FRACEP, J. A. Giannini (5/23/2016)


THE FRACEP MODEL, Part 5:
What Is The Structure Of The Bosons And Field Mechanisms?

May 23, 2016

CONTENTS

1.0 INTRODUCTION

1.1 The Standard Model Bosons

2.0 THE FRACEP COMPOSITE BOSONS

2.1 The Light (Mass-less) Bosons

2.1.1 The Photon

2.1.2 The Gluons and the Color Charge

2.1.2.1 The Color Charge Structure

2.1.2.2 The Gluon Structure

2.2 The Heavy Bosons

2.2.1 The W+ and W-

2.2.2 The Z0

2.2.3 The Higgs

3.0 CONCLUSIONS

4.0 REFERENCES

Return to Book Table of Contents

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1.0 INTRODUCTION

The Standard Model of Particle Physics (SM) is a model of the world of the small (atoms and molecules, and sub-atomic particles). Its theoretical part is based on quantum mechanics; and, its data base includes a set of elementary particles (the fermions and bosons). These elementary particles are modeled as fundamental – that is, in the quantum mechanical theory, they each are represented by a single waveform indicating there are no internal components. Because many of the fermions spontaneously decay, some physicists recognize the likelihood that most of them really may have internal components even though the single waveform representation works well in quantum theory.

The FRACEP Model was developed to address the feasibility of describing fermions and bosons as composite particles. This work is Part 5 of the series of papers describing the FRACEP model and addresses the composition of the bosons and the field mechanisms that govern the particle interactions.

Part 1a (Ref. 1) of the series developed the structures (required components) for all the fermions and anti-fermions based on a set of Intermediate Building Blocks that were themselves built up from fractal-like structures of only two fundamental zero-spin, zero-charge particles (G0p and G0m). The mass of G0p = +1.724934058534x10-22 MeV/c2 and the mass of G0m = -G0p. (The negative mass concept is discussed in Part 1a.)

The built-up composite FRACEP fermions agree with the SM fundamental fermions in four characteristics: mass, spin, electromagnetic charge, and decay products. But, they have some differences from the SM fermions. The FRACEP captures spin and charge in spin-carriers and charge-carriers that are components of the composite structure. This is different from the SM which assumes spin and charge are inseparable inherent characteristics of the fermions.

Part 1b (Ref. 2) of the series developed estimates of the physical size for the G0p and G0m fundamental particles, the Intermediate Building Blocks, and the composite fermions. The size referred to is the physical size defined as the classical radius, Rclass rather than the Compton wavelength which is the usual size reference for sub-atomic particles. This means that the Rclass-G0p = lp*( the Planck length, 3.3075190x10-35m).

The FRACEP composite fermions have physical size estimates that progressively increases with mass (i.e., ~10-25 m for the electron neutrino (the smallest mass fermion) to 4.5x10-19 m for the bottom quark (the largest mass fermion). These sizes are all less than the maximum expected size of the SM fermions, ~10-18 m based on their scattering cross-section – a measure of closest possible approach. Because of the assumption of fundamental-ness in its fermions, the SM specifies little distinction in its fermion sizes, and treats them as point sources.

Having defined the composite fermions in Part 1a and Part 1b, we now turn to the bosons – the second type of fundamental particles in the SM. In this paper (Part 5 of the series), a possible structure for each of the composite bosons is proposed. These structures are based on the FRACEP composite fermions. Further, since the strong force associated with gluon exchange among quarks requires the concept of color charge (qc), a structure for the color charge – which was not considered in Part 1 of the series – is proposed. Before continuing with the composite bosons, a brief discussion of the Standard Model bosons is presented.

1.1 The Standard Model Bosons

Physics has identified four fundamental forces: the electromagnetic, the strong (nuclear), the weak (nuclear), and gravity. The electromagnetic (EM) force impacts the interaction of particles carrying an electric charge, qe, (like the electron family and the quarks). The strong force impacts the behavior of the quarks within nucleons (like the proton) and keeps atoms together. The weak force is responsible for radioactive decay; and, gravity is the force that keeps macroscopic bodies together.

The Standard Model (SM) has incorporated the electromagnetic, the strong and the weak forces into its theory, but has yet to successfully integrate gravity. So, the SM is a mathematical model that identifies its fundamental particles of nature and the rules for their interaction – including a description of the phenomenology of that interaction.

In the SM, there are two sets of fundamental particles – the fermions and the bosons. The fermions define the nature of matter in the universe; while the forces describe how the universe operates. Forces are associated with corresponding fields that provide a mathematical picture of space in which the forces operate. All of the forces are recognized as an exchange of particles. The bosons are seen as the intermediaries between the matter and the fields. That is, they allow the fermions to interact with the fields. Because of this, the bosons are referred to as the field exchange particles.

Like the fermions, the bosons have corresponding anti-particles. And like the fermions, contact between a boson and its corresponding anti-boson will cause the pair to annihilate each other. Table 1 presents the SM bosons and some of their identifying characteristic.


TABLE 1. This shows characteristics of the Standard Model bosons
including: particle name, symbol; masses (Ref. 3) with their
measurement uncertainties in parentheses (in units of MeV/c2);
em-charge (qe, in units of the electron charge); number of
color charges (qc) carried, and the fields with which they interact.



Among the bosons, the photon is considered its own anti-particle. Recall that an anti-particle has the same mass as its corresponding particle, but the opposite spin and qe (EM-charge). Since the photon has no qe, but it does have a spin, some physicists wonder if there is an anti-photon that has not yet been discovered (or theoretically hypothesized). Like the photon, Z0 may or may not be its own anti-particle for the same reason. The higgs is in a separate category and will be discussed later along with a discussion of what a higgs field is.

1.2 The EM Interaction

The EM interaction is accomplished through an exchange of a photon. The range of the interaction is considered infinite because the mass of the photon is zero. The interaction only takes place between electrically charged particles (like electrons and quarks.) It does not involve neutral particles like the neutrinos.

The EM interaction is recognized by its signature – the attraction of particles with opposite charge and the repulsion of particles with like charge. For example, a proton (+ charge) attracts an electron (– charge); while, two electrons will repel each other.

The EM interaction is the phenomenon associated with the excitation of an electron around an atomic nucleus. (An electron absorbs a photon putting it in an excited state of higher energy. Then when that electron emits the photon, it returns to its ground state.)

There is another type of EM interaction, the electron-positron annihilation (Ref. 4). When an electron (e-) and its anti-particle (the positron, e+) collide, they annihilate each other producing a (virtual – short-lived) photon (g). That photon immediately decays into a pair of fermions or quarks. For example, e- + e+ -> g -> m+ + m-. The muon (m) is a member of the electron family. It has a mass larger than the electron, but a spin and qe that are the same.

1.3 The Strong Interaction

The strong interaction is mediated by the exchange of gluons. It gives composite particles, like the proton, their cohesion. It can only take place between particles carrying a strong (color) charge (that is, quarks and gluons.)

The SM recognizes characteristics of its fundamental particles, for example, mass, electric charge (qe), and spin. These characteristics are seen in all of the fermions (the electron family, the neutrinos, and the quarks.) But, for quarks, there is an additional characteristic, color charge (qc), that is not seen in the other fermions. This is the characteristic that allows quarks to feel the strong force and interact with the strong field exchange particles (the gluons).

In the SM, there are three types of color charge (called red, blue and green.) Color charge is not related to the physical colors we see. It is only a name that is used to designate three independent types of the strong charge characteristic.

The strong interaction is the result of the exchange of gluons – the only bosons to carry color charge (Ref. 5). Gluons carry both a color charge (qc) and an anti-color charge (qc*), while quarks only carry a single color charge. There are eight different gluons based on their color-anti-color combination (for example, qc(red)-qc*(anti-green), qc(red)-qc*(anti-blue), qc(green)-qc*(anti-blue), …).

When a gluon interacts with a quark, it causes the exchange of the color charge with the quark. In this way, the quark can change from one color to a different color. This continuous interchange of color among the three quarks in a proton (mediated by the gluons) is believed to hold the proton together – making the proton stable. Gluon exchange is also the mechanism that converts other large multi-quark particles into different varieties. For example, the decay chain is f(s-,s+) -> g -> p+(u+,d-) + p-(d-,u-). Here, the f is a bound state of the strange quark (s-) and its anti-strange quark partner (s+). The p+ is a bound state of the up quark (u+) and the anti-down quark (d+); and, the p- is a bound state of the down quark (d-) and the anti-up quark (u+).

1.4 The Weak Interaction

The weak interaction (Ref. 6) can transform a fermion in the electron family into its corresponding neutrino (e.g., e- -> ne-). It can also transform a quark of the negative qe family into its corresponding positive qe family quark (e.g., d- -> u+). This transformation is accomplished by an exchange of weak interaction bosons (W+, W-, Z0). Because of the large masses of these bosons, the weak interaction is limited in distance to ~10-3 fm (10-18 m).

The weak interaction bosons and their anti-particles are created in scattering experiments and are seen to decay with small but measurable times (around 10-13 seconds – more or less). For example, a collision between an electron and its anti-particle (the positron) can produce Z0 or the (W+,W-) pair depending on the energies of the scattering particles. The e-- e+ collision must occur at a much higher energy to produce a (W+,W-) pair because of the larger resulting mass.

Once created, the zero-charged weak boson (Z0) decays into a zero-charge pair of electron family particles such as the electron or muon. That is, Z0 -> e+ + e- or Z0 -> m+ + m-. Analogously, the charged weak bosons (W+ and W-) decay into a charged pair. For example: W+ -> e+ + ne-, or W- -> m- + nm+. Note that in scattering experiments, charged particles leave a trail which identifies them when measuring their energy. For an uncharged particle, like the neutrino (n), the existence of the particle is inferred from the balance of energy (total energy in equals total energy out – this is referred to as the missing mass problem).

Having briefly discussed the SM fundamental bosons and their actions, we can now proceed to consider the proposed composite FRACEP bosons and their behavior.

2.0 THE FRACEP COMPOSITE BOSONS

In developing the FRACEP model, the philosophy was maintained that the composite fermions proposed in Part 1a and Part 1b of this series are the building blocks of matter. Likewise, the bosons are the mediators between the particles and the fields. This philosophy of particle functionality is consistent with the SM picture. Unlike the SM, the FRACEP particles are modeled as composite (rather than fundamental as in the SM).

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. The second set includes the “dark universe” fermions. These are equivalent to the bright universe fermions but with opposite mass – that is, the mass is negative.

The FRACEP dark universe particles are not the SM anti-particles. FRACEP has both particles and anti-particles among its bright universe fermions. And, it has both particles and anti-particles among its dark universe fermions. There is no equivalent to the negative mass particles in the SM. The SM only has the equivalent of the bright universe particles. However, the FRACEP dark universe fermions (and bosons) may be related to the “dark matter” (and “dark energy”) that appear to be responsible for the observed expansion of the universe – but more about that at another time.

This brings us to the FRACEP bosons. It is proposed, here, that the FRACEP bosons (as previously stated) are composite particles – unlike the SM bosons. It is agreed that they mediate between the fermions and the fields – like the SM. But, in addition, it is hypothesized that the FRACEP bosons are the connection between the bright universe and the dark universe. This connection is particularly apparent in the photon and the gluons because of their zero mass.

To achieve zero mass, it is necessary for these particles to have equal, but opposite, components (one from the bright universe and one from the dark universe) whose masses exactly cancel. As is shown below for example with the photon, the field-mediating mechanism connects the two universes, and, that connection results in the annihilation of particles and anti-particles in collisions.

We now discuss each of the boson types – including their components and how they perform in their field exchange operation. Further, the gluon discussion includes the definition of the color charge. Color charge is part of the quark structure, but it was not previously addressed in Part 1a or Part 1b of the series when defining the quarks.

2.1 The Light (Mass-less) Bosons

2.1.1 The Photon

As the field exchange particle for the EM field, the photon interacts only with particles carrying EM charge (qe). According to the SM, its mass is, at most, less than 2x10-22 MeV/c2, but it is generally considered to be zero. These characteristics suggest two components for the photon. One, it has a (bright universe) electron (e-) as one of its components. Recall, the bright universe electron is the SM electron. Two, it has a dark universe electron (ed+) as its other component. Recall, the dark universe electron has an equal but opposite mass from the bright universe electron – that is mass(ed+) = -mass(e-). But, qe(ed+) is positive, where qe(e-) is negative. This means that the photon has zero mass and zero charge – as required by the SM observations.

The choice of the electron is suggested by the apparent nature of the EM field that is often described as electrons popping in and out of existence. The interpretation of FRACEP of this observation is that, in the absence of an EM source, space is teeming with electrons (both bright and dark) and anti-electrons (both bright and dark) that are always moving randomly through it (see Fig.1). When an e- and an ed+ come in contact, they form a virtual (short-lived) bonded pair that has zero mass and zero charge (the photon, g) that is not detectable by measurement devices. That is, the e- pops out of existence. The bonded pair quickly separates because it is an unstable configuration and the e- pops back into existence – again detectable by instrumentation. A similar situation occurs when e+ and ed- come into contact forming the FRACEP anti-photon (g*). The SM does not generally recognize the photon and the anti-photon as separate particles.



Figure 1. This shows the EM field effect. In the absence of a charged source,
particles move randomly through space so that each area has 1) zero energy/mass (equal
number of positive and negative masses) and 2) zero charge (equal number of positive
and negative charges). The symbols show the e(mass, spin, charge) for each of the electron
types: e-(e-, ½ , -1), e+(e--d, -½ , +1), ed+(-e-, -½ , +1), ed-(-e-+d, ½ , -1),
d = 1.45x10-9. For the masses, ed+ = -e- and ed- = -e+. The g is the
short-lived pair (e-, ed+) and the g* is (e+, ed-) – the FRACEP photon and anti-photon.


When an EM source is present, there is an alignment of the charged particles relative to the source. In this situation the popping in and out of the e- occurs along regular field lines. Current instrumentation is not able to observe the dark universe particles directly so there is no observation of the popping of ed+ at the same time as e-. The photon is accepted as a having a spin of one. In the FRACEP model, the spins of e- and ed+ are also equal and opposite. That would imply that the spin of the composite photon is zero. However, it is hypothesized that the loosely bound pair has a spin of one because of rotational motion as the e- and ed+ orbit one another.

The photon is often associated with a flash of “light”. In FRACEP this light does not come with the formation of g. It occurs when the two components of g separate spontaneously releasing their rotational energy to become vibrations in the fabric of space. It is this energy of transformation that is interpreted as a flash of light. In the case when a source is not present, the flashes occur randomly in any area of space. When a source is present, the flashes occur along regular field lines.

Another interesting case is the annihilation event when e- and e+ collide in a scattering experiment. Here, the energy of the collision forces the colliding e- and e+ (along with the randomly moving e-, e+, ed+ and ed-) into a small tight space. During this interaction, the particles form a sea of zero-mass, zero-charge bonded groups in space – the annihilation phase. This short-lived phase is followed immediately by decay of the short-lived bonded pairs, releasing the e- and e+. These two particles separate, carrying the collision energy and moving according to the scattering laws to be seen by the detectors.

2.1.2 The Gluons and the Color Charge

As the field exchange particle for the strong field, the gluon interacts only with particles carrying color charge (qc). The action of the gluon is recognized as the exchange of color charge between quarks to hold together particles like the proton which contains two up-quarks and one down quark.

The discussion of structure of the gluon and the color charge is given below. But first, the action of the gluon and qc exchange is considered. In the SM, the up-quarks and the down-quarks both have color charge independent of one another. In the qc exchange, an up-quark of qc(red), for example, can become an up-quark of qc(blue). This means there is a change in its inherent characteristic of color charge.

In FRACEP, only up-quarks carry color charge as components. A down-quark has color charge only because it has an up-quark as one of its components. This means that the qc exchange process has the gluon facilitating the down-quark giving away its up-quark component and replacing it with a different up-quark component with a different qc. An example of the qc exchange process in FRACEP is shown in Figure 2.



Figure 2. This shows the Strong field effect and the color charge exchange among the
quarks in a typical proton. The initial configuration has a down-quark with qc(green)
(D = Ds + U2(g)), an up-quark with qc(blue) (U1(b)), and an up-quark with qc(red)
(U3(r)). Through eight steps, the down-quark exchanges qc to blue (step 3),
then red (step 6) and finally back to green (step 8).


The color-exchange process (shown in Fig. 2.) can be described in the following way.

Step 0: Our proton begins with the configuration p{U1(b), D2(g), U3(r)}. That is, in a closely oriented configuration, there are two up-quarks, U1(qc(b) = U1(b) and U3(qc(r) = U3(r) and one down-quark, D2(qc(g) = D2(g). Through the following description, the down-quark will be referred to by its two components: the Ds (which does not change during the color exchange process) and its up-quark component (which is exchanged).

Step 1: U1(b) moves away from its close position to the 3-particle group. A gluon (G(qc*(g*), qc(b)) = G(g*,b)) joins with the down-quark (D = Ds + U2(g)). The qc*(g*) (anti-green color) breaks the weak bond between the Ds and its U2(g) pushing the Ds away from its former U2(g) partner in the D.

Step 2: At this point the old down quark becomes an unattached up-quark (U2(g) and a free Ds group attached to the G(g*,b). The qc = b of the gluon (G(g*,b) attracts the qc = b of the U1(b) that is moving away and draws it back.

Step 3: The Ds joins with the U1(b) to form a new down quark and the weak bond between the Ds and the G(g*,b) breaks. This allows the G(g*,b) to spin off. At this point the proton configuration now has a U(g), an U(r) and a D(b). That is: the up-quark appears to have exchanged color charge with the down-quark.

Steps 4-6: Steps 1-3 are repeated with a different gluon, G(b*,r), to cause the D(b) to exchange color charge with the U(r).

Steps 7-9: Steps 1-3 are again repeated with another gluon, G(r*,g) to cause the D(r) with the U(g) and return to the original configuration. (The final stabilized step 9 = step 0 and is not shown separately).

The pattern shows the apparent color exchange between the up and down quarks and is summarized as:



Note that the color charge concept arose from the need to explain the workings of the quarks within the proton. Within the structure of the proton there are three quarks. Quantum mechanics requires that the quarks be distinguishable in their quantum numbers. Since all the quarks are fermions with ½ spin, a new quantum number (characteristic) was needed to make the three quarks distinguishable. That new characteristic was color charge with three different values (red, blue and green). In the case of the SM, one up-quark might have qc = red, the second up-quark might have qc = green, and the down-quark would then have qc = blue.

Since color charge in FRACEP quarks is only a component of up-quarks, we still satisfy the requirement of quantum mechanics by giving each of the up-quarks (the two independent ones and the one that is part of the down-quark) a different color charge. In every other way, our three quarks in the color exchange process (as shown in Figure 2) are indistinguishable. So the movement of Ds from one up-quark to a different up-quark looks like color exchange between quarks.

According to the SM, the gluon mass is generally considered to be approximately zero. Like the photon, this suggests a composite gluon that has components from both the bright and the dark universes. We will now consider the gluon and color charge configurations.

2.1.2.1 The Color Charge Structure

Consider first the structure of the color charges. Like the photon, the color charges are combinations of elementary particles from both the bright and the dark universes. Recall, the photons were combinations of electrons and anti-electrons with a net mass of zero. There were only two combinations (g and g*). The color charges, on the other hand, have combinations of only spin components (that is: electron neutrinos and anti-neutrinos) of the bright and dark universes.

There are three varieties of color charge: qc(red), qc(blue) and qc(green). There are also three varieties of anti-color charge: qc*(red*), qc*(blue*) and qc*(green*). The masses for the color charges are small to zero and positive. The masses for the anti-color charges are small to zero and negative (Table 2).


TABLE 2. This shows color charge (qc) structure and mass. The stable groupings
that make up each of the neutrinos are shown in parentheses. In the mass column,
the contributors to the non-zero mass are shown in parentheses. The electron
neutrino (ne-) and its anti particle (ne+) are bright universe particles; and the dark
electron neutrino (ned+) and its anti particle (ned-) are dark universe particles.
The stable groupings S0p and MSp have only positive mass; and, the stable
groupings S0m and MSm have only negative mass.


So the components of qc*(r*) are the anti-particles of qc(r). The components of qc(r) are the corresponding bright and dark universe pairs which have equal and opposite masses, so the qc(r) mass is zero. The components of qc*(b*) are the anti-particles of qc(b). In this case the components of qc(b) are the bright particle and dark anti-particle, so only the momentum part of the components have equal and opposite masses leaving a net (small) mass for qc(b). For the green color charge, the components of qc*(g*) are the dark universe versions of the components in the bright universe qc(g). In this case, only the spin part of the components have equal and opposite masses leaving a net (small) mass (but one that is larger than the blue color charge.

2.1.2.2 The Gluon Structure

Now consider the gluons. Each gluon has one color charge, one anti-color charge and a base. Recall, in the Standard Model, there are eight combinations of color charges to give eight gluons: rg*, rb*, gr*, gb*, br*, bg*, plus two mixed states (\/ ½ (rr* - gg*) and \/ 1/6 (rr* + gg* - 2bb*). The tacit assumption here is that the color and anti-color charges are inherent characteristics of the gluon. So mixed states are mathematical expressions of the color state.

For FRACEP, there is a difference. Since color charge is a component attached to a base gluon, the mixed states cannot be a physical reality. Instead, to achieve the eight gluon combinations, there must be several varieties of the base gluons.

As a minimum set, there are five base gluons which are loosely bound pairs of two ring momentum carriers (R22p and R22m). Again, the loosely bound pair is a bridge between the bright and dark universes – R22p with positive mass and R22m with negative mass. Different spin carriers (the neutrinos and anti-neutrinos) attach to the rings to produce the complete gluon base set.

With the attachment of the color charges and anti-color charges, the five gluon base set produces eight gluon exchange groups that have a zero (or very near zero) mass (Table 3). It is this set of groupings that mediate the color exchange between quarks.

Table 3 shows that the net masses for the configurations have three possible values. Four configurations have a mass of zero; two have a mass of 1x10?10; and two have a mass of ?1x10?10. These net non-zero masses are considered here to be sufficiently small as to satisfy the SM about zero mass for the gluons.


TABLE 3. This shows gluon base configurations and masses. The last
column shows the color charge and anti-color charge that can attach to
the base. It also shows the net mass of the full gluon exchange groups.


Based on the gluon base construction (Table 3) and the color charge construction (Table 2), we see that the gluon base G1 is its own anti-base. Similarly, G2 and G5 are their own anti-bases. We also note that G3 is the anti-base of G4. We also note that G1 and G2 are bright universe-dark universe pairs – that is, they have equal and opposite masses. With that information we observe that G1,g,r* (G1,qc(g),qc*(r*)) is the anti-grouping of G2*,g*,r (which is equal to G2,g*,r because G2 = G2*). Similarly, G1,g,b* is the anti-grouping of G2,g*,b. Also, G3,b,r* is the anti-grouping of G4,b*,r. And finally, G5,b,r* is the anti-grouping of G5,b*,r – again because G5 = G5*. This means that the eight gluon grouping set is its own set of anti-groupings, and there is no independent anti-grouping set – as is implied by the SM independent sets of gluons and anti-gluons.

The eight gluons in the SM likely are associated with an independent set of anti-gluons that are different from the gluons themselves (again all positive to zero mass). In FRACEP, the construction of the gluon bases (and the color charges and anti-color charges attached to the bases) bridge the bright and dark universes – that is they have both positive and negative mass in their particle and anti-particle components. For this reason, there is no independent set of anti-gluons (or groupings) associated with the gluons or their groupings.

We consider the gluon groupings (analogous to the SM gluons) and the anti-gluon possibilities. The SM gluons have one qc and one qc* as an integral part of the particle. The equivalent FRACEP grouping has three parts (the base, the qc, and the qc*) any one of which can have an anti-component that contributes to an anti-gluon grouping – the functional equivalent to a SM anti-gluon.

2.2 The Heavy Bosons


Not Yet Available

2.2.1 The W+ and W-


Not Yet Available

2.2.2 The Z0


Not Yet Available

2.2.3 The Higgs


Not Yet Available

3.0 CONCLUSIONS


Not Yet Available

4.0 REFERENCES

1 J.A. Giannini, "The FRACEP Model, Part 1a: A Look Inside the Elementary Particles of the Standard Model", Chapter 1 in Fractal Rings and Composite Elementary Particles (FRACEP) Model (2012) (http://www.jagnetbooks.org).

2 J.A. Giannini, "The FRACEP Model, Part 1b: What Is the Size of the Composite Particles ", Chapter 2 in Fractal Rings and Composite Elementary Particles (FRACEP) Model (2012) (http://www.jagnetbooks.org).

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

4 B. Povh, K. Rith, C. Scholz, and F. Zetsche, “Particle Production in e+e- Collisions” in Particles and Nuclei, ed. 2, Springer, NY (1999) Chapter 9.

5 B. Povh, K. Rith, C. Scholz, and F. Zetsche, “Quarks, Gluons and the Strong Interaction” in Particles and Nuclei, ed. 2, Springer, NY (1999) Chapter 8.

6 B. Povh, K. Rith, C. Scholz, and F. Zetsche, “Phenomenology of the Weak Interaction” in Particles and Nuclei, ed. 2, Springer, NY (1999) Chapter 10.

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