decay path.

B.1. The FRACEP Up-quark (u⁺), (Figure A2.a) as in the SM, is assumed to be stable inside the potential well of a nucleon (like a proton) otherwise decaying as u⁺ -> 2(1/3e⁺ ) + n_m-. The details of the decay of the FRACEP u⁺ are discussed in Part 2 ^{[Ref. 19]}. Note that the particle (as opposed to the anti-particle) has a positive em-charge (unlike the electron family whose particle has a negative em-charge). The anti-up-quark (u^- ) replaces QGp with QGm ; n_m- with n_m+ and e^- with e⁺ in the up-quark. The anti-up-quark is also unstable.

B.2. The FRACEP Down-quark (d^- ) (Figure A2.b) decays as d^- -> u⁺ + e^- + n_e- (e.g., the same as in the SM). The anti-down quark (d⁺) replaces QGp with QGm; n_m- with n_m+; n_e+ with n_e- ; and e^- with e⁺ in the down-quark. It is unstable. As with the electron family, the down-quark family particles have a negative em-charge, and their anti-particles are positive.

B.3. The FRACEP Muon (m^-) (Figure A2.c) is part of the electron family, and decays as m^- -> e^- + n_m- + n_e+ (e.g., the same as in the SM). Note, the muon has a core structure with an additional momentum carrier group (93R22p). The anti-muon (n_m+) replaces n_m- with n_m+ ; n_e+ with n_e- ; and e^- with e⁺ in the muon. The muon and its anti-muon are unstable.

Figure A2. This shows the three secondary composite fermions of the FRACEP:
a) down-quark, d^-; b) muon, m^-; c) up-quark, u⁺

C. The Heavy Composite Fermions have multiple decay paths.

C.1. The FRACEP Tau-Neutrino (n_t-), (Figure A3.a). It appears to oscillate with other neutrino types as in the SM. The primary oscillation path seems to be: n_e- -> n_m- -> n_t- ; but it may also go directly to n_e-. The anti-tau-neutrino (n_t+) replaces n_m- with n_m+ in the tau-neutrino, and it will be unstable.

C.2. The FRACEP Charm-quark (c⁺) (Figure A3.b) is unstable decaying by two paths. The first is a cascading decay ^{(Ref. 17)} as:

The second can be directly to the u⁺ decay products as indicated in B1 above as: c⁺ -> 2(1/3e^-) + n_m-.

As a member of the up-quark family, the charm-quark, c⁺, (as opposed to the anti-charm-quark, c^-) has a positive em-charge. The c⁺ has a core structure with an additional momentum carrier group. The anti-charm quark replaces n_m- with n_m+ and u⁺ with u^- in the c⁺. Like the charm quark, the anti-charm quark is unstable.

C.3. FRACEP Strange-quark (s^-) (Figure A3.c) is unstable and part of the down-quark family, decaying by three paths. The first is s^- -> c⁺ + e^- + n_e+. The second is s^- -> u⁺ + e^- + n_e-. The third is directly to the u⁺ decay products in B1 above as: s^- -> [2(1/3e⁺) + n_m-] + e^- + n_e+ .

The anti-strange-quark (s⁺) replaces n_m- with n_m+; n_e+ with n_e-; e^- with e⁺; and u⁺ with u^- in the strange-quark. Note that the structure of c⁺ and s^- are determined from the decay of the SM meson K⁰, which has a mass 497.6479987218+/- 0.002 MeV/c^{2 [Ref. 14]}. The K⁰ is defined and decays as K⁰ = d^-s⁺ -> p⁺(u⁺d⁺) + p^-(d^-u^-). The p⁺ and p^- are defined in Table 2 above both with a mass 139.5701702880+/- 5.3x10^-5 MeV/c².

C.4. FRACEP Tau (t^-) (Figure A3.d) is unstable and part of the electron family, decaying by three paths: t^- -> e^- + n_e+ + n_t- , t^- -> m^- + n_m+ + n_t-, or t^- -> p^-(d^-u^-) + n_t- which is the same as the SM decay path. Note, the tau has a core structure with additional momentum carrier groups.

The anti-tau (t⁺) replaces n_t- with n_t+ ; n_m- with n_m+ ; n_e+ with n_e- ; e^- with e⁺; and u⁺ with u^- in the strange-quark. Note that the structure of t⁺ is determined from t⁺ -> p⁺ + n_t+ , where p⁺ = d⁺u⁺.

C.5. FRACEP Top-quark (t⁺) (Figure A3.e) is unstable and part of the up-quark family. It has three decay paths. One is t⁺ -> c⁺ + n_t- + n_m+. The second is to u⁺ + n_t- + n_m+. The third is directly to the u⁺ decay products as t⁺ -> 2(1/3e⁺) + n_m-. The cascade decay of the SM is interpreted in the FRACEP as a series of scatterings followed by decay. That is,

where t⁺ to b^- is a scattering, b^- to c⁺ is a decay, c⁺ to s^- is a scattering, and s^- to u⁺ is a decay.

Note that the top-quark has a core structure with an additional momentum carrier group. The anti-top-quark (t⁺) replaces n_m- with n_m+ and c⁺ with c^- in the top-quark.

C.6. FRACEP Bottom-quark (b^-) (Figure A3.f) is unstable and part of the down-quark family. It has four decay paths. The first is b^- -> t⁺ + e^- + n_e-. The second is b^- -> c⁺ + e^- + n_e+. The third is b^- -> u⁺ + e^- + n_e+. The fourth is directly to the u⁺ decay products b_- -> [2(1/3e⁺) + n_m-] + n_m- + e^- + n_e+.

The anti-bottom-quark (b^-) replaces t⁺ with t^- ; n_e+ with n_e- and e^- with e⁺ in the bottom-quark.

Figure A3. This shows the six heavy composite fermions of the FRACEP:
a) tau-neutrino, n_t- ; b) charm-quark, c⁺ ; c) strange-quark, s^- ; d) tau, t^- ;
e) top-quark, t⁺ ; f) bottom-quark, b^-.