PART 1

ELEMENTARY PARTICLE SPATIAL MODEL

1. BACKGROUND - BILLIARD BALLS WITH ENGLISH

A good response to a Jeopardy quiz show answer; "Protons, neutrons, electrons and photons" would be "What are the elementary particles for matter and light?" However, scientists have been expanding that answer over the last sixty or more years. The first new particle added to the list was the neutrino which was needed to account for how electrons, called beta particles in this case, are ejected from nuclei during the beta decay process. After the discovery of the neutrino there has been a long list of newly discovered particles numbering into the hundreds. The increasing number of elementary particles seems to be in one area, the hadrons. The leptons and photon have been relatively well behaved.

The hadrons are particles that interact through the strong force which is the force that holds the protons and neutrons together in atomic nuclei. Hadrons in turn are divided into two subgroups, the baryons and the mesons. Baryons include particles such as protons and neutrons. Mesons include the pi mesons or pions. The leptons are particles such as the electron and the neutrino that do not interact through the strong force. To date there are only six known leptons and these have been divided into three subgroups or generations. The leptons are listed in Table 1-1 for future reference.

Notes: 1) In order that the Greek alphabet letters can be read, please set your browser preference to use page-specified fonts.

2) The symbol * is used to indicate an "anti-" particle.

Table 1-1

LEPTONS

First Generation
e-	The electron is the negative charge particle of electricity and is stable.
ne	The neutrino or electron-neutrino is neutral in charge, is stable and may be massless.
Second Generation
m-	The muon is similar to the electron but is over 200 times heavier and is unstable.
nm	The muon-neutrino is similar to the electron-neutrino.
Third Generation
t-	The tau is similar to the electron but is over 3500 times heavier and is unstable.
nt	The tau-neutrino is similar to the electron-neutrino.

The photon, g, (gamma), is the only particle associated with electromagnetic radiation which in a limited energy range is called light. X-rays, microwaves, and radio waves represent other photon energy ranges.

Many times the elementary particles are represented merely by their letter notation, such as "p" for the proton and "n" for the neutron. Sometimes the electric charges "+", "-", or "0" are also added. In order to give the elementary particles some substance, they have been shown as either circles or spheres. Light is usually depicted either by the g symbol or by a sine wave curve.

Each of the elementary particles has a quantized spin associated with it which is a multiple of Planck's constant (h) divided by 2 pi, or h/2pi. Planck's constant is an extremely small number. The quantizes spin is either a non integral multiple (1/2, 3/2, 5/2,...) or an integral multiple (0, 1, 2,...) of h/2pi. In many cases, including here, the h/2pi is dropped as being understood. The spins for the various particle types have been determined. The hadrons have particles with both spin types. The baryons have non integral spins and the mesons have integral spins. All leptons have spin 1/2. The photon has a spin of 1. The non integral and integral spin particles follow very different rules. The particles with non integral spin follow the Pauli Exclusion Principle which does not allow two particles to have the same quantum state. The particles with the integral spin do not follow the Pauli Exclusion Principle. Thus, two electrons (each with spin 1/2) in a single atom must differ from each other while many photons may be exactly the same. One way that two spin 1/2 particles, such as two electrons, can follow the Pauli Exclusion Principle is to have their spins align in opposite or non parallel directions.

Spin is not always shown in the representation of the elementary particles. However when the particle's spin is shown, it is usually shown either as an arrow on a circle or as a curved arrow above a sphere. The comparison of the arrows from one particle to another depicts if their spins are aligned or not.

Particles also have masses which can be expressed in terms of energy by use of the Einstein energy-mass conversion equation, E = mc² . The mass unit which shall be used here is the Gev (Giga-electron volts) which gives convenient numbers for particle masses. For example, the proton mass can be expressed as 0.938 Gev and the electron mass can be expressed as 0.00051 Gev. In addition, each of the particles has an antiparticle; e.g., the positron is the antiparticle of the electron. A particle~antiparticle pair will annihilate each other and release energy in accordance with the above energy-mass conversion equation.

Returning to the multiplying hadrons concern, it became apparent in the 1960's that the hadrons might not be elementary particles after all. In 1964 Murray Gell-Mann proposed the quark model for the hadrons. There are now considered to be six quarks which are divided into three subgroups with two quarks in each subgroup. Each pair of quarks has been associated with the corresponding lepton generation described above. The quarks have some unusual properties including fractional charges and the fact that a quark has never been isolated.

The six quarks are called flavors. The quark flavors are up (u), down (d), strange (s), charm (c), top (t) and bottom (b). The last two quarks have also been called truth and beauty. In addition, each quark has an antiparticle of the same mass but opposite charge. So how does this solve the hadron problem? What Murray Gell-Mann discovered is that every meson could be represented by q*q, where q* represents a generalized (i.e., not specified) quark antiparticle and q represents a generalized quark particle. Also, every baryon could be represented by qqq. For examples, the pi+ meson is represented by d*u, the proton is represented by uud, and the neutron is represented by udd. Currently, the graphic representations of the quarks within particles such as pi+, p and n are usually by either circles or spheres along with quark symbols and possibly arrows for spin.

Normally, the antiquark is represented by the corresponding letter with a bar above it; however, this form does not always transfer well between computer programs. Talking about conventions, the spelled-out Greek letters will usually be used rather than the symbols for ease of the internet presentation. In addition, the superscript and subscripts were lost in the transfer by the hmtl editor and were not restored because it is not clear how the various web browsers would present them.

Table 1-2 lists the quarks, symbols, charges, and calculated masses.

Table 1-2

QUARKS

Quark	Quark Symbol	Anti-quark Symbol	Quark Charge	Anti-Quark Charge	~ Mass
First Generation:
up	u	u*	+ 2/3	-2/3	0.3 Gev
down	d	d*	- 1/3	+1/3	0.3 Gev
Second Generation:
charm	c	c*	+ 2/3	-2/3	1.5 Gev
strange	s	s*	- 1/3	+1/3	0.45 Gev
Third Generation
top	t	t*	+2/3	-2/3	>45 Gev
bottom	b	b*	- 1/3	+1/3	4.9 Gev

The quarks are grouped into generations similar to the leptons. The first generation of quarks and leptons make up our everyday world of protons, neutrons, electrons, and neutrinos. The quarks have fractional charges of -1/3 and +2/3 as compared to integral charges of -1 for the electron and +1 for the proton. Each quark also has an antiquark which has the opposite charge of its corresponding quark. The calculated masses of the quarks can be compared to the masses of the proton and neutron which are both just under 1 Gev.

Each quark has a spin of 1/2 and the spins are additive to determine the hadron's overall spin. The spins can cancel each other out if the are in opposite direction or the spins can add to each other if they are in the same direction. However, a particle cannot have two quarks of the same flavor with the same spin orientation unless something else is different because of the Pauli Exclusion Principle. For a while this lead to some concern because apparently the Pauli Exclusion Principle was being broken by the Delta particles of the uuu and ddd quark structures with their spin 3/2. All three quarks for each of these two Delta particles have the same flavor (either all u's or all d's) and all three quarks are in the same spin alignment such that the total spin is 1/2 + 1/2 + 1/2 or 3/2. What was needed was another attribute to distinguish the three u quarks from each other and likewise the three d quarks from each other. The concept of color (red, green and blue) was added to the quark theory. The attribute is not really related to color. The color concept has saved the Pauli Exclusion Principle and has lead to a theory for the strong nuclear force. Yes, the spheres can now show color in addition to spin arrows and letter symbols.

Harald Fritzsch in his book "Quarks, The Stuff of Matter" provided two experimental results in the support of the quarks having three colors. The first one is the lifetime of the pi 0 meson before it decays. The calculated lifetime is a factor of nine greater than the observed lifetime. The introduction of three d quark colors and three u quark colors provided a correction factor of 3x3 or 9 compared to the no color model. This factor of 9 provides the correction factor needed to have the calculated and observed values agree.

The second case provided by Harald Fritzsch involves the ratio of the production rates of hadrons to the production rate of muon-antimuon pairs in electron-positron annihilation experiments at an energy level such that only u, d and s quark containing particles can be produced. The ratio of the production rates is the ratio of the sum of the squares of the particle charges; thus, this ratio equals: [3(e_u)² + (e_d)² + (e_s)² ] / (e_m)² .

Where the terms are defined as follows:

eu	+2/3 ecu for the u quark
ed	-1/3 ecu for the d quark
es	-1/3 ecu for the s quark
em	1 or -1 ecu for the muon or antimuon
3	Number of colors for eacg quark flavor.

Hence, the ratio of the production rates equals:

3[(+2/3)² + (-1/3)² + (-1/3)²] / 1² = 3(4/9 + 1/9 + 1/9) = 18/9 = 2.

The experimental values are "...about 2.1 or 2.2." The factor of 3 in the equation was to account for the 3 colors for each quark. The calculated value would have been 2/3 without the factor of 3 to account for the colors.

The quarks have not been isolated. In fact, it may be impossible to isolate a quark. Thus, it could be said that physicists do not know really if quarks exist. However, physicists do know from high energy experiments that the proton and neutron have internal structures. They also have accepted the quark theory to the extent that Murray Gell-Mann received the Nobel prize in 1969 for his theory.

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