- Preface (updated 5/27/16)
Table of Contents (updated 5/27/16)
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The subject of this work is an alternate view of the fundamental Standard Model fermions and bosons. This new model, the FRACEP Model, treats those particles as composite rather than fundamental.

According to the Standard Model of Particle Physics, the fundamental pieces of matter that make up the universe include particles known as fermions and bosons. This collection of particles (if you include the anti-fermions and anti-bosons) numbers on the order of 50 particles. The Fermions include such particles as electrons, quarks and neutrinos. The bosons include photons, gluons and the infamous Higgs among others.

There are three characteristics that are considered necessary for a particle to be fundamental. These are identified as: 1) homogeneity, 2) uniformity, and indivisibility. Imagine a fundamental particle as a small sphere.

A particle is homogeneous if everything within the sphere is the same stuff. This differs from an atom, for example, because the atom has a core of positively charged protons and zero-charge neutrons. Surrounding the core is a negatively charged electron cloud. Simply put, the core is not the same stuff as the cloud, so the atom as a whole is not a homogeneous particle.

A particle is uniform if the stuff inside the sphere is not lumpy. This means that the content of the sphere is like smooth peanut butter rather than chunky peanut butter. In the atom, the core (nucleus) is like a lump in the electron cloud, so the atom is not a uniform particle.

Finally, a particle is indivisible if it cannot break into pieces. For example, atoms can be split into two pieces if they are collided with fast moving small particles in accelerators. Some atoms spontaneously decay into smaller pieces because they are radioactive. So atoms are not indivisible particles.

Beginning in the early twentieth century, one-by-one the fermions and bosons were observed as experimental techniques developed. At the same time, quantum mechanics was developed and proved to provide accurate descriptions of fermion and boson interactions. Because of their size, the technology of the day did not allow probing the homogeneity or uniformity of these particles. However, a significant number of these particles were observed to spontaneously decay. This appears to violate the indivisibility requirement for a fundamental particle.

By the mid 1970’s, efforts were underway to reconcile the apparent incompatibility of spontaneous decay with the requirement of indivisibility. One such effort was the development of preon models. These models are quantum-mechanically based theories that assume that the fermions and bosons do have internal structure. They have had some success, but have not been accepted as the standard which still treats the fermions and bosons as fundamental.

This brings us to the new FRACEP Model. Unlike the preon models, FRACEP is not based on quantum mechanics. It is a purely heuristic model (at this time). It is philosophical in nature and intended to provide a different view of the nature of matter. It is based on simple arithmetic to add the masses of components to produce mass estimates for the composite particles that agree with the observed properties of the fermions and bosons.

(It is known in nuclear physics that the sum of the masses of the components of atoms equals more that the total mass of the bound atom because of binding energy. At nuclear scales this difference is relatively small. We keep this in mind, but we do not address this issue for the FRACEP composite particles at this time.)

FRACEP hypothesizes a minimum set of truly fundamental particles. It shows how these particles combine to form Intermediate Building Blocks that then combine to construct all of the fermions, anti-fermions, bosons and anti-bosons.

This work, THE FRACTAL RINGS AND COMPOSIT ELEMENTARY PARTICLES (FRACEP) MODEL, presents a collection of papers. Each one provides details of different aspects of the model.

The first paper (__Part 1a__)
begins the process of defining the model. Section 1 provides a historical perspective on the search for the
fundamental nature of matter. This includes an overview of the Standard Model (SM).
Section 2 defines the two fundamental FRACEP particles, the structure of the
Intermediate Building Blocks, and finally the structure of the composite fermions.

Both of the FRACEP fundamental particles have zero spin and zero charge. They have equal and opposite mass.

G0p = +1.724934x10^{-22 } MeV/c^{2}

and

G0m = -1.724934x10^{
-22 }MeV/c^{2}.

For its Intermediate Building Blocks, FRACEP has two spin carriers (one spin and one anti-spin), two charge carriers (one charge and one anti-charge), and a family of momentum carrying particles and rings. The masses of the spin and charge carriers are
~5x10^{-4} and
~1x10^{-6} MeV/c^{2}
respectively). For comparison, this is only a tiny fraction of the mass of the electron
(~0.5 MeV/c^{2}). This view differs from the SM which assumes that charge and spin are inherent and un-separable properties of the fermions.

All of these Intermediate Building Blocks are based on the positive fundamental G0p particle; but, the anti-spin and anti-charge carriers have contributions from the negative fundamental G0m particle. These are the components of the Bright Universe that we see.

However, there is a second possible set of building blocks based on the negative G0m. The structures are identical to the Bright Universe building blocks but the G0m and G0p are interchanged. These are the components of what the FRACEP refers to as the Dark Universe. Although they have not been fully explored at this time, they offer a possible explanation to the nature of the dark matter and dark energy that astronomers believe populate the cosmos.

Finally, this paper defines the FRACEP composite structures for the fermions. It shows that the mass, charge and spin agree with the SM observations of the fermions within the experimental uncertainty. Also, the FRACEP structures provide the same decay components as the unstable SM fermions.

The second paper (__Part 1b__)
considers the question of physical size for the FRACEP composite structures. After a general
introduction in Section 1, Section 2 provides a detailed discussion of the meanings and measures
of size over the range from the macro world down to the quantum world. Section 3 goes on to discuss the fundamental scales of nature. These length-, mass-, and time-scales are the smallest scales in the universe and are an integral part of any size estimate of fundamental particles
and composite fermions.

Section 4 defines the assumptions used in making the size estimates. It goes on to estimate the physical size of the G0p and Intermediate Building Blocks. For the purposes of this paper, physical size is defined as the classical radius of the particle rather than its quantum mechanical Compton wavelength. Because G0p is the smallest possible particle, its size equals the smallest possible length scale in the universe.

Classical Radius of the G0p =
3.3075190x10^{-35}m.

Finally, Section 5 develops the size estimate for the composite
fermions. The maximum expected fermion size estimated by the SM
is <10^{-18 }m. It makes no size
distinction based on fermion mass. FRACEP, on the other hand, builds up the fermions as composite particles. This means it has the capability to distinguish size based on increasing mass.
The FRACEP mass estimates for the composite
fermions range between 9.92x10^{-25}m
and 4.46x10^{-19 }m for the
smallest to the largest masses.

The sixth paper (__Part 5__)
presents the composite structure of the bosons and considers the field mechanisms. Section 1 provides a summary of the philosophy and observations of the Standard Model (SM) regarding the elementary bosons and the field mechanisms relating those bosons to the elementary fermions. Section 2 describes the structure of the FRACEP composite bosons and their corresponding anti-particles as composed of combinations of the FRACEP composite fermions.

In defining the composite fermion structure, two sets of fermions are proposed by FRACEP. One set includes the “bright universe” fermions – that correspond to the SM fermions and anti-fermions. The second set includes the “negative universe” (dark) fermions and (dark) anti-fermions. These are equivalent to the bright universe fermions but with opposite mass – that is, the mass is negative.

It is hypothesized here that the FRACEP bosons are the connection between the bright universe and the negative universe. There are four types of bosons: the electromagnetic field exchange particle (the photon), the strong field exchange particles (the gluons), the weak field exchange particles (the W^{-}, W^{+} amd Z^{0}), and the higgs that gives all its particles mass according to the Standard Model.

As the connection between the bright and negative universes, FRACEP proposes that each of its composite bosons have components from both universes.
The photon is described as a loosely bound state of the bright universe electron (e^{-}) and the
negative universe dark electron (e_{d}^{+}). Because the negative universe electron has an equal but opposite mass from the bright universe electron, the loosely bound pair has a net zero mass as required by the SM. FRACEP also proposes an anti-photon composed of the anti-particles in its composite photon. This anti-photon is not directly observable with current technology or techniques; and, it is not recognized in the SM.

FRACEP proposes that a gluon is composed of a base structure plus a color charge structure and an anti-color charge structure. The combination of five different bases and three color charges and three anti-color charges provides the necessary eight gluons and their anti-particles as defined by the SM. The gluon base structures and the color charges and anti-color charges are composed of combinations of bright universe and negative universe electron-neutrinos and anti-electron-neutrinos. The varying combinations of the components provides zero (or near-zero) masses for the gluons as required by the SM.

The eighth paper (__Part 7__)
addresses the issue of the interaction potential. Physics has identified four fundamental forces that drive matter interactions: the electromagnetic, the nuclear strong, the nuclear weak, and gravity. The potential functions that describe the particle and object interactions for each of the four forces are different but have some characteristic similarities.

It is assumed here that the interaction of matter, regardless of scale, follows the same potential rule - that is, it can be modeled with the same mathematical function. The difference in the appearance (apparent functional form) of the potential at the different (nuclear, macro, or cosmic) scales is the result of the limiting behavior of the function at the different scales.

The FRACEP potential presented here represents the initial effort to develop a universal, multi-term function that agrees, in behavior, with the standard interaction potentials at all scales - though not necessarily with the specific recognized mathematical functions at each scale.

Section 1 of this paper describes the two well-known interaction potentials: 1) the macro scale potential of gravity, and 2) the quantum scale nuclear potential. Section 2 defines the FRACEP potential - including its mathematical form and a comparison with the two well-known potantials from the smallest to the largest scales.

The FRACEP potential takes the form:

V_{FRACEP} = (A_{0}(M) + B_{0}(M))
x sin(arg(r,M)) x exp(K_{4}(M) r)

and

arg(r,M) = (150p/180)
[K_{1}(M) r^{2} + K_{2}(M) /r +
f(M) /r^{3}+ K_{3}(M)]

where M is a scaled mass. All of the scaling factors were determined to provide the best fit to the behavior of the recognized potentials. This potential demonstrates not only the traditional behavior in each of the scaled regions, but, also behavior in the transition between the macro scales of the gravitational force and the quantum scales of the nuclear forces.

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The following papers represent ongoing investigations that will be included when results become available.

Paper three (Part 2) will consider the origin of the mass instabilities, decay paths and half-life of the composite particles.

Paper four (Part 3) will discuss the nature of the charge effect. The relation between the total mass and total charge will be quantified.

Paper five (Part 4) will discuss the nature of the spin and anomalous magnetic moment effects.

Paper seven (Part 6) will discuss the FRACEP Dark Universe (negative mass) particles as in relation to the nature of dark matter and dark energy.

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