FRACEP Model, Part 1a

One of the most challenging activities in physics is to determine the "correct" description of the fundamental nature of matter. Today, this description is captured in the Standard Model (SM), which contains a set of fundamental particles (fermions and bosons) that are treated as point-like lumps of homogeneous stuff. Considerable evidence supports the idea that these particles may be composites of more fundamental particles.

The new FRACEP Model presented here provides a description of a set of composite fermions and bosons with internal components that are consistent with the observed characteristics of the SM particles. To fully appreciate this change of view of the fundamental world, it is helpful to consider the evolution of ideas on the fundamental nature of matter over time.

When one wishes to wax eloquently about the nature of matter and physical phenomena, one invariably turns to the beginning to provide enlightenment regarding the evolving picture. We are immediately reminded of the mythological basis of man's attempts to understand his world and the universe at large. Mythologies of the ancient civilizations all, to one degree or another, personify the celestial bodies, including earth, in their gods, and attribute physical effects to the actions of those deities ^{[Ref. 1]}. This mindset led inevitably to temple building (celestial observatories) and the mathematical tools that allowed accurate observation of the sun, moon and stars.

Based on astronomical analysis of temple orientation, Lockyer dates the earliest observatories in Egypt to possibly as early as 6400 BC, and some Greek temples, showing signs of Egyptian inspiration, to as early as 1500 BC ^{[Ref. 2]}. According to Yoke, Chinese astronomical observations can be traced to earlier than 1500 BC, but how early is uncertain mainly because of lack of surviving documents and monuments of greater antiquity ^{[Ref. 3]}.

These early observatories and their accompanying mathematical tools mark the beginning of science in the human race. However, the mere acceptance of the existence of the universe, as an end to his inquiries, was not sufficient. Once the origin of all things was suitably explained (albeit in mythological terms), attention was turned to a finer look at the structure of matter. This study, which has been on-going for a few thousands of years now, is what has developed into the chemistry ^{[Ref. 4, 5]} and physics ^{[Ref. 6, 7, and 8]} that we know and love today.

The earliest musings on the composition of nature that has directly filtered into western science (where there is definitive writing on the subject), dates back to the classic Greek philosophers. Thales, in 5^th century BC, proposed the prime matter to be water because of its ability to change states from gas to liquid to solid (inspired by the Babylonians who believed that water was the origin of the cosmos). Later, Empedocles introduced the 4-element theory which stated that the four elements (fire, water, earth and air) were composed of minute, unchanging particles; and, for the first time, there were forces describing matter interaction (Love and Strife) which caused elements to combine or separate.

In the early 4^th century BC, Demokritos introduced the ideas of a void in which the 4 elements were in continuous, random motion, and, of shaped atoms that became entangled to produce visible substances. A competing theory by Aristotle proposed that all matter was made of the same stuff (hyle), and that the different substances were the result of varying amounts of the properties of hyle in the 4 elements. He believed that all substances were homogeneous and continuous, and that there were three types of elemental combination by which the original elements lost their basic character to produce new substances (transmutation). These early Greek ideas are a long way from the current understanding of matter but they captured the concept of fundamental lumps of stuff in the large-scale substances of nature.

The Aristotelian picture was accepted throughout the Middle Ages with little change in the notion until the 16^th century when it began to be challenged. The atomist theory started to gain acceptance as the combination of experiments, coupled with mathematical abstraction, allowed the development of the advances evident in modern science. By the end of the 19^th century, it was known that all matter was composed of indivisible atoms that made up a set of nearly 100 fixed elements.

In 1905, Mendeleev published his successful organization of those elements into the Periodic Table still in use today ^{[Ref. 5]}. For a period of almost 40 years, he studied the elements and their properties, advancing the notion that there were simple bodies (containing a single element) and compound bodies (containing two or more elements), and identifying a phenomenon known as allotropy (that molecules of a given element can exist in several different configurations), but rejecting the notion of substructure in the atoms even in the face of rising evidence to support the idea.

This period, from the 16^th through the 19^th centuries, represented a time of growing complexity - from four fundamental substances that made up everything to over 100 types of fundamental stuff (each a different type of atom). We recognize today that the sheer number of elements and the periodic regularity of their properties strongly suggest sub-atomic components. This evidence of complexity (based on something more fundamental as yet undiscovered) was only beginning to be recognized in Mendeleev's time.

The first hard evidence of these smaller particles came in 1896 with the discovery of radioactive decay by Becquerel when he observed the transmutation of one element to another ^{[Ref. 6, Chapter 15]}. A second piece of evidence came in 1897 with the discovery of the electron by Thomson ^{[Ref. 6, Chapter 16]}. The modern concept of the atom began to take shape in 1919 with the experiments of Rutherford who described the atom as a dense positively charged nucleus surrounded by a negatively charged electron cloud ^{[Ref. 6, Chapter 19]}. Further, he proposed the nucleus consisted of positively charged particles (protons) and neutral particles. The neutron (Rutherford's neutral particle) was discovered in 1932 by Chadwick ^{[Ref. 6, Chapter 20]}. Thus, the field of elementary particles began to take shape.

Because of these discoveries, it became clear that there were fundamental building blocks (electron, proton and neutron) that were smaller than the atom (what had previously been thought to be fundamental). At this point, the understanding of nature began to return to simplicity - from over 100 fundamental types of matter to only three fundamental particles that combined to produce all the variety of nature.

With new experiments since the time of Chadwick, the initial family of three fundamental particles began to grow again. The positron (also called the anti-electron - an electron with positive rather than negative charge) was discovered in 1932. Then heavy particles (~ 200-300 times the mass of electron, but only about 1/3 the mass of the proton) were discovered. These heavy particles (the Mu -meson, discovered in 1936, and the Pi -meson in 1946) were believed to be related to the working of the nuclear force that held the atomic nucleus together and therefore must be fundamental.

In addition to experimental discoveries, the 20^th century saw an entirely new picture of the world emerging in the theoretical developments of the time. Quantum Mechanics ^[Ref.
9] and Relativity ^{[Ref. 10]} provided the tools to understand the smaller world of the new particles that were being discovered, accurately predicting the outcome of the ever more sophisticated scattering experiments and pointing the way to new particles that were needed to explain observations.

The experiments in the 1950's and 1960's produced evidence of so many new particles (over 100) that a reorganization of the elementary particles into groups based on their common properties was needed. The growing complexity of so many fundamental particles indicated the need to recognize the truly fundamental nature from the composite nature in the "zoo" of what had been thought to be fundamental particles. As a result, the particles were grouped into two types: 1) fundamental with no internal structure, and 2) composite with internal, smaller components.

Because of the new organization, some particles, previously believed to be fundamental (like the proton and neutron that make up the atom nuclei) were demoted to composite status. Once again, the understanding of nature was returning to a simpler configuration - from a "zoo" of fundamental particles to a few fundamental particles that combined to produce the composite particles. But is this current organization truly simple enough?

The focus of this paper will be a different description of the fundamental particles of the SM database. As a primarily heuristic model (at this time), the FRACEP demonstrates the possibility of a set of only two truly fundamental particles that can be used to construct the fermions and the bosons. The demonstration takes the form of spherical building blocks with the necessary a-priori characteristics with a more detailed discussion of those characteristics presented later. In light of this emphasis, a discussion of the quantum mechanical based theory of the SM will not be included here, but, can be found in detail in Povh ^{[Ref. 11]}. Before proceeding to the FRACEP, a general description of the SM is provided for reference.

The Standard Model^{[Ref. 12]}was developed during the 1960's and 1970's to explain the experimental observations, as well as, to elucidate the fundamental nature of matter. This model is a semi-empirical model that contains a database of fundamental particles and their characteristics, a mathematical formalism based on quantum mechanics for encoding the rules for particle interactions, and, a long list of composite particles including their composition of the fundamental particles.

The SM fundamental particles are shown in Table 1. They are modeled as point-like (zero-size), with no internal structure. Their numbers include: 12 fermions, 12 gauge bosons and one Higgs (vector) boson for 25 elementary particles. Each particle is associated with an anti-particle of equal mass but opposite charge and spin, giving a total of 50 fundamental particles. (Traditionally the word fundamental implies: homogeneous - the same stuff throughout; uniform - even distribution throughout; indivisible - inability to break apart into pieces either spontaneously or by scattering; and, with intrinsic properties like spin and charge).

The characteristic of spin causes the particle to act as if it were spinning like a top on its axis, and affects the observed particle energy. The superscripted + and - indicate the sign of the particle electromagnetic charge. For the fermions, the particles of the electron family and the down-quark family have a negative charge while the anti-particles have positive charge. The up-quark family particles have a positive charge, with the anti-particles having the negative charge. The universe in which we live, and can see, is populated mostly by particles rather than anti-particles. The neutrino family has zero charge, so the distinguishing characteristic for the anti-neutrino is its negative spin.

TABLE 1. This shows the characteristics of the fundamental particles of the Standard Model including: em-charge (q_e, in units of the electron charge); particle name, symbol and masses ^{[Ref. 13]} with their measurement uncertainties in parentheses (in units of MeV/c²). Note the bosons do not have the family structure of the fermions.

Fermions: Leptons (spin ½)
q_e	Generation 1	Generation 2	Generation 3
0	e-neutrino ( n _{e -} ) 15x10 ^- ⁶	m -neutrino ( n_m- ) <0.17	t -neutrino ( n_t- ) 18.2
- 1	electron (e ^- ) 0.5109989 ( +4.0x10 ^- ⁸	muon ( m ^- ) 105.65835 (+4.9x10 ^- ⁸	tau ( t ^- ) 1777.0529 (+1.6x10 ^- ⁴
Fermions: Quarks (spin ½)
+²/₃	up (u⁺ ) 1.5-4.5	charm (c⁺ ) 1100-1400	top (t⁺ ) 173,700-182,300
- ¹/ ₃	down (d ^- ) 5.0-8.0	strange (s ^- ) 88-155	bottom (b^- ) 4100-4400
Gauge (Vector) Bosons (spin 1)
q_e	Particle
0	photon (g ) <2x10^- ²²
+1	W⁺ 80,423(+39)
- 1	W^- 80,423 (+ 39)
0	Z⁰ 91187.6 (+ 2.1)
0	8 gluons (g_i ) ~ 0
Higgs (Scalar) Boson (spin 0)
0	higgs (H) ~117,000

Note that traditionally the three neutrinos were believed to have zero mass, but models of the sun's energy production were inconsistent with the number of measured solar neutrinos. To address this problem, the model was adjusted to include neutrino oscillation (transformation from one neutrino type to another during flight) among the three types, requiring the mass limits currently accepted as shown in the table ^{[Ref. 14]}. An attempt to measure the neutrino mass by Elgaroy et al. ^[Ref.
14] using cosmological data and a model, that includes cold dark matter and a cosmological constant, concluded that the sum of the masses of the three neutrinos was no more than 2.2x10^-6 MeV. This value does not represent a definitive change in the mass estimates of the SM at this time.

The fermions have spin ½. There are four types each with a different electromagnetic charge. Each type has three family members within which the properties are identical except for the mass which increases with each generation over the mass of the previous one. Of the fermions, only the electron is stable. The others spontaneously decay into lighter fermions. It is not clear if the oscillation of the neutrinos (the zero charge type) represents evidence of the particles’ compositeness.

Of the electron family, the muon has a single decay path (m^--> e^-+ n_e₊ + n_m-), but the tau has three paths (t^--> e^-+ <15.0pt'>+ n_m+ + n_t- ; and t^- -> p^- + n_t- , where p^- is a coupled pair of quarks, d^-u^- ). For the quark families, the up-quark is considered stable in the proton or neutron but the down-quark decays as: d^--> u⁺+ e^-+ n_e₊.

The Bosons have integer spin. Unlike the fermions, there are no mass increasing generations for the different types. Each of the particles is associated with one of the fundamental fields. The photon is coupled to the electromagnetic field; the W⁺, W^- and Z⁰ are coupled to the weak field responsible for radioactive decay; and the gluons are coupled to the strong nuclear field that holds complex particles and atomic nuclei together. The higgs couples to the Higgs field which, theory postulates, is responsible in some way for the mass that all the other particles have, but this is yet to be verified. Of the bosons, only the photon and the gluons are considered stable. The Z⁰ decays by multiple paths (Z⁰ -> e⁺ + e^-; Z⁰ -> m⁺ + m^-; and Z⁰ -> t⁺ + t^-). Likewise, the W⁺ and W^- decay paths include: (W⁺ -> e⁺ + n_e_-; W⁺ -> m⁺ + n_m-; and W⁺ -> t⁺ + n_t-) and (W^- -> e^- + n_e₊; W^- -> m^- + n_m+; and W^- -> t^- + n_t+).

Of the SM fundamental particles, only the e, m, t and the photon have been directly observed. All the others are indirectly observed from their decay products; and, the gluons and higgs still have no experimentally observed evidence.

In addition to the fundamental particles, the SM defines about 100 composite particles (the hadrons) which have two types: the baryons and the mesons. The baryons and mesons mentioned above are listed in Table 2. A more complete listing is given in Guth ^{[Ref. 15, p. 122]}.

The Baryons are spin ½ particles composed of three quarks. (The only known stable baryon is the proton, the next longest lived is the neutron at 886.7 seconds; all others have lifetimes less than 10^-7 seconds). The Mesons are integer spin particles and are composed of quark - anti-quark pairs. None are stable and all have lifetimes less than 10^-7 seconds. Like the fundamental particles, the composite particles are each associated with an anti-particle. Because this paper is concerned with the SM fundamental particles, the SM composite particles will not be discussed; however, more information can be found in Guth ^{[Ref.
15, chapter 7]} and Kane ^{[Ref. 12]}.

The size and energy scales of the SM particles can be compared to the scales of what was previously considered fundamental in times past as an example of how thoughts have changed with new insight.

(1) Quarks, leptons and gauge bosons are point-like (radius <10^-¹⁸m) - current SM fundamental particles.

(2) Baryons, like the proton, are ~ 10^-15m with excitation energies ~0.3GeV or more - listed among the fundamental particles in the 1920s', but currently classified as composite.

(3) Atomic nuclei (e.g., lead, ²⁰⁸Pb) are ~ 10^-14m with excitation energies ~3MeV or more.

(4) The atom (e.g., nucleus plus electron cloud, ²³Na) is ~ 10^-10m with excitation energies ~3eV or more - considered fundamental in Mendeleev time (1906) though the details of the atom structure were unknown until Rutherford's model.

TABLE 2. This shows the characteristics of selected composite particles of the Standard Model mentioned above are shown with particle name, symbol and quark composition; masses ^[Ref.
16] (in units of MeV/c²); spin; em-charge (q_e, in units of the electron charge); and half-life decay time (in seconds). A more complete list of the composite particles can be found in Guth ^{[Ref. 15]}.

Composition	Mass (MeV/c²)	Spin	q_e	Half-life (seconds)
Baryons
proton (p) (u⁺u⁺d^-)	938.3	½	+1	stable ( i.e., >10³² yrs)
neutron (n) (d^-d^-u⁺)	939.6	½	0	886.7
Mesons
Pi-minus (p^-) (d^-u^-)	139.6	0	-1	2.6.10^-⁸
Pi-plus (p^-) (d⁺u⁺)	139.6	0	+1	2.6.10^-⁸

One final point about the SM should be addressed. Current thinking on the fundamental nature of the fermions and bosons recognizes the evidence pointing to the possible compound nature of the particles. Research on some fronts (on going since the 1980's ^{[Ref. 17]}, though not the accepted standard) addresses the internal particles (preons) that compose the fermions and bosons in preon theory.

In standard quantum mechanics, each fundamental particle (e.g., the electron) is represented by a single wave function which can have more than one state, so some processes are represented by weighted sums of the multiple states. In preon theory, the fermions and bosons are represented by multiple wave functions (each for one of the preon components in the fermion) in a quantum mechanical-like frame-work. A fully developed theory has not yet been accomplished; and, a consistent minimum set of fundamental preons (with specific characteristics) has not yet been identified.

The motivation for the FRACEP development was to determine the feasibility of constructing a composite structure for the fermions and bosons that (1) is based on a minimum set of only two fundamental particles, and (2) is consistent with the SM observations.

The SM has had remarkable success in its predictive capability; however, as with any model attempting to describe phenomena that cannot be seen directly, it has difficulties yet to be solved. Throughout his book, Povh ^{[Ref. 11]} list no less than two dozen unresolved issues.

The FRACEP was intended to address some of those points by providing a look inside the smallest known particles because the current observations are highly suggestive of internal structure. These observations are very much the same as those that directly preceded the new level of understanding about the nature of the fundamental particles at the close of the 19^th century, and, can be stated today as: (1) the large number of SM fundamental particles - at least 25 if you don't count anti-particles, (2) the spontaneous decay of most of the SM fundamental particles, and (3) the obvious family structure (of unknown origin) of the leptons and quarks.

The FRACEP construction has a set of only two fundamental particles (of equal but opposite mass, i.e., plus M and -M) which are clumped in fractal-like groupings to produce the intermediate building blocks of momentum, spin and charge carriers that make up the fermions and bosons. The FRACEP construction, presented here, satisfies the SM observed mass, spin, charge, and decay path for those particles. Other particle characteristics in the SM are not addresses in this initial work.

The FRACEP takes a different look at the fundamental em-charges, which some observations suggest may be fractional and symmetric. In the SM view, the fundamental em-charges include: (1) -1e for the electron family, (2) +2/3e for the up quark family, and (3) -1/3e for the down quark family. (To put it another way, the fundamental charge, -1e, is rotated through a phase-like angle to produce the charges on the quarks).

The FRACEP construction includes only two basic em-charge carriers (-1/3e and +1/3e) which are components in the composite structure of the observed charged particles. Other aspects of the FRACEP particles are considered separately. Part 1b ^[Ref.
18] presents the estimated size of the composite fermions.

Further ongoing investigations will be included in future reports. Part 2 ^{[Ref. 19]} will provide an explanation of the origin of the mass instabilities, decay paths and half-life. Part 3 ^{[Ref. 20]} will discuss the nature of the charge effect and the relation between the mass and charge is quantified. Part 4 ^[Ref.
21] will discuss the nature of the spin and anomalous magnetic moment effects. Part 5 ^{[Ref. 22]} will present the composite structure of the bosons and the field mechanisms.