Page 1 of 10

European Journal of Applied Sciences – Vol. 11, No. 5

Publication Date: October 25, 2023

DOI:10.14738/aivp.115.15597

Giannini, J. (2023). Mass and Size Characterization of FRACEP Composite Elementary Fermions. European Journal of Applied

Sciences, Vol - 11(5). 212-221.

Services for Science and Education – United Kingdom

Mass and Size Characterization of FRACEP Composite Elementary

Fermions

Judith Giannini

Independent Researcher/USA

ABSTRACT

The FRACEP model characterizes the entire set of Standard Model elementary

fermions as composite particles having a preon-like fractal-based structure. The

internal components have several levels of complexity, beginning with the fractal

structures of the momentum carriers, and the dynamic charge carriers and spin

carriers. These base structures combine in a series of nested 3-element preon-like

components that build up the composite fermions (the subject of this paper) and

composite bosons. The entire structure is based on only two fundamental particles

forming the basis of a Dual Universe containing positive mass particles, negative

mass particles, and mixed mass particles. This system offers an intuitive

explanation for the observed decay of the particles that are otherwise assumed to

be fundamental because only positive mass particles or negative mass particles are

long-term stable. Repulsion within a mixed mass particle is only quasi-stable for

very short times. The estimate masses for the composite fermions are consistent

with the Particle Data Group’s 2016/2020-update estimates, and the estimated

radii are consistent with published expected upper size limits for the Standard

Model’s fundamental elementary fermions.

Keywords: Composite Elementary Particles, Standard Model Elementary Particles,

Fractals, Particle Radii Estimates, Negative Mass, Preons.

INTRODUCTION

The spontaneous decay of most of the Standard Model Elementary Particles (SMEP) suggests

the possibility of a composite nature in particles generally assumed to be fundamental. D'Souza

and Kalman [1] provide a good summary of the concerns of the completeness of the Standard

Model, and the issues leading to the interest in compositeness in its particles. FRACEP [2] was

developed as an arithmetically-based model that presents a composite structure with fractal- based components for the SMEP, providing an intuitive explanation for why the SMEP (assumed

all positive mass) decay.

The Standard Model is highly successful at predicting the behavior of the world of the small. It

has a quantum mechanical-based theoretical part treating the particles as fundamental and

describing particle interaction; and, an empirical part characterizing the SMEP set containing

24 fermion-class (spin-1/2) particles, and 26 boson-class (integer spin) particles. The

designations fermion and boson indicate both the particles and their corresponding anti- particles.

The fermions include six leptons divided equally among two families, plus an equal number of

anti-particles, and, six quarks divided equally among two families, plus their anti-particles.

Page 2 of 10

213

Giannini, J. (2023). Mass and Size Characterization of FRACEP Composite Elementary Fermions. European Journal of Applied Sciences, Vol - 11(5).

212-221.

URL: http://dx.doi.org/10.14738/aivp.115.15597

They have mass (acquired through the Higgs mechanism) and inherent characteristics of spin,

most with electric charge, and quarks with color charges.

The bosons are the field-exchange particles: 1) the photon for the electromagnetic field, the W+,

W-, and Z0 for the weak field, the eight gluons for the strong field, and the higgs that couples to

the Higgs field providing all the particles with mass. The bosons have Higgs provided mass and

the inherent characteristics of spin, some with electric charge, and some with color charge.

The FRACEP model characterizes the entire set of SMEP as composite particles built up from

top-level internal components that are preon-like repeated groupings of three fractal carrier

types: momentum-carriers, charge-carriers, and spin-carriers. The fractal structures are built

up from the two fundamental particles. Color charge is a component composed of composite

neutrinos and anti-neutrinos. Because the components are fractal structures, we consider the

composite versions of the SEMPs to be fractal-like structures as well. This paper focuses on the

preon-like fractal-based structure of the composite fermions. The discussion of the bosons is

reserved for another work.

THE FUNDAMENTAL PARTICLES AND SCALES

There are two fundamental particles that are used to build up all of the internal components of

the FRACEP composite particles [2], The Gp, and Gn have zero electric charge, zero spin, and

mass (m(Gp) = +1.724934x10-22 MeV/c2, and m(Gn) = -m(Gp)). The mass is inherent, and the

Higgs mechanism is not required for them because of their total symmetry at creation (in pairs).

This results in a Dual Universe concept – a Bright Universe (mostly positive mass), and a Dark

Universe (mostly negative mass), allowing a possible answer to the Dark Matter/Energy

problem in cosmology. FRACEP hypothesizes that the classical radius of Gp is the scale- invariant Planck length derived by Hoyle, r(Gp) = 3.307519x10 [3]. This reflects a symmetry in

nature. where the smallest mass particle (FRACEP’s Gp) is assumed to be the reciprocal of the

largest mass particle (the Planck particle, mass mp*= 5.97x1021 MeV/c2). FRACEP’s potential

computations [4] indicate the closest stable approach of any two Gp‘s is ~r(Gp). Also, the Gp

and Gn cannot approach closer than this because their repulsion only allows the configuration

to be quasi-stable in the oscillating region of the potential.

THE CARRIER COMPONENTS

The Momentum Carriers

The momentum carriers are composed only of the fundamental particles. They have zero spin

and zero charge, and are the basis of the structure of all of the composite particles. The basic

general particle is spherical, composed of a 6-element ring plus three additional elements at

any fractal level such that the mass is m(MGXp) = m(Gp) • 9

X within a radius r(MGXp) = 4X

r(Gp). A similar structure based on Gn also exist.

The ring structure is a regular hexagonal composed of six particles at any fractal level such that

the mass is m(MRXp) = 6 • [m(Gp) • 9

X]. A similar structure based on Gn also exist. The ring is

confined to a two-dimensional plane. At any fractal level, its radius is r(MRXp) = 4X+1 r(Gp),

and its thickness equals the diameter of its particles, h(MRXp) = 2X+1 r(Gp).

Page 3 of 10

Services for Science and Education – United Kingdom 214

European Journal of Applied Sciences (EJAS) Vol. 11, Issue 5, October-2023

Fig. 1: The general particle and ring structure at the zero and first fractal levels.

All of the separation distances between pairs of elements along the ring are exactly the same

length. To maintain equal separation between particle pairs in the general particle, the three

additional elements must be out of the plane of the ring. Two of the particles are above the ring

plane and one is below [5].

The Charge-Carriers

The charge-carriers are fractal configurations composed only of the fundamental particles.

They have mass and charge, but zero spin, and are components in all of the composite particles

with the exception of the neutrino family particles, their anti-particles, and their dark

counterparts because those particles have zero charge.

The charge-carrier structure is composed of two charge-carrier-specific parts: 1) a charge- momentum part (MQp with only positive mass, or MQn with only negative mass), and 2) a

charge-effect part (QEp with only positive mass and a negative charge, or QEn with only

negative mass and a positive charge). MQp and MQn carry the bulk of the mass but no charge

or spin. The mass is m(MQp) = m(MG19p) + 2 m(MG13p) + 48 m(MR13p) + 121 m(MR16p). A

similar structure exists for MQn using Gn with m(MQn) = –m(MQp). QEp and QEn are dynamic

structures producing the observed charge, but have only a small amount of mass and no spin.

The charge effect is captured in a pair of linear chains where the mass of the pair is m(QEp) = 2

m (Gp) • 4

19, or m(QEn) = 2 m (Gn) • 4

19

.

The charge-carrier is assumed to be roughly spherical, with the components within MQp

organizing into a spherical configuration, while the QEp remains a chain. The radius of the