**3. Generation model of particle physics**

The Generation Model (GM) of particle physics has been developed over the last decade. In the initial paper (Robson, 2002) a new classification of the elementary particles, the six leptons and the six quarks, of the SM was proposed. This classification was based upon the use of only three additive quantum numbers: charge (*Q*), particle number (*p*) and generation quantum number (*g*), rather than the nine additive quantum numbers (see Table 1) of the SM. Thus the new classification is both simpler and unified in that leptons and quarks are assigned the same kind of additive quantum numbers unlike those of the SM. It will be discussed in more detail in Subsection 3.1.

Another feature of the new classification scheme is that all three additive quantum numbers, *Q*, *p* and *g*, are required to be conserved in all leptonic and hadronic processes. In particular the generation quantum number *g* is strictly conserved in weak interactions unlike some of the quantum numbers, e.g. strangeness *S*, of the SM. This latter requirement led to a new treatment of quark mixing in hadronic processes (Robson, 2002; Evans and Robson, 2006), which will be discussed in Subsection 3.2.

The development of the GM classification scheme, which provides a unified description of leptons and quarks, indicated that leptons and quarks are intimately related and led to the development of composite versions of the GM, which we refer to as the Composite Generation Model (CGM) (Robson, 2005; 2011a). The CGM will be discussed in Subsection 3.3.

Subsection 3.4 discusses the fundamental interactions of the GM.

coupling between mass eigenstate quarks from different generations. This latter requirement corresponds to the conservation of the generation quantum number *g* in the CC weak

The Generation Model of Particle Physics 9

Secondly, the GM postulates that hadrons are composed of weak eigenstate quarks such as *d*� and *s*� given by Eqs. (11) and (12) in the two generation approximation, rather than the

To maintain lepton-quark universality for CC weak interaction processes in the two

Eqs. (18) and (19) are the analogues of Eqs. (4) and (5) for leptons. Thus the quark pairs (*u*, *d*) and (*c*,*s*) in the GM form weak isospin doublets, similar to the lepton pairs (*νe*,*e*−) and (*νμ*, *μ*−), thereby establishing a close lepton-quark parallelism with respect to weak isospin

To account for the reduced transition probabilities for neutron and Λ<sup>0</sup> *β*-decays, the GM postulates that the neutron and Λ<sup>0</sup> baryon are composed of weak eigenstate quarks, *u*, *d*�

where we have used Eqs. (18) and (19). This gives the same transition probability for neutron

The GM differs from the SM in that it treats quark mixing differently from the method introduced by Cabibbo (1963) and employed in the SM. Essentially, in the GM, the quark mixing is placed in the quark states (wave functions) rather than in the CC weak interactions. This allows a unified and simpler classification of both leptons and quarks in terms of only three additive quantum numbers, *Q*, *p* and *g*, each of which is conserved in all interactions.

; *W*−) given by

; *W*−) = *a*(*u*, *d*; *W*−) cos *θ<sup>c</sup>* + *a*(*u*,*s*; *W*−) sin *θ<sup>c</sup>* = *gw* cos *θ<sup>c</sup>* , (21)

; *W*−) = −*a*(*u*, *d*; *W*−) sin *θ<sup>c</sup>* + *a*(*u*,*s*; *W*−) cos *θ<sup>c</sup>* = −*gw* sin *θ<sup>c</sup>* . (23)

. Thus, neutron *β*-decay is to be interpreted as the sequential transition

*d*� → *u* + *W*<sup>−</sup> , *W*<sup>−</sup> → *e*

� → *u* + *W*<sup>−</sup> , *W*<sup>−</sup> → *e*

*a*(*u*, *d*; *W*−) = *a*(*c*,*s*; *W*−) = *gw* (18)

*a*(*u*,*s*; *W*−) = *a*(*c*, *d*; *W*−) = 0 . (19)

− + *ν*¯*<sup>e</sup>* . (20)

− + *ν*¯*<sup>e</sup>* . (22)

*<sup>w</sup>* sin2 *<sup>θ</sup>c*) relative to muon decay (*g*<sup>4</sup>

*w*)

*<sup>w</sup>*) as the SM. Similarly, Λ<sup>0</sup> *β*-decay is to be

; *W*−) given by

corresponding mass eigenstate quarks, *d* and *s*, as in the SM.

generation approximation, the GM postulates that

and generation quantum number conservation gives

The primary transition has the amplitude *a*(*u*, *d*�

*<sup>w</sup>* cos2 *θc*) relative to muon decay (*g*<sup>4</sup>

*s*

In this case the primary transition has the amplitude *a*(*u*,*s*�

Thus Λ<sup>0</sup> *β*-decay has the same transition probability (*g*<sup>4</sup>

*a*(*u*, *d*�

*a*(*u*,*s* �

as that given by the SM.

interpreted as the sequential transition

interaction processes.

symmetry.

*β*-decay (*g*<sup>4</sup>

and *s*�

#### **3.1 Unified classification of leptons and quarks**

Table 2 displays a set of three additive quantum numbers: charge (*Q*), particle number (*p*) and generation quantum number (*g*) for the unified classification of the leptons and quarks corresponding to the current CGM (Robson, 2011a). As for Table 1 the corresponding antiparticles have the opposite sign for each particle additive quantum number.


Table 2. CGM additive quantum numbers for leptons and quarks

Each generation of leptons and quarks has the same set of values for the additive quantum numbers *Q* and *p*. The generations are differentiated by the generation quantum number *g*, which in general can have multiple values. The latter possibilities arise from the composite nature of the leptons and quarks in the CGM.

The three conserved additive quantum numbers, *Q*, *p* and *g* are sufficient to describe all the observed transition amplitudes for both hadronic and leptonic processes, provided each "force" particle, mediating the various interactions, has *p* = *g* = 0.

Comparison of Tables 1 and 2 indicates that the two models, SM and CGM, have only one additive quantum number in common, namely electric charge *Q*, which serves the same role in both models and is conserved. The second additive quantum number of the CGM, particle number *p*, replaces both lepton number *L* and baryon number *A* of the SM. The third additive quantum number of the CGM, generation quantum number *g*, effectively replaces the remaining additive quantum numbers of the SM, *Lμ*, *Lτ*, *S*, *C*, *B* and *T*.

Table 2 shows that the CGM provides both a simpler and *unified* classification scheme for leptons and quarks. Furthermore, the generation quantum number *g* is conserved in the CGM unlike the additive quantum numbers, *S*, *C*, *B* and *T* of the SM. Conservation of *g* requires a new treatment of quark mixing in hadronic processes, which will be discussed in the next subsection.

#### **3.2 Quark mixing in hadronic CC weak interaction processes in the GM**

The GM differs from the SM in two fundamental ways, which are essential to preserve the universality of the CC weak interaction for both leptonic and hadronic processes. In the SM this was accomplished, initially by Cabibbo (1963) for the first two generations by the introduction of "Cabibbo quark mixing", and later by Kobayashi and Maskawa (1973), who generalized quark mixing involving the CKM matrix elements to the three generations.

Firstly, the GM postulates that the mass eigenstate quarks of the same generation, e.g. (*u*, *d*), form weak isospin doublets and couple with the full strength of the CC weak interaction, *gw*, like the lepton doublets, e.g. (*νe*,*e*−). Unlike the SM, the GM requires that there is no 8 Will-be-set-by-IN-TECH

Table 2 displays a set of three additive quantum numbers: charge (*Q*), particle number (*p*) and generation quantum number (*g*) for the unified classification of the leptons and quarks corresponding to the current CGM (Robson, 2011a). As for Table 1 the corresponding

particle *Qp g* particle *Qp g*

Each generation of leptons and quarks has the same set of values for the additive quantum numbers *Q* and *p*. The generations are differentiated by the generation quantum number *g*, which in general can have multiple values. The latter possibilities arise from the composite

The three conserved additive quantum numbers, *Q*, *p* and *g* are sufficient to describe all the observed transition amplitudes for both hadronic and leptonic processes, provided each

Comparison of Tables 1 and 2 indicates that the two models, SM and CGM, have only one additive quantum number in common, namely electric charge *Q*, which serves the same role in both models and is conserved. The second additive quantum number of the CGM, particle number *p*, replaces both lepton number *L* and baryon number *A* of the SM. The third additive quantum number of the CGM, generation quantum number *g*, effectively replaces

Table 2 shows that the CGM provides both a simpler and *unified* classification scheme for leptons and quarks. Furthermore, the generation quantum number *g* is conserved in the CGM unlike the additive quantum numbers, *S*, *C*, *B* and *T* of the SM. Conservation of *g* requires a new treatment of quark mixing in hadronic processes, which will be discussed in the next

The GM differs from the SM in two fundamental ways, which are essential to preserve the universality of the CC weak interaction for both leptonic and hadronic processes. In the SM this was accomplished, initially by Cabibbo (1963) for the first two generations by the introduction of "Cabibbo quark mixing", and later by Kobayashi and Maskawa (1973), who generalized quark mixing involving the CKM matrix elements to the three generations.

Firstly, the GM postulates that the mass eigenstate quarks of the same generation, e.g. (*u*, *d*), form weak isospin doublets and couple with the full strength of the CC weak interaction, *gw*, like the lepton doublets, e.g. (*νe*,*e*−). Unlike the SM, the GM requires that there is no

3 1 <sup>3</sup> 0

3 1 <sup>3</sup> 0

3 1 <sup>3</sup> ±1

3 1 <sup>3</sup> ±1

3 1 <sup>3</sup> 0, ±2

3 1 <sup>3</sup> 0, ±2

antiparticles have the opposite sign for each particle additive quantum number.

*<sup>ν</sup><sup>e</sup>* <sup>0</sup> <sup>−</sup>1 0 *<sup>u</sup>* <sup>+</sup><sup>2</sup>

*<sup>e</sup>*<sup>−</sup> <sup>−</sup><sup>1</sup> <sup>−</sup>1 0 *<sup>d</sup>* <sup>−</sup><sup>1</sup>

*νμ* <sup>0</sup> <sup>−</sup><sup>1</sup> <sup>±</sup><sup>1</sup> *<sup>c</sup>* <sup>+</sup><sup>2</sup>

*<sup>μ</sup>*<sup>−</sup> <sup>−</sup><sup>1</sup> <sup>−</sup><sup>1</sup> <sup>±</sup><sup>1</sup> *<sup>s</sup>* <sup>−</sup><sup>1</sup>

*ντ* <sup>0</sup> <sup>−</sup>1 0, <sup>±</sup><sup>2</sup> *<sup>t</sup>* <sup>+</sup><sup>2</sup>

*<sup>τ</sup>*<sup>−</sup> <sup>−</sup><sup>1</sup> <sup>−</sup>1 0, <sup>±</sup><sup>2</sup> *<sup>b</sup>* <sup>−</sup><sup>1</sup>

Table 2. CGM additive quantum numbers for leptons and quarks

"force" particle, mediating the various interactions, has *p* = *g* = 0.

the remaining additive quantum numbers of the SM, *Lμ*, *Lτ*, *S*, *C*, *B* and *T*.

**3.2 Quark mixing in hadronic CC weak interaction processes in the GM**

**3.1 Unified classification of leptons and quarks**

nature of the leptons and quarks in the CGM.

subsection.

coupling between mass eigenstate quarks from different generations. This latter requirement corresponds to the conservation of the generation quantum number *g* in the CC weak interaction processes.

Secondly, the GM postulates that hadrons are composed of weak eigenstate quarks such as *d*� and *s*� given by Eqs. (11) and (12) in the two generation approximation, rather than the corresponding mass eigenstate quarks, *d* and *s*, as in the SM.

To maintain lepton-quark universality for CC weak interaction processes in the two generation approximation, the GM postulates that

$$a(u, d; \mathcal{W}^-) = a(\mathbf{c}, \mathbf{s}; \mathcal{W}^-) = \mathcal{g}\_w \tag{18}$$

and generation quantum number conservation gives

$$a(u, s; W^{-}) = a(c, d; W^{-}) = 0 \,. \tag{19}$$

Eqs. (18) and (19) are the analogues of Eqs. (4) and (5) for leptons. Thus the quark pairs (*u*, *d*) and (*c*,*s*) in the GM form weak isospin doublets, similar to the lepton pairs (*νe*,*e*−) and (*νμ*, *μ*−), thereby establishing a close lepton-quark parallelism with respect to weak isospin symmetry.

To account for the reduced transition probabilities for neutron and Λ<sup>0</sup> *β*-decays, the GM postulates that the neutron and Λ<sup>0</sup> baryon are composed of weak eigenstate quarks, *u*, *d*� and *s*� . Thus, neutron *β*-decay is to be interpreted as the sequential transition

$$d' \to \mathfrak{u} + \mathcal{W}^- \,, \qquad \mathcal{W}^- \to \mathcal{e}^- + \vec{\nu}\_{\mathcal{E}} \,. \tag{20}$$

The primary transition has the amplitude *a*(*u*, *d*� ; *W*−) given by

$$a(\mathfrak{u}, d'; \mathcal{W}^-) = a(\mathfrak{u}, d; \mathcal{W}^-) \cos \theta\_\mathfrak{c} + a(\mathfrak{u}, \mathfrak{s}; \mathcal{W}^-) \sin \theta\_\mathfrak{c} = \mathfrak{g}\_\mathfrak{w} \cos \theta\_\mathfrak{c} \,\,\,\,\tag{21}$$

where we have used Eqs. (18) and (19). This gives the same transition probability for neutron *β*-decay (*g*<sup>4</sup> *<sup>w</sup>* cos2 *θc*) relative to muon decay (*g*<sup>4</sup> *<sup>w</sup>*) as the SM. Similarly, Λ<sup>0</sup> *β*-decay is to be interpreted as the sequential transition

$$s' \to \mathfrak{u} + \mathcal{W}^- \,, \quad \mathcal{W}^- \to \mathfrak{e}^- + \mathfrak{v}\_\ell \,. \tag{22}$$

In this case the primary transition has the amplitude *a*(*u*,*s*� ; *W*−) given by

$$a(\mathfrak{u}, \mathfrak{s}'; W^-) = -a(\mathfrak{u}, d; W^-) \sin \theta\_{\mathfrak{c}} + a(\mathfrak{u}, \mathfrak{s}; W^-) \cos \theta\_{\mathfrak{c}} = -\mathfrak{g}\_{\mathfrak{w}} \sin \theta\_{\mathfrak{c}} \,. \tag{23}$$

Thus Λ<sup>0</sup> *β*-decay has the same transition probability (*g*<sup>4</sup> *<sup>w</sup>* sin2 *<sup>θ</sup>c*) relative to muon decay (*g*<sup>4</sup> *w*) as that given by the SM.

The GM differs from the SM in that it treats quark mixing differently from the method introduced by Cabibbo (1963) and employed in the SM. Essentially, in the GM, the quark mixing is placed in the quark states (wave functions) rather than in the CC weak interactions. This allows a unified and simpler classification of both leptons and quarks in terms of only three additive quantum numbers, *Q*, *p* and *g*, each of which is conserved in all interactions.

description of the first generation of leptons and quarks. Both models treat leptons and quarks as composites of two kinds of spin-1/2 particles, which Harari named "rishons" from the Hebrew word for first or primary. This name has been adopted for the constituents of leptons and quarks. The CGM is constructed within the framework of the GM, i.e. the *same* kind of additive quantum numbers are assigned to the constituents of both leptons and quarks, as

The Generation Model of Particle Physics 11

In the Harari-Shupe Model (HSM), two elementary spin-1/2 rishons and their corresponding antiparticles are employed to construct the leptons and quarks: (i) a *T*-rishon with *Q* = +1/3 and (ii) a *V*-rishon with *Q* = 0. Their antiparticles (denoted in the usual way by a bar over the defining particle symbol) are a *T*¯-antirishon with *Q* = -1/3 and a *V*¯ -antirishon with *Q* = 0, respectively. Each spin-1/2 lepton and quark is composed of three rishons/antirishons.

Table 3 shows the proposed structures of the first generation of leptons and quarks in the

particle *structure Q e*<sup>+</sup> *TTT* +1 *u TTV*, *TVT*, *VTT* +<sup>2</sup> <sup>3</sup> ¯*d TVV*, *VTV*, *VVT* <sup>+</sup><sup>1</sup>

*ν<sup>e</sup> VVV* 0 *ν*¯*<sup>e</sup> V*¯ *V*¯ *V*¯ 0 *<sup>d</sup> <sup>T</sup>*¯*V*¯ *<sup>V</sup>*¯ , *<sup>V</sup>*¯ *<sup>T</sup>*¯*V*¯ , *<sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>T</sup>*¯ <sup>−</sup><sup>1</sup>

*<sup>u</sup>*¯ *<sup>T</sup>*¯*T*¯*V*¯ , *<sup>T</sup>*¯*V*¯ *<sup>T</sup>*¯, *<sup>V</sup>*¯ *<sup>T</sup>*¯*T*¯ <sup>−</sup><sup>2</sup>

*<sup>e</sup>*<sup>−</sup> *<sup>T</sup>*¯*T*¯*T*¯ <sup>−</sup><sup>1</sup>

It should be noted that no composite particle involves mixtures of rishons and antirishons, as emphasized by Shupe. Both Harari and Shupe noted that quarks contained mixtures of the two kinds of rishons, whereas leptons did not. They concluded that the concept of color related to the different internal arrangements of the rishons in a quark: initially the ordering *TTV*, *TVT* and *VTT* was associated with the three colors of the *u*-quark. However, at this stage, no underlying mechanism was suggested for color. Later, a dynamical basis was proposed by Harari and Seiberg (1981), who were led to consider color-type local gauged *SU*(3) symmetries, namely *SU*(3)*<sup>C</sup>* × *SU*(3)*H*, at the rishon level. They proposed a new super-strong color-type (hypercolor) interaction corresponding to the *SU*(3)*<sup>H</sup>* symmetry, mediated by massless *hypergluons*, which is responsible for binding rishons together to form hypercolorless leptons or quarks. This interaction was assumed to be analogous to the strong color interaction of the SM, mediated by massless gluons, which is responsible for binding quarks together to form baryons or mesons. However, in this dynamical rishon model, the color force corresponding to the *SU*(3)*<sup>C</sup>* symmetry is also retained, with the *T*-rishons and *V*-rishons carrying colors and anticolors. respectively, so that leptons are colorless but quarks are colored. Similar proposals were made by others (Casalbuoni and Gatto, 1980; Squires, 1980; 1981). In each of these proposals, both the color force and the new hypercolor interaction are assumed to exist independently of one another so that the original rishon model loses some of its economical description. Furthermore, the HSM does not provide a satisfactory

understanding of the second and third generations of leptons and quarks.

3

3

3

were previously allotted in the GM to leptons and quarks (see Table 2).

Table 3. HSM of first generation of leptons and quarks

HSM.

#### **3.3 Composite generation model**

The unified classification scheme of the GM makes feasible a composite version of the GM (CGM) (Robson, 2005). This is not possible in terms of the non-unified classification scheme of the SM, involving different additive quantum numbers for leptons than for quarks and the non-conservation of some additive quantum numbers, such as strangeness, in the case of quarks. Here we shall present the current version (Robson, 2011a), which takes into account the mass hierarchy of the three generations of leptons and quarks. There is evidence that leptons and quarks, which constitute the elementary particles of the SM, are actually composites.

Firstly, the electric charges of the electron and proton are opposite in sign but are *exactly* equal in magnitude so that atoms with the same number of electrons and protons are neutral. Consequently, in a proton consisting of quarks, the electric charges of the quarks are intimately related to that of the electron: in fact, the up quark has charge *Q* = +<sup>2</sup> <sup>3</sup> and the down quark has charge *<sup>Q</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> , if the electron has electric charge *Q* = −1. These relations are readily comprehensible if leptons and quarks are composed of the same kinds of particles.

Secondly, the leptons and quarks may be grouped into three generations: (i) (*νe*,*e*−, *u*, *d*), (ii) (*νμ*, *μ*−, *c*,*s*) and (iii) (*ντ*, *τ*−, *t*, *b*), with each generation containing particles which have similar properties. Corresponding to the electron, *e*−, the second and third generations include the muon, *μ*−, and the tau particle, *τ*−, respectively. Each generation contains a neutrino associated with the corresponding leptons: the electron neutrino, *νe*, the muon neutrino, *νμ*, and the tau neutrino, *ντ*. In addition, each generation contains a quark with *Q* = +<sup>2</sup> <sup>3</sup> (the *u*, *<sup>c</sup>* and *<sup>t</sup>* quarks) and a quark with *<sup>Q</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> (the *d*, *s* and *b* quarks). Each pair of leptons, e.g. (*νe*,*e*−), and each pair of quarks, e.g. (*u*, *d*), are connected by isospin symmetries, otherwise the grouping into the three families is according to increasing mass of the corresponding family members. The existence of three repeating patterns suggests strongly that the members of each generation are composites.

Thirdly, the GM, which provides a *unified* classification scheme for leptons and quarks, also indicates that these particles are intimately related. It has been demonstrated (Robson, 2004) that this unified classification scheme leads to a relation between strong isospin (*I*) and weak isospin (*i*) symmetries. In particular, their third components are related by an equation:

*i*<sup>3</sup> = *I*<sup>3</sup> + 1 2 *g* , (24)

where *g* is the generation quantum number. In addition, electric charge is related to *I*3, *p*, *g* and *i*<sup>3</sup> by the equations:

$$Q = I\_3 + \frac{1}{2}(p + \mathfrak{g}) = i\_3 + \frac{1}{2}p\,\,. \tag{25}$$

These relations are valid for both leptons and quarks and suggest that there exists an underlying flavor *SU*(3) symmetry. The simplest conjecture is that this new flavor symmetry is connected with the substructure of leptons and quarks, analogous to the flavor *SU*(3) symmetry underlying the quark structure of the lower mass hadrons in the Eightfold Way (Gell-Mann and Ne'eman, 1964).

The CGM description of the first generation is based upon the two-particle models of Harari (1979) and Shupe (1979), which are very similar and provide an economical and impressive 10 Will-be-set-by-IN-TECH

The unified classification scheme of the GM makes feasible a composite version of the GM (CGM) (Robson, 2005). This is not possible in terms of the non-unified classification scheme of the SM, involving different additive quantum numbers for leptons than for quarks and the non-conservation of some additive quantum numbers, such as strangeness, in the case of quarks. Here we shall present the current version (Robson, 2011a), which takes into account the mass hierarchy of the three generations of leptons and quarks. There is evidence that leptons and quarks, which constitute the elementary particles of the SM, are actually

Firstly, the electric charges of the electron and proton are opposite in sign but are *exactly* equal in magnitude so that atoms with the same number of electrons and protons are neutral. Consequently, in a proton consisting of quarks, the electric charges of the quarks are intimately

Secondly, the leptons and quarks may be grouped into three generations: (i) (*νe*,*e*−, *u*, *d*), (ii) (*νμ*, *μ*−, *c*,*s*) and (iii) (*ντ*, *τ*−, *t*, *b*), with each generation containing particles which have similar properties. Corresponding to the electron, *e*−, the second and third generations include the muon, *μ*−, and the tau particle, *τ*−, respectively. Each generation contains a neutrino associated with the corresponding leptons: the electron neutrino, *νe*, the muon neutrino, *νμ*, and the tau neutrino, *ντ*. In addition, each generation contains a quark with *Q* = +<sup>2</sup>

(*νe*,*e*−), and each pair of quarks, e.g. (*u*, *d*), are connected by isospin symmetries, otherwise the grouping into the three families is according to increasing mass of the corresponding family members. The existence of three repeating patterns suggests strongly that the members of

Thirdly, the GM, which provides a *unified* classification scheme for leptons and quarks, also indicates that these particles are intimately related. It has been demonstrated (Robson, 2004) that this unified classification scheme leads to a relation between strong isospin (*I*) and weak isospin (*i*) symmetries. In particular, their third components are related by an equation:

where *g* is the generation quantum number. In addition, electric charge is related to *I*3, *p*, *g*

These relations are valid for both leptons and quarks and suggest that there exists an underlying flavor *SU*(3) symmetry. The simplest conjecture is that this new flavor symmetry is connected with the substructure of leptons and quarks, analogous to the flavor *SU*(3) symmetry underlying the quark structure of the lower mass hadrons in the Eightfold Way

The CGM description of the first generation is based upon the two-particle models of Harari (1979) and Shupe (1979), which are very similar and provide an economical and impressive

1 2

(*p* + *g*) = *i*<sup>3</sup> +

1

*i*<sup>3</sup> = *I*<sup>3</sup> +

1 2

*Q* = *I*<sup>3</sup> +

<sup>3</sup> , if the electron has electric charge *Q* = −1. These relations are readily

<sup>3</sup> (the *d*, *s* and *b* quarks). Each pair of leptons, e.g.

*g* , (24)

<sup>2</sup> *<sup>p</sup>* . (25)

<sup>3</sup> and the down quark

<sup>3</sup> (the *u*,

related to that of the electron: in fact, the up quark has charge *Q* = +<sup>2</sup>

comprehensible if leptons and quarks are composed of the same kinds of particles.

**3.3 Composite generation model**

composites.

has charge *<sup>Q</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup>

*<sup>c</sup>* and *<sup>t</sup>* quarks) and a quark with *<sup>Q</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup>

each generation are composites.

and *i*<sup>3</sup> by the equations:

(Gell-Mann and Ne'eman, 1964).

description of the first generation of leptons and quarks. Both models treat leptons and quarks as composites of two kinds of spin-1/2 particles, which Harari named "rishons" from the Hebrew word for first or primary. This name has been adopted for the constituents of leptons and quarks. The CGM is constructed within the framework of the GM, i.e. the *same* kind of additive quantum numbers are assigned to the constituents of both leptons and quarks, as were previously allotted in the GM to leptons and quarks (see Table 2).

In the Harari-Shupe Model (HSM), two elementary spin-1/2 rishons and their corresponding antiparticles are employed to construct the leptons and quarks: (i) a *T*-rishon with *Q* = +1/3 and (ii) a *V*-rishon with *Q* = 0. Their antiparticles (denoted in the usual way by a bar over the defining particle symbol) are a *T*¯-antirishon with *Q* = -1/3 and a *V*¯ -antirishon with *Q* = 0, respectively. Each spin-1/2 lepton and quark is composed of three rishons/antirishons.

Table 3 shows the proposed structures of the first generation of leptons and quarks in the HSM.


Table 3. HSM of first generation of leptons and quarks

It should be noted that no composite particle involves mixtures of rishons and antirishons, as emphasized by Shupe. Both Harari and Shupe noted that quarks contained mixtures of the two kinds of rishons, whereas leptons did not. They concluded that the concept of color related to the different internal arrangements of the rishons in a quark: initially the ordering *TTV*, *TVT* and *VTT* was associated with the three colors of the *u*-quark. However, at this stage, no underlying mechanism was suggested for color. Later, a dynamical basis was proposed by Harari and Seiberg (1981), who were led to consider color-type local gauged *SU*(3) symmetries, namely *SU*(3)*<sup>C</sup>* × *SU*(3)*H*, at the rishon level. They proposed a new super-strong color-type (hypercolor) interaction corresponding to the *SU*(3)*<sup>H</sup>* symmetry, mediated by massless *hypergluons*, which is responsible for binding rishons together to form hypercolorless leptons or quarks. This interaction was assumed to be analogous to the strong color interaction of the SM, mediated by massless gluons, which is responsible for binding quarks together to form baryons or mesons. However, in this dynamical rishon model, the color force corresponding to the *SU*(3)*<sup>C</sup>* symmetry is also retained, with the *T*-rishons and *V*-rishons carrying colors and anticolors. respectively, so that leptons are colorless but quarks are colored. Similar proposals were made by others (Casalbuoni and Gatto, 1980; Squires, 1980; 1981). In each of these proposals, both the color force and the new hypercolor interaction are assumed to exist independently of one another so that the original rishon model loses some of its economical description. Furthermore, the HSM does not provide a satisfactory understanding of the second and third generations of leptons and quarks.

particle *structure Q p g e*<sup>+</sup> *TTT* +1 +1 0

The Generation Model of Particle Physics 13

*<sup>ν</sup><sup>e</sup> <sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>V</sup>*¯ <sup>0</sup> <sup>−</sup>1 0 *ν*¯*<sup>e</sup> VVV* 0 +1 0

*<sup>e</sup>*<sup>−</sup> *<sup>T</sup>*¯*T*¯*T*¯ <sup>−</sup><sup>1</sup> <sup>−</sup>1 0

baryons (or antibaryons) of the SM. These leptons are built out of *T*- and *V*-rishons or their

It is envisaged that each lepton of the first generation exists in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons), since each of the three color interactions between pairs of rishons (or antirishons) is expected to be strongly attractive

In the CGM, it is assumed that each quark of the first generation is a composite of a colored rishon and a colorless rishon-antirishon pair, (*TV*¯ ) or (*VT*¯), so that the quarks carry a color charge. Similarly, the antiquarks are a composite of an anticolored antirishon and a colorless

In order to preserve the universality of the CC weak interaction processes involving first generation quarks, e.g. the transition *d* → *u* + *W*−, it is assumed that the first generation

*<sup>C</sup>*¯�) , down quark : *VC*(*VC*�*T*¯

*<sup>b</sup>*)/ √

*<sup>b</sup>*)/ √

*<sup>r</sup>*¯*T*¯*g*¯*T*¯¯

*<sup>r</sup>*¯*T*¯*g*¯*T*¯¯

*<sup>b</sup>* <sup>+</sup> *VrVgVbT*¯

*ur* = *Tr*(*TgV*¯*g*¯ + *TbV*¯¯

*dr* = *Vr*(*VgT*¯*g*¯ + *VbT*¯¯

*<sup>b</sup>* <sup>→</sup> *TrTgV*¯*g*¯ <sup>+</sup> *VrVgVbT*¯

which take place with equal probabilities. In these transitions, the *W*− boson is assumed to be a three *T*¯-antirishon and a three *V*-rishon colorless composite particle with additive quantum numbers *<sup>Q</sup>* <sup>=</sup> <sup>−</sup>1, *<sup>p</sup>* <sup>=</sup> *<sup>g</sup>* <sup>=</sup> 0. The corresponding *<sup>W</sup>*<sup>+</sup> boson has the structure [*TrTgTbV*¯

respectively. For *dr* → *ur* + *W*−, conserving color, one has the two transitions:

*VrVgT*¯*g*¯ <sup>→</sup> *TrTbV*¯¯

*VrVbT*¯¯

*<sup>C</sup>*¯�) , with *C*� �= *C*. (26)

2 , (27)

2 , (28)

*<sup>b</sup>* (29)

*<sup>b</sup>* , (30)

*<sup>r</sup>*¯*V*¯*g*¯*V*¯¯ *b*],

<sup>3</sup> <sup>+</sup><sup>1</sup> <sup>3</sup> 0

<sup>3</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> 0

<sup>3</sup> <sup>+</sup><sup>1</sup> <sup>3</sup> 0

<sup>3</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> 0

*u TTV*¯ +<sup>2</sup>

¯*d TV*¯ *V*¯ +<sup>1</sup>

*<sup>d</sup> TVV* ¯ <sup>−</sup><sup>1</sup>

*<sup>u</sup>*¯ *<sup>T</sup>*¯*TV*¯ <sup>−</sup><sup>2</sup>

antiparticles *T*¯ and *V*¯ , all of which have generation quantum number *g* = 0.

rishon-antirishon pair, so that the antiquarks carry an anticolor charge.

Thus a red *u*-quark and a red *d*-quark have the general color structures:

Table 5. CGM of first generation of leptons and quarks

(Halzen and Martin, 1984).

and

and

quarks have the general color structures:

up quark : *TC*(*TC*�*V*¯


Table 4. CGM additive quantum numbers for rishons

In order to overcome some of the deficiencies of the simple HSM, the two-rishon model was extended (Robson, 2005; 2011a), within the framework of the GM, in several ways.

Firstly, following the suggested existence of an *SU*(3) flavor symmetry underlying the substructure of leptons and quarks by Eq. (25), a third type of rishon, the *U*-rishon, is introduced. This *U*-rishon has *Q* = 0 but carries a non-zero generation quantum number, *g* = −1 (both the *T*-rishon and the *V*-rishon are assumed to have *g* = 0). Thus, the CGM treats leptons and quarks as composites of *three* kinds of spin-1/2 rishons, although the *U*-rishon is only involved in the second and third generations.

Secondly, in the CGM, each rishon is allotted both a particle number *p* and a generation quantum number *g*. Table 4 gives the three additive quantum numbers allotted to the three kinds of rishons. It should be noted that for each rishon additive quantum number *N*, the corresponding antirishon has the additive quantum number −*N*.

Historically, the term "particle" defines matter that is naturally occurring, especially electrons. In the CGM it is convenient to define a matter "particle" to have *p >* 0, with the antiparticle having *p <* 0. This definition of a matter particle leads to a modification of the HSM structures of the leptons and quarks which comprise the first generation. Essentially, the roles of the *V*-rishon and its antiparticle *V*¯ are interchanged in the CGM compared with the HSM. Table 5 gives the CGM structures for the first generation of leptons and quarks. The particle number *p* is clearly given by <sup>1</sup> <sup>3</sup> (number of rishons - number of antirishons). Thus the *u*-quark has *p* = +<sup>1</sup> <sup>3</sup> , since it contains two *<sup>T</sup>*-rishons and one *<sup>V</sup>*¯ -antirishon. It should be noted that it is essential for the *<sup>u</sup>*-quark to contain a *<sup>V</sup>*¯ -antirishon (*<sup>p</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> ) rather than a *<sup>V</sup>*-rishon (*<sup>p</sup>* = +<sup>1</sup> 3 ) to obtain a value of *p* = +<sup>1</sup> <sup>3</sup> , corresponding to baryon number *<sup>A</sup>* = +<sup>1</sup> <sup>3</sup> in the SM.

In the CGM, no significance is attached to the ordering of the *T*-rishons and the *V*¯ -antirishons (compare HSM) so that, e.g. the structures *TTV*¯ ,*TVT*¯ and *VTT* ¯ for the *u*-quark are considered to be equivalent. The concept of color is treated differently in the CGM: it is assumed that all three rishons, *T*, *V* and *U* carry a color charge, red, green or blue, while their antiparticles carry an anticolor charge, antired, antigreen or antiblue. The CGM postulates a strong color-type interaction corresponding to a local gauged *SU*(3)*<sup>C</sup>* symmetry (analogous to QCD) and mediated by massless *hypergluons*, which is responsible for binding rishons and antirishons together to form colorless leptons and colored quarks. The proposed structures of the quarks requires the composite quarks to have a color charge so that the dominant residual interaction between quarks is essentially the same as that between rishons, and consequently the composite quarks behave very like the elementary quarks of the SM. In the CGM we retain the term "hypergluon" as the mediator of the strong color interaction, rather than the term "gluon" employed in the SM, because it is the rishons rather than the quarks, which carry an elementary color charge.

In the CGM each lepton of the first generation (Table 5) is assumed to be colorless, consisting of three rishons (or antirishons), each with a different color (or anticolor), analogous to the 12 Will-be-set-by-IN-TECH

rishon *Qp g T* +<sup>1</sup>

*V* 0 +<sup>1</sup>

*U* 0 +<sup>1</sup>

extended (Robson, 2005; 2011a), within the framework of the GM, in several ways.

In order to overcome some of the deficiencies of the simple HSM, the two-rishon model was

Firstly, following the suggested existence of an *SU*(3) flavor symmetry underlying the substructure of leptons and quarks by Eq. (25), a third type of rishon, the *U*-rishon, is introduced. This *U*-rishon has *Q* = 0 but carries a non-zero generation quantum number, *g* = −1 (both the *T*-rishon and the *V*-rishon are assumed to have *g* = 0). Thus, the CGM treats leptons and quarks as composites of *three* kinds of spin-1/2 rishons, although the *U*-rishon is

Secondly, in the CGM, each rishon is allotted both a particle number *p* and a generation quantum number *g*. Table 4 gives the three additive quantum numbers allotted to the three kinds of rishons. It should be noted that for each rishon additive quantum number *N*, the

Historically, the term "particle" defines matter that is naturally occurring, especially electrons. In the CGM it is convenient to define a matter "particle" to have *p >* 0, with the antiparticle having *p <* 0. This definition of a matter particle leads to a modification of the HSM structures of the leptons and quarks which comprise the first generation. Essentially, the roles of the *V*-rishon and its antiparticle *V*¯ are interchanged in the CGM compared with the HSM. Table 5 gives the CGM structures for the first generation of leptons and quarks. The particle number

<sup>3</sup> , since it contains two *<sup>T</sup>*-rishons and one *<sup>V</sup>*¯ -antirishon. It should be noted that it is

<sup>3</sup> , corresponding to baryon number *<sup>A</sup>* = +<sup>1</sup>

In the CGM, no significance is attached to the ordering of the *T*-rishons and the *V*¯ -antirishons (compare HSM) so that, e.g. the structures *TTV*¯ ,*TVT*¯ and *VTT* ¯ for the *u*-quark are considered to be equivalent. The concept of color is treated differently in the CGM: it is assumed that all three rishons, *T*, *V* and *U* carry a color charge, red, green or blue, while their antiparticles carry an anticolor charge, antired, antigreen or antiblue. The CGM postulates a strong color-type interaction corresponding to a local gauged *SU*(3)*<sup>C</sup>* symmetry (analogous to QCD) and mediated by massless *hypergluons*, which is responsible for binding rishons and antirishons together to form colorless leptons and colored quarks. The proposed structures of the quarks requires the composite quarks to have a color charge so that the dominant residual interaction between quarks is essentially the same as that between rishons, and consequently the composite quarks behave very like the elementary quarks of the SM. In the CGM we retain the term "hypergluon" as the mediator of the strong color interaction, rather than the term "gluon" employed in the SM, because it is the rishons rather than the quarks, which carry an

In the CGM each lepton of the first generation (Table 5) is assumed to be colorless, consisting of three rishons (or antirishons), each with a different color (or anticolor), analogous to the

<sup>3</sup> (number of rishons - number of antirishons). Thus the *u*-quark has

<sup>3</sup> ) rather than a *<sup>V</sup>*-rishon (*<sup>p</sup>* = +<sup>1</sup>

<sup>3</sup> in the SM.

3 )

Table 4. CGM additive quantum numbers for rishons

only involved in the second and third generations.

*p* is clearly given by <sup>1</sup>

to obtain a value of *p* = +<sup>1</sup>

elementary color charge.

*p* = +<sup>1</sup>

corresponding antirishon has the additive quantum number −*N*.

essential for the *<sup>u</sup>*-quark to contain a *<sup>V</sup>*¯ -antirishon (*<sup>p</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup>

<sup>3</sup> <sup>+</sup><sup>1</sup> <sup>3</sup> 0

<sup>3</sup> 0

<sup>3</sup> −1


Table 5. CGM of first generation of leptons and quarks

baryons (or antibaryons) of the SM. These leptons are built out of *T*- and *V*-rishons or their antiparticles *T*¯ and *V*¯ , all of which have generation quantum number *g* = 0.

It is envisaged that each lepton of the first generation exists in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons), since each of the three color interactions between pairs of rishons (or antirishons) is expected to be strongly attractive (Halzen and Martin, 1984).

In the CGM, it is assumed that each quark of the first generation is a composite of a colored rishon and a colorless rishon-antirishon pair, (*TV*¯ ) or (*VT*¯), so that the quarks carry a color charge. Similarly, the antiquarks are a composite of an anticolored antirishon and a colorless rishon-antirishon pair, so that the antiquarks carry an anticolor charge.

In order to preserve the universality of the CC weak interaction processes involving first generation quarks, e.g. the transition *d* → *u* + *W*−, it is assumed that the first generation quarks have the general color structures:

$$\text{up quark}: \quad T\_{\mathbb{C}}(T\_{\mathbb{C}'} \bar{V}\_{\mathbb{C}'}) \,, \quad \text{down quark}: \quad V\_{\mathbb{C}}(V\_{\mathbb{C}'} \bar{T}\_{\mathbb{C}'}) \,, \quad \text{with } \mathbb{C}' \neq \mathbb{C}. \tag{26}$$

Thus a red *u*-quark and a red *d*-quark have the general color structures:

$$
\mu\_r = T\_r(T\_\S \mathcal{V}\_\S + T\_b \mathcal{V}\_{\bar{b}}) / \sqrt{2} \,\,\,\,\,\tag{27}
$$

and

$$d\_{\bar{r}} = V\_{\bar{r}}(V\_{\bar{\mathcal{S}}}\bar{T}\_{\bar{\mathcal{S}}} + V\_{\bar{b}}\bar{T}\_{\bar{b}}) / \sqrt{2} \,, \tag{28}$$

respectively. For *dr* → *ur* + *W*−, conserving color, one has the two transitions:

$$V\_r V\_\mathcal{S} \vec{T}\_\mathcal{\mathcal{S}} \to T\_r T\_b \vec{V}\_{\tilde{b}} + V\_r V\_\mathcal{S} V\_b \vec{T}\_\mathcal{\mathcal{T}} \vec{T}\_\mathcal{\mathcal{S}} \vec{T}\_{\tilde{b}} \tag{29}$$

and

$$
\bar{V}\_{\bar{r}}V\_{\bar{b}}\bar{T}\_{\bar{b}} \to T\_{\bar{r}}T\_{\mathcal{S}}\bar{V}\_{\mathcal{S}} + V\_{\bar{r}}V\_{\mathcal{S}}V\_{\bar{b}}\bar{T}\_{\bar{r}}\bar{T}\_{\bar{\mathcal{S}}}\bar{T}\_{\bar{b}}\tag{30}
$$

which take place with equal probabilities. In these transitions, the *W*− boson is assumed to be a three *T*¯-antirishon and a three *V*-rishon colorless composite particle with additive quantum numbers *<sup>Q</sup>* <sup>=</sup> <sup>−</sup>1, *<sup>p</sup>* <sup>=</sup> *<sup>g</sup>* <sup>=</sup> 0. The corresponding *<sup>W</sup>*<sup>+</sup> boson has the structure [*TrTgTbV*¯ *<sup>r</sup>*¯*V*¯*g*¯*V*¯¯ *b*],

particle *structure Q p g <sup>τ</sup>*<sup>+</sup> *TTT*ΠΠ <sup>+</sup><sup>1</sup> <sup>+</sup>1 0, <sup>±</sup><sup>2</sup>

The Generation Model of Particle Physics 15

*ντ <sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>V</sup>*¯ ΠΠ <sup>0</sup> <sup>−</sup>1 0, <sup>±</sup><sup>2</sup> *ν*¯*<sup>τ</sup> VVV*ΠΠ 0 +1 0, ±2

*<sup>τ</sup>*<sup>−</sup> *<sup>T</sup>*¯*T*¯*T*¯ΠΠ <sup>−</sup><sup>1</sup> <sup>−</sup>1 0, <sup>±</sup><sup>2</sup>

and each particle of the third generation is a similar quantum mechanical mixture of *g* = 0, ±2 components. The color structures of both second and third generation leptons and quarks have been chosen so that the CC weak interactions are universal. In each case, the additional colorless rishon-antirishon pairs, (*UV*¯ ) and/or (*VU*¯ ), essentially act as spectators during any CC weak interaction process. Again it should be noted that for any given transition the generation quantum number is required to be conserved, although each particle of the third generation now has three possible values of *g*. Furthermore, in the CGM the three independent additive quantum numbers, charge *Q*, particle number *p* and generation quantum number *g*, which are conserved in all interactions, correspond to the conservation of

where *n*(*R*) and *n*(*R*¯) are the numbers of rishons and antirishons, respectively. Thus, the conservation of *g* in weak interactions is a consequence of the conservation of the three kinds of rishons (*T*, *V* and *U*), which also prohibits transitions between the third generation and the first generation via weak interactions even for *g* = 0 components of third generation particles.

The GM recognizes only two fundamental interactions in nature: (i) the usual electromagnetic interaction and (ii) a strong color-type interaction, mediated by massless hypergluons, acting

The only essential difference between the strong color interactions of the GM and the SM is that the former acts between color charged rishons and/or antirishons while the latter acts between color charged elementary quarks and/or antiquarks. For historical reasons we use the term "hypergluons" for the mediators of the strong color interactions at the rishon level, rather than the term "gluons" as employed in the SM, although the effective color interaction between composite quarks and/or composite antiquarks is very similar to that between the

<sup>3</sup> <sup>+</sup><sup>1</sup>

<sup>3</sup> <sup>−</sup><sup>1</sup>

<sup>3</sup> <sup>+</sup><sup>1</sup>

<sup>3</sup> <sup>−</sup><sup>1</sup>

*TTT*ΠΠ = *TTT*[(*UV*¯ )(*UV*¯ )+(*UV*¯ )(*VU*¯ )+(*VU*¯ )(*UV*¯ )+(*VU*¯ )(*VU*¯ )]/2 (36)

*<sup>n</sup>*(*T*) + *<sup>n</sup>*(*V*) + *<sup>n</sup>*(*U*) <sup>−</sup> *<sup>n</sup>*(*T*¯) <sup>−</sup> *<sup>n</sup>*(*V*¯) <sup>−</sup> *<sup>n</sup>*(*U*¯ ) = <sup>3</sup>*<sup>p</sup>* , (39)

<sup>3</sup> 0, ±2

<sup>3</sup> 0, ±2

<sup>3</sup> 0, ±2

<sup>3</sup> 0, ±2

*<sup>n</sup>*(*T*) <sup>−</sup> *<sup>n</sup>*(*T*¯) = <sup>3</sup>*<sup>Q</sup>* , (37) *<sup>n</sup>*(*U*¯ ) <sup>−</sup> *<sup>n</sup>*(*U*) = *<sup>g</sup>* , (38)

*t TTV*¯ ΠΠ +<sup>2</sup>

*b TV*¯ *V*¯ ΠΠ +<sup>1</sup>

*<sup>b</sup> TVV* ¯ ΠΠ <sup>−</sup><sup>1</sup>

¯*<sup>t</sup> <sup>T</sup>*¯*TV*¯ ΠΠ <sup>−</sup><sup>2</sup>

¯

Table 7. CGM of third generation of leptons and quarks

each of the three kinds of rishons (Robson, 2005):

**3.4 Fundamental interactions of the GM**

between color charged rishons and/or antirishons.

elementary quarks and/or elementary antiquarks of the SM.

The rishon structure of the *τ*<sup>+</sup> particle is


Table 6. CGM of second generation of leptons and quarks

consisting of a colorless set of three *T*-rishons and a colorless set of three *V*¯ -antirishons with additive quantum numbers *Q* = +1, *p* = *g* = 0 (Robson, 2005).

The rishon structures of the second generation particles are the same as the corresponding particles of the first generation plus the addition of a colorless rishon-antirishon pair, Π, where

$$
\Pi = [(\bar{\mathcal{U}}V) + (\bar{\mathcal{V}}\mathcal{U})] / \sqrt{2} \,, \tag{31}
$$

which is a quantum mechanical mixture of (*UV*¯ ) and (*VU*¯ ), which have *Q* = *p* = 0 but *g* = ±1, respectively. In this way, the pattern for the first generation is repeated for the second generation. Table 6 gives the CGM structures for the second generation of leptons and quarks.

It should be noted that for any given transition the generation quantum number is required to be conserved, although each particle of the second generation has two possible values of *g*. For example, the decay

$$
\mu^- \to \nu\_{\mu} + \mathcal{W}^- \,. \tag{32}
$$

at the rishon level may be written

$$
\vec{T}\vec{T}\vec{T}\Pi \to \vec{V}\vec{V}\vec{V}\Pi + \vec{T}\vec{T}\vec{T}V\vec{V}\vec{V} \tag{33}
$$

which proceeds via the two transitions:

$$
\vec{T}\vec{T}\vec{T}(\vec{U}V) \to \vec{V}\vec{V}\vec{V}(\vec{U}V) + \vec{T}\vec{T}\vec{T}VVV\tag{34}
$$

and

$$
\bar{T}\bar{T}\bar{T}(\bar{V}\mathcal{U}) \to \bar{V}\bar{V}\bar{V}(\bar{V}\mathcal{U}) + \bar{T}\bar{T}\bar{T}V\mathcal{V}V\tag{35}
$$

which take place with equal probabilities. In each case, the additional colorless rishon-antirishon pair, (*UV*¯ ) or (*VU*¯ ), essentially acts as a spectator during the CC weak interaction process.

The rishon structures of the third generation particles are the same as the corresponding particles of the first generation plus the addition of two rishon-antirishon pairs, which are a quantum mechanical mixture of (*UV*¯ ) and (*VU*¯ ) and, as for the second generation, are assumed to be colorless and have *Q* = *p* = 0 but *g* = ±1. In this way the pattern of the first and second generation is continued for the third generation. Table 7 gives the CGM structures for the third generation of leptons and quarks.

14 Will-be-set-by-IN-TECH

particle *structure Q p g <sup>μ</sup>*<sup>+</sup> *TTT*<sup>Π</sup> <sup>+</sup><sup>1</sup> <sup>+</sup><sup>1</sup> <sup>±</sup><sup>1</sup>

*νμ <sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>V</sup>*¯ <sup>Π</sup> <sup>0</sup> <sup>−</sup><sup>1</sup> <sup>±</sup><sup>1</sup> *ν*¯*<sup>μ</sup> VVV*Π 0 +1 ±1

*<sup>μ</sup>*<sup>−</sup> *<sup>T</sup>*¯*T*¯*T*¯<sup>Π</sup> <sup>−</sup><sup>1</sup> <sup>−</sup><sup>1</sup> <sup>±</sup><sup>1</sup>

consisting of a colorless set of three *T*-rishons and a colorless set of three *V*¯ -antirishons with

The rishon structures of the second generation particles are the same as the corresponding particles of the first generation plus the addition of a colorless rishon-antirishon pair, Π, where

which is a quantum mechanical mixture of (*UV*¯ ) and (*VU*¯ ), which have *Q* = *p* = 0 but *g* = ±1, respectively. In this way, the pattern for the first generation is repeated for the second generation. Table 6 gives the CGM structures for the second generation of leptons and quarks. It should be noted that for any given transition the generation quantum number is required to be conserved, although each particle of the second generation has two possible values of *g*.

which take place with equal probabilities. In each case, the additional colorless rishon-antirishon pair, (*UV*¯ ) or (*VU*¯ ), essentially acts as a spectator during the CC weak

The rishon structures of the third generation particles are the same as the corresponding particles of the first generation plus the addition of two rishon-antirishon pairs, which are a quantum mechanical mixture of (*UV*¯ ) and (*VU*¯ ) and, as for the second generation, are assumed to be colorless and have *Q* = *p* = 0 but *g* = ±1. In this way the pattern of the first and second generation is continued for the third generation. Table 7 gives the CGM structures

Π = [(*UV*¯ )+(*VU*¯ )]/

<sup>3</sup> <sup>+</sup><sup>1</sup> <sup>3</sup> ±1

<sup>3</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> ±1

<sup>3</sup> <sup>+</sup><sup>1</sup> <sup>3</sup> ±1

<sup>3</sup> <sup>−</sup><sup>1</sup> <sup>3</sup> ±1

√

2 , (31)

*μ*<sup>−</sup> → *νμ* + *W*<sup>−</sup> , (32)

*<sup>T</sup>*¯*T*¯*T*¯<sup>Π</sup> <sup>→</sup> *<sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>V</sup>*¯ <sup>Π</sup> <sup>+</sup> *<sup>T</sup>*¯*T*¯*TVVV* ¯ , (33)

*<sup>T</sup>*¯*T*¯*T*¯(*UV*¯ ) <sup>→</sup> *<sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>V</sup>*¯(*UV*¯ ) + *<sup>T</sup>*¯*T*¯*TVVV* ¯ (34)

*<sup>T</sup>*¯*T*¯*T*¯(*VU*¯ ) <sup>→</sup> *<sup>V</sup>*¯ *<sup>V</sup>*¯ *<sup>V</sup>*¯(*VU*¯ ) + *<sup>T</sup>*¯*T*¯*TVVV* ¯ , (35)

*c TTV*¯ Π +<sup>2</sup>

*s T* ¯ *V*¯ *V*¯ Π +<sup>1</sup>

*<sup>s</sup> TVV* ¯ <sup>Π</sup> <sup>−</sup><sup>1</sup>

*<sup>c</sup>*¯ *<sup>T</sup>*¯*TV*¯ <sup>Π</sup> <sup>−</sup><sup>2</sup>

Table 6. CGM of second generation of leptons and quarks

For example, the decay

and

interaction process.

at the rishon level may be written

which proceeds via the two transitions:

for the third generation of leptons and quarks.

additive quantum numbers *Q* = +1, *p* = *g* = 0 (Robson, 2005).


Table 7. CGM of third generation of leptons and quarks

The rishon structure of the *τ*<sup>+</sup> particle is

$$\text{TTTTIII} = \text{TTT}[(\text{\eth}V)(\text{\eth}V) + (\text{\eth}V)(\text{\eth}V) + (\text{\eth}V)(\text{\eth}V) + (\text{\eth}V)(\text{\eth}I)]/2 \tag{36}$$

and each particle of the third generation is a similar quantum mechanical mixture of *g* = 0, ±2 components. The color structures of both second and third generation leptons and quarks have been chosen so that the CC weak interactions are universal. In each case, the additional colorless rishon-antirishon pairs, (*UV*¯ ) and/or (*VU*¯ ), essentially act as spectators during any CC weak interaction process. Again it should be noted that for any given transition the generation quantum number is required to be conserved, although each particle of the third generation now has three possible values of *g*. Furthermore, in the CGM the three independent additive quantum numbers, charge *Q*, particle number *p* and generation quantum number *g*, which are conserved in all interactions, correspond to the conservation of each of the three kinds of rishons (Robson, 2005):

$$n(T) - n(\bar{T}) = \Im Q \, , \tag{37}$$

$$
\pi(\bar{\mathcal{U}}) - \pi(\mathcal{U}) = \mathcal{g} \; , \tag{38}
$$

$$n(T) + n(V) + n(\mathcal{U}) - n(\mathcal{T}) - n(\mathcal{V}) - n(\mathcal{U}) = \mathfrak{F} \,\prime \,\, \, \tag{39}$$

where *n*(*R*) and *n*(*R*¯) are the numbers of rishons and antirishons, respectively. Thus, the conservation of *g* in weak interactions is a consequence of the conservation of the three kinds of rishons (*T*, *V* and *U*), which also prohibits transitions between the third generation and the first generation via weak interactions even for *g* = 0 components of third generation particles.

#### **3.4 Fundamental interactions of the GM**

The GM recognizes only two fundamental interactions in nature: (i) the usual electromagnetic interaction and (ii) a strong color-type interaction, mediated by massless hypergluons, acting between color charged rishons and/or antirishons.

The only essential difference between the strong color interactions of the GM and the SM is that the former acts between color charged rishons and/or antirishons while the latter acts between color charged elementary quarks and/or antiquarks. For historical reasons we use the term "hypergluons" for the mediators of the strong color interactions at the rishon level, rather than the term "gluons" as employed in the SM, although the effective color interaction between composite quarks and/or composite antiquarks is very similar to that between the elementary quarks and/or elementary antiquarks of the SM.

to be essentially cancelled or at least made finite. It does this for hadrons in two ways: either by bringing an antiquark close to a quark (i.e forming a meson) or by bringing three quarks, one of each color, together (i.e. forming a baryon) so that in each case the composite hadron is colorless. However, quantum mechanics prevents the quark and the antiquark of opposite colors or the three quarks of different colors from being placed exactly at the same place. This means that the color fields are not exactly cancelled, although sufficiently it seems to remove the infinities associated with isolated quarks. The distribution of the quark-antiquark pairs or the system of three quarks is described by quantum mechanical wave functions. Many different patterns, corresponding to the various hadrons, occur. Each pattern has a characteristic energy, because the color fields are not entirely cancelled and because the quarks are somewhat localized. This characteristic energy, *E*, gives the characteristic mass, via Eq.

The Generation Model of Particle Physics 17

The above picture, within the framework of the SM, provides an understanding of hadron masses as arising mainly from internal energies associated with the strong color interactions. However, as discussed in Subsection 2.2.3, the masses of the elementary particles of the SM, the leptons, the quarks and the *W* and *Z* bosons, are interpreted in a completely different way. A "condensate" called the Higgs scalar field (Englert and Brout, 1964; Higgs, 1964), analogous to the Cooper pairs in a superconducting material, is assumed to exist. This field couples, with an appropriate strength, to each lepton, quark and vector boson and endows an originally massless particle with its physical mass. Thus, the assumption of a Higgs field within the framework of the SM not only adds an extra field but also leads to the introduction of 14 new parameters. Moreover, as pointed out by Lyre (2008), the introduction of the Higgs field in the SM to spontaneously break the *U*(1) × *SU*(2)*<sup>L</sup>* local gauge symmetry of the electroweak interaction to generate the masses of the *W* and *Z* bosons, simply corresponds mathematically to putting in "by hand" the masses of the elementary particles of the SM: the so-called Higgs mechanism does *not* provide any physical explanation for the origin of the masses of the

In the CGM (Robson, 2005; 2011a), the elementary particles of the SM have a substructure, consisting of massless rishons and/or antirishons bound together by strong color interactions, mediated by massless neutral hypergluons. This model is very similar to that of the SM in which the quarks and/or antiquarks are bound together by strong color interactions, mediated by massless neutral gluons, to form hadrons. Since, as discussed above, the mass of a hadron arises mainly from the energy of its constituents, the CGM suggests (Robson, 2009) that the mass of a lepton, quark or vector boson arises entirely from the energy stored in the motion of its constituent rishons and/or antirishons and the energy of the color hypergluon fields, *E*, according to Eq. (40). A corollary of this idea is: *if a particle has mass, then it is composite*.

Thus, unlike the SM, the GM provides a *unified* description of the origin of *all* mass.

Table 8 shows the observed masses of the charged leptons together with the estimated masses of the quarks: the masses of the neutral leptons have not yet been determined but are known to be very small. Although the mass of a single quark is a somewhat abstract idea, since quarks do not exist as particles independent of the environment around them, the masses of the quarks may be inferred from mass differences between hadrons of similar composition. The strong binding within hadrons complicates the issue to some extent but rough estimates of the quark masses have been made (Veltman, 2003), which are sufficient for our purposes.

(40), of the hadron.

leptons, quarks and the *W* and *Z* bosons.

**4.2 Mass hierarchy of leptons and quarks**

In the GM both gravity and the weak interactions are considered to be residual interactions of the strong color interactions. Gravity will be discussed in some detail in Subsection 4.3. In the GM the weak interactions are assumed to be mediated by composite massive vector bosons, consisting of colorless sets of three rishons and three antirishons as discussed in the previous subsection, so that they are not elementary particles, associated with a *U*(1) × *SU*(2)*<sup>L</sup>* local gauge theory as in the SM. The weak interactions are simply residual interactions of the CGM strong color force, which binds rishons and antirishons together, analogous to the strong nuclear interactions, mediated by massive mesons, being residual interactions of the strong color force of the SM, which binds quarks and antiquarks together. Since the weak interactions are not considered to be fundamental interactions arising from a local gauge theory, there is no requirement for the existence of a Higgs field to generate the boson masses within the framework of the GM (Robson, 2008).

### **4. Consequences**

In this section it will be shown that new paradigms arising from the GM provide some understanding concerning: (i) the origin of mass; (ii) the mass hierarchy of leptons and quarks; (iii) the origin of gravity and (iv) the origin of "apparent" CP violation in the *<sup>K</sup>*<sup>0</sup> <sup>−</sup> *<sup>K</sup>*¯ <sup>0</sup> system.

#### **4.1 Origin of mass**

Einstein (1905) concluded that the mass of a body *m* is a measure of its energy content *E* and is given by

$$
\mathfrak{m} = \mathbb{E}/\mathfrak{c}^2 \,, \tag{40}
$$

where *c* is the speed of light in a vacuum. This relationship was first tested by Cockcroft and Walton (1932) using the nuclear transformation

7Li <sup>+</sup> *<sup>p</sup>* <sup>→</sup> <sup>2</sup>*<sup>α</sup>* <sup>+</sup> 17.2 MeV , (41)

and it was found that the decrease in mass in this disintegration process was consistent with the observed release of energy, according to Eq. (40). Recently, relation (40) has been verified (Rainville *et al.*, 2005) to within 0.00004%, using very accurate measurements of the atomic-mass difference, Δ*m*, and the corresponding *γ*-ray wavelength to determine *E*, the nuclear binding energy, for isotopes of silicon and sulfur.

It has been emphasized by Wilczek (2005) that approximate QCD calculations (Butler *et al.*, 1993; Aoki *et al.*, 2000; Davies *et al.*, 2004) obtain the observed masses of the neutron, proton and other baryons to an accuracy of within 10%. In these calculations, the assumed constituents, quarks and gluons, are taken to be massless. Wilczek concludes that the calculated masses of the hadrons arise from both the energy stored in the motion of the quarks and the energy of the gluon fields, according to Eq. (40): basically the mass of a hadron arises from internal energy.

Wilzcek (2005) has also discussed the underlying principles giving rise to the internal energy, hence the mass, of a hadron. The nature of the gluon color fields is such that they lead to a runaway growth of the fields surrounding an isolated color charge. In fact all this structure (via virtual gluons) implies that an isolated quark would have an infinite energy associated with it. This is the reason why isolated quarks are not seen. Nature requires these infinities 16 Will-be-set-by-IN-TECH

In the GM both gravity and the weak interactions are considered to be residual interactions of the strong color interactions. Gravity will be discussed in some detail in Subsection 4.3. In the GM the weak interactions are assumed to be mediated by composite massive vector bosons, consisting of colorless sets of three rishons and three antirishons as discussed in the previous subsection, so that they are not elementary particles, associated with a *U*(1) × *SU*(2)*<sup>L</sup>* local gauge theory as in the SM. The weak interactions are simply residual interactions of the CGM strong color force, which binds rishons and antirishons together, analogous to the strong nuclear interactions, mediated by massive mesons, being residual interactions of the strong color force of the SM, which binds quarks and antiquarks together. Since the weak interactions are not considered to be fundamental interactions arising from a local gauge theory, there is no requirement for the existence of a Higgs field to generate the boson masses within the

In this section it will be shown that new paradigms arising from the GM provide some understanding concerning: (i) the origin of mass; (ii) the mass hierarchy of leptons and quarks; (iii) the origin of gravity and (iv) the origin of "apparent" CP violation in the *<sup>K</sup>*<sup>0</sup> <sup>−</sup> *<sup>K</sup>*¯ <sup>0</sup> system.

Einstein (1905) concluded that the mass of a body *m* is a measure of its energy content *E* and

where *c* is the speed of light in a vacuum. This relationship was first tested by Cockcroft and

and it was found that the decrease in mass in this disintegration process was consistent with the observed release of energy, according to Eq. (40). Recently, relation (40) has been verified (Rainville *et al.*, 2005) to within 0.00004%, using very accurate measurements of the atomic-mass difference, Δ*m*, and the corresponding *γ*-ray wavelength to determine *E*, the

It has been emphasized by Wilczek (2005) that approximate QCD calculations (Butler *et al.*, 1993; Aoki *et al.*, 2000; Davies *et al.*, 2004) obtain the observed masses of the neutron, proton and other baryons to an accuracy of within 10%. In these calculations, the assumed constituents, quarks and gluons, are taken to be massless. Wilczek concludes that the calculated masses of the hadrons arise from both the energy stored in the motion of the quarks and the energy of the gluon fields, according to Eq. (40): basically the mass of a hadron arises

Wilzcek (2005) has also discussed the underlying principles giving rise to the internal energy, hence the mass, of a hadron. The nature of the gluon color fields is such that they lead to a runaway growth of the fields surrounding an isolated color charge. In fact all this structure (via virtual gluons) implies that an isolated quark would have an infinite energy associated with it. This is the reason why isolated quarks are not seen. Nature requires these infinities

*m* = *E*/*c*<sup>2</sup> , (40)

7Li <sup>+</sup> *<sup>p</sup>* <sup>→</sup> <sup>2</sup>*<sup>α</sup>* <sup>+</sup> 17.2 MeV , (41)

framework of the GM (Robson, 2008).

Walton (1932) using the nuclear transformation

nuclear binding energy, for isotopes of silicon and sulfur.

**4. Consequences**

**4.1 Origin of mass**

from internal energy.

is given by

to be essentially cancelled or at least made finite. It does this for hadrons in two ways: either by bringing an antiquark close to a quark (i.e forming a meson) or by bringing three quarks, one of each color, together (i.e. forming a baryon) so that in each case the composite hadron is colorless. However, quantum mechanics prevents the quark and the antiquark of opposite colors or the three quarks of different colors from being placed exactly at the same place. This means that the color fields are not exactly cancelled, although sufficiently it seems to remove the infinities associated with isolated quarks. The distribution of the quark-antiquark pairs or the system of three quarks is described by quantum mechanical wave functions. Many different patterns, corresponding to the various hadrons, occur. Each pattern has a characteristic energy, because the color fields are not entirely cancelled and because the quarks are somewhat localized. This characteristic energy, *E*, gives the characteristic mass, via Eq. (40), of the hadron.

The above picture, within the framework of the SM, provides an understanding of hadron masses as arising mainly from internal energies associated with the strong color interactions. However, as discussed in Subsection 2.2.3, the masses of the elementary particles of the SM, the leptons, the quarks and the *W* and *Z* bosons, are interpreted in a completely different way. A "condensate" called the Higgs scalar field (Englert and Brout, 1964; Higgs, 1964), analogous to the Cooper pairs in a superconducting material, is assumed to exist. This field couples, with an appropriate strength, to each lepton, quark and vector boson and endows an originally massless particle with its physical mass. Thus, the assumption of a Higgs field within the framework of the SM not only adds an extra field but also leads to the introduction of 14 new parameters. Moreover, as pointed out by Lyre (2008), the introduction of the Higgs field in the SM to spontaneously break the *U*(1) × *SU*(2)*<sup>L</sup>* local gauge symmetry of the electroweak interaction to generate the masses of the *W* and *Z* bosons, simply corresponds mathematically to putting in "by hand" the masses of the elementary particles of the SM: the so-called Higgs mechanism does *not* provide any physical explanation for the origin of the masses of the leptons, quarks and the *W* and *Z* bosons.

In the CGM (Robson, 2005; 2011a), the elementary particles of the SM have a substructure, consisting of massless rishons and/or antirishons bound together by strong color interactions, mediated by massless neutral hypergluons. This model is very similar to that of the SM in which the quarks and/or antiquarks are bound together by strong color interactions, mediated by massless neutral gluons, to form hadrons. Since, as discussed above, the mass of a hadron arises mainly from the energy of its constituents, the CGM suggests (Robson, 2009) that the mass of a lepton, quark or vector boson arises entirely from the energy stored in the motion of its constituent rishons and/or antirishons and the energy of the color hypergluon fields, *E*, according to Eq. (40). A corollary of this idea is: *if a particle has mass, then it is composite*. Thus, unlike the SM, the GM provides a *unified* description of the origin of *all* mass.

#### **4.2 Mass hierarchy of leptons and quarks**

Table 8 shows the observed masses of the charged leptons together with the estimated masses of the quarks: the masses of the neutral leptons have not yet been determined but are known to be very small. Although the mass of a single quark is a somewhat abstract idea, since quarks do not exist as particles independent of the environment around them, the masses of the quarks may be inferred from mass differences between hadrons of similar composition. The strong binding within hadrons complicates the issue to some extent but rough estimates of the quark masses have been made (Veltman, 2003), which are sufficient for our purposes.

so that the electron will have a substantially greater characteristic energy and hence a greater mass than the electron neutrino, as observed. This large difference in the masses of the *e*− and *ν<sup>e</sup>* leptons (see Table 8) indicates that the mass of a particle is extremely sensitive to the degree of localization of its constituents. Similarly, the up, charmed and top quarks, each containing two charged *T*-rishons, are expected to have a greater mass than their weak isospin partners, the down, strange and bottom quark, respectively, which contain only a single charged *T*¯-antirishon. This is true provided one takes into account quark mixing (Evans and Robson, 2006) in the case of the up and down quarks, although Table 8 indicates that the down quark is more massive than the up quark, leading to the neutron having a greater mass than the proton. This is understood within the framework of the GM since due to the manner in which quark masses are estimated, it is the *weak eigenstate* quarks, whose masses are given in Table 8. Since each succeeding generation is significantly more massive than the previous one, any mixing will noticeably increase the mass of a lower generation quark. Thus the weak

The Generation Model of Particle Physics 19


be significantly more massive than the mass eigenstate *d*-quark (see Subsection 3.2). We shall now discuss the mass hierarchy of the three generations of leptons and quarks in more detail. It is envisaged that each lepton of the *first* generation exists in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons) since each of the three color interactions between pairs of rishons (or antirishons) is expected to be strongly attractive (Halzen and Martin, 1984). As indicated above, the charged leptons are predicted to have larger masses than the neutral leptons, since the electromagnetic interaction in the charged leptons will cause their constituent rishons (or antirishons) to be less localized than those constituting the uncharged leptons, leading to a substantially greater characteristic energy

In the CGM, each quark of the *first* generation is a composite of a colored rishon and a colorless rishon-antirishon pair, (*TV*¯ ) or a (*VT*¯) (see Table 5). This color charge structure of the quarks is expected to lead to a quantum mechanical linear distribution of the constituent rishons and antirishons, corresponding to a considerably larger mass than that of the leptons, since the constituents of the quarks are less localized. This is a consequence of the character (i.e. attractive or repulsive) of the color interactions at small distances (Halzen and Martin, 1984).

(i) rishons (or antirishons) of like colors (or anticolors) repel: those having different colors (or anticolors) attract, unless their colors (or anticolors) are interchanged and the two rishons (or antirishons) do not exist in an antisymmetric color state (e.g. as in the case of leptons);

Furthermore, the electromagnetic interaction occurring within the up quark, leads one to

Each lepton of the *second* generation is envisaged to basically exist in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons), as for the corresponding lepton of the first generation. The additional colorless rishon-antirishon pair, (*VU*¯ ) or (*UV*¯ ), is expected to be attached externally to this triangular distribution, leading quantum mechanically to a less localized distribution of the constituent rishons and/or

eigenstate *d*�

and a correspondingly greater mass.

The general rules for small distances of separation are:

expect it to have a larger mass than that of the down quark.

(ii) rishons and antirishons of opposite colors attract but otherwise repel.


Table 8. Masses of leptons and quarks

The SM is unable to provide any understanding of either the existence of the three generations of leptons and quarks or their mass hierarchy indicated in Table 8; whereas the CGM suggests that both the existence and mass hierarchy of these three generations arise from the substructures of the leptons and quarks (Robson, 2009; 2011a).

Subsection 3.3 describes the proposed rishon and/or antirishon substructures of the three generations of leptons and quarks and indicates how the pattern of the first generation is followed by the second and third generations. Section 4.1 discusses the origin of mass in composite particles and postulates that the mass of a lepton or quark arises from the energy of its constituents.

In the CGM it is envisaged that the rishons and/or antirishons of each lepton or quark are very strongly localized, since to date there is no direct evidence for any substructure of these particles. Thus the constituents are expected to be distributed according to quantum mechanical wave functions, for which the product wave function is significant for only an *extremely small* volume of space so that the corresponding color fields are *almost cancelled*. The constituents of each lepton or quark are localized within a very small volume of space by strong color interactions acting between the colored rishons and/or antirishons. We call these *intra-fermion* color interactions. However, between any two leptons and/or quarks there will be a residual interaction, arising from the color interactions acting between the constituents of one fermion and the constituents of the other fermion. We refer to these interactions as *inter-fermion* color interactions. These will be associated with the gravitational interaction and are discussed in the next subsection.

The mass of each lepton or quark corresponds to a characteristic energy primarily associated with the intra-fermion color interactions. It is expected that the mass of a composite particle will be greater if the degree of localization of its constituents is smaller (i.e. the constituents are on average more widely separated). This is a consequence of the nature of the strong color interactions, which are assumed to possess the property of "asymptotic freedom" (Gross and Wilczek, 1973; Politzer, 1973), whereby the color interactions become stronger for larger separations of the color charges. In addition, it should be noted that the electromagnetic interactions between charged *T*-rishons or between charged *T*¯-antirishons will also cause the degree of localization of the constituents to be smaller causing an increase in mass.

There is some evidence for the above expectations. The electron consists of three *T*¯-antirishons, while the electron neutrino consists of three neutral *V*¯ -antirishons. Neglecting the electric charge carried by the *T*¯-antirishon, it is expected that the electron and its neutrino would have identical masses, arising from the similar intra-fermion color interactions. However, it is anticipated that the electromagnetic interaction in the electron case will cause the *T*¯-antirishons to be less localized than the *V*¯ -antirishons constituting the electron neutrino 18 Will-be-set-by-IN-TECH

The SM is unable to provide any understanding of either the existence of the three generations of leptons and quarks or their mass hierarchy indicated in Table 8; whereas the CGM suggests that both the existence and mass hierarchy of these three generations arise from the

Subsection 3.3 describes the proposed rishon and/or antirishon substructures of the three generations of leptons and quarks and indicates how the pattern of the first generation is followed by the second and third generations. Section 4.1 discusses the origin of mass in composite particles and postulates that the mass of a lepton or quark arises from the energy

In the CGM it is envisaged that the rishons and/or antirishons of each lepton or quark are very strongly localized, since to date there is no direct evidence for any substructure of these particles. Thus the constituents are expected to be distributed according to quantum mechanical wave functions, for which the product wave function is significant for only an *extremely small* volume of space so that the corresponding color fields are *almost cancelled*. The constituents of each lepton or quark are localized within a very small volume of space by strong color interactions acting between the colored rishons and/or antirishons. We call these *intra-fermion* color interactions. However, between any two leptons and/or quarks there will be a residual interaction, arising from the color interactions acting between the constituents of one fermion and the constituents of the other fermion. We refer to these interactions as *inter-fermion* color interactions. These will be associated with the gravitational interaction and

The mass of each lepton or quark corresponds to a characteristic energy primarily associated with the intra-fermion color interactions. It is expected that the mass of a composite particle will be greater if the degree of localization of its constituents is smaller (i.e. the constituents are on average more widely separated). This is a consequence of the nature of the strong color interactions, which are assumed to possess the property of "asymptotic freedom" (Gross and Wilczek, 1973; Politzer, 1973), whereby the color interactions become stronger for larger separations of the color charges. In addition, it should be noted that the electromagnetic interactions between charged *T*-rishons or between charged *T*¯-antirishons will also cause the

There is some evidence for the above expectations. The electron consists of three *T*¯-antirishons, while the electron neutrino consists of three neutral *V*¯ -antirishons. Neglecting the electric charge carried by the *T*¯-antirishon, it is expected that the electron and its neutrino would have identical masses, arising from the similar intra-fermion color interactions. However, it is anticipated that the electromagnetic interaction in the electron case will cause the *T*¯-antirishons to be less localized than the *V*¯ -antirishons constituting the electron neutrino

degree of localization of the constituents to be smaller causing an increase in mass.

Generation 1 *ν<sup>e</sup> e*− *u d* Mass *<* 0.3 eV 0.511 MeV 5 MeV 10 MeV Generation 2 *νμ μ*− *c s* Mass *<* 0.3 eV 106 MeV 1.3 GeV 200 MeV Generation 3 *ντ τ*− *t b* Mass *<* 0.3 eV 1.78 GeV 175 GeV 4.5 GeV

<sup>3</sup> <sup>−</sup><sup>1</sup>

3

Charge 0 <sup>−</sup><sup>1</sup> <sup>+</sup><sup>2</sup>

Table 8. Masses of leptons and quarks

are discussed in the next subsection.

of its constituents.

substructures of the leptons and quarks (Robson, 2009; 2011a).

so that the electron will have a substantially greater characteristic energy and hence a greater mass than the electron neutrino, as observed. This large difference in the masses of the *e*− and *ν<sup>e</sup>* leptons (see Table 8) indicates that the mass of a particle is extremely sensitive to the degree of localization of its constituents. Similarly, the up, charmed and top quarks, each containing two charged *T*-rishons, are expected to have a greater mass than their weak isospin partners, the down, strange and bottom quark, respectively, which contain only a single charged *T*¯-antirishon. This is true provided one takes into account quark mixing (Evans and Robson, 2006) in the case of the up and down quarks, although Table 8 indicates that the down quark is more massive than the up quark, leading to the neutron having a greater mass than the proton. This is understood within the framework of the GM since due to the manner in which quark masses are estimated, it is the *weak eigenstate* quarks, whose masses are given in Table 8. Since each succeeding generation is significantly more massive than the previous one, any mixing will noticeably increase the mass of a lower generation quark. Thus the weak eigenstate *d*� -quark, which contains about 5% of the mass eigenstate *s*-quark, is expected to be significantly more massive than the mass eigenstate *d*-quark (see Subsection 3.2). We shall now discuss the mass hierarchy of the three generations of leptons and quarks in more detail.

It is envisaged that each lepton of the *first* generation exists in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons) since each of the three color interactions between pairs of rishons (or antirishons) is expected to be strongly attractive (Halzen and Martin, 1984). As indicated above, the charged leptons are predicted to have larger masses than the neutral leptons, since the electromagnetic interaction in the charged leptons will cause their constituent rishons (or antirishons) to be less localized than those constituting the uncharged leptons, leading to a substantially greater characteristic energy and a correspondingly greater mass.

In the CGM, each quark of the *first* generation is a composite of a colored rishon and a colorless rishon-antirishon pair, (*TV*¯ ) or a (*VT*¯) (see Table 5). This color charge structure of the quarks is expected to lead to a quantum mechanical linear distribution of the constituent rishons and antirishons, corresponding to a considerably larger mass than that of the leptons, since the constituents of the quarks are less localized. This is a consequence of the character (i.e. attractive or repulsive) of the color interactions at small distances (Halzen and Martin, 1984). The general rules for small distances of separation are:

(i) rishons (or antirishons) of like colors (or anticolors) repel: those having different colors (or anticolors) attract, unless their colors (or anticolors) are interchanged and the two rishons (or antirishons) do not exist in an antisymmetric color state (e.g. as in the case of leptons);

(ii) rishons and antirishons of opposite colors attract but otherwise repel.

Furthermore, the electromagnetic interaction occurring within the up quark, leads one to expect it to have a larger mass than that of the down quark.

Each lepton of the *second* generation is envisaged to basically exist in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons), as for the corresponding lepton of the first generation. The additional colorless rishon-antirishon pair, (*VU*¯ ) or (*UV*¯ ), is expected to be attached externally to this triangular distribution, leading quantum mechanically to a less localized distribution of the constituent rishons and/or

to be colorless. The electron is composed of three *T*¯-antirishons, each carrying a different anticolor charge, antired, antigreen or antiblue. Both the proton and neutron are envisaged (as in the SM) to be composed of three quarks, each carrying a different color charge, red, green or blue. All three particles are assumed to be essentially in a three-color antisymmetric state, so that their behavior with respect to the strong color interactions is expected basically to be the same. This similar behavior suggests that the proposed residual interaction has several

The Generation Model of Particle Physics 21

Firstly, the residual interaction between any two of the above colorless particles, arising from

Secondly, assuming that the strong color fields are almost completely cancelled at large distances, it seems plausible that the residual interaction, mediated by massless hypergluons, should have an infinite range, and tend to zero as 1/*r*2. These properties may be attributed to the fact that the constituents of each colorless particle are very strongly localized so that the strength of the residual interaction is *extremely weak*, and consequently the hypergluon self-interactions are also practically negligible. This means that one may consider the color interactions using a perturbation approach: the residual color interaction is the sum of all the two-particle color charge interactions, each of which may be treated perturbatively, i.e. as a single hypergluon exchange. Using the color factors (Halzen and Martin, 1984) appropriate for the *SU*(3) gauge field, one finds that the residual color interactions between any two

Since the mass of a body of ordinary matter is essentially the total mass of its constituent electrons, neutrons and protons, the total interaction between two bodies of masses, *m*<sup>1</sup> and *m*2, will be the sum of all the two-particle contributions so that the total interaction will be proportional to the product of these two masses, *m*1*m*2, provided that each two-particle interaction contribution is also proportional to the product of the masses of the two particles. This latter requirement may be understood if each electron, neutron or proton is considered physically to be essentially a quantum mechanical triangular distribution of three differently colored rishons or antirishons. In this case, each particle may be viewed as a distribution of three color charges throughout a small volume of space with each color charge having a certain probability of being at a particular point, determined by its corresponding color wave function. The total residual interaction between two colorless particles will then be the sum of all the intrinsic interactions acting between a particular triangular distribution of one particle

Now the mass *m* of each colorless particle is considered to be given by *m* = *E*/*c*2, where *E* is a characteristic energy, determined by the degree of localization of its constituent rishons and/or antirishons. Thus the significant volume of space occupied by the triangular distribution of the three differently colored rishons or antirishons is larger the greater the mass of the particle. Moreover, due to antiscreening effects (Gross and Wilczek, 1973; Politzer, 1973) of the strong color fields, the average strength of the color charge within each unit volume of the larger localized volume of space will be increased. If one assumes that the mass of a particle is proportional to the integrated sum of the intra-fermion interactions within the significant volume of space occupied by the triangular distribution, then the total residual interaction between two such colorless particles will be proportional to the product of their

the inter-fermion color interactions, is predicted to be of a *universal* character.

properties associated with the usual gravitational interaction.

colorless particles (electron, neutron or proton) are each *attractive*.

with that of the other particle.

masses.

antirishons, so that the lepton has a significantly larger mass than its corresponding first generation lepton.

Each quark of the *second* generation has a similar structure to that of the corresponding quark of the first generation, with the additional colorless rishon-antirishon pair, (*VU*¯ ) or (*UV*¯ ), attached quantum mechanically so that the whole rishon structure is essentially a linear distribution of the constituent rishons and antirishons. This structure is expected to be less localized, leading to a larger mass relative to that of the corresponding quark of the first generation, with the charmed quark having a greater mass than the strange quark, arising from the electromagnetic repulsion of its constituent two charged *T*-rishons.

Each lepton of the *third* generation is considered to basically exist in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons), as for the corresponding leptons of the first and second generations. The two additional colorless rishon-antirishon pairs, (*VU*¯ )(*VU*¯ ), (*VU*¯ )(*UV*¯ ) or (*UV*¯ )(*UV*¯ ), are expected to be attached externally to this triangular distribution, leading to a considerably less localized quantum mechanical distribution of the constituent rishons and/or antirishons, so that the lepton has a significantly larger mass than its corresponding second generation lepton.

Each quark of the *third* generation has a similar structure to that of the first generation, with the additional two rishon-antirishon pairs (*VU*¯ ) and/or (*UV*¯ ) attached quantum mechanically so that the whole rishon structure is essentially a linear distribution of the constituent rishons and antirishons. This structure is expected to be even less localized, leading to a larger mass relative to that of the corresponding quark of the second generation, with the top quark having a greater mass than the bottom quark, arising from the electromagnetic repulsion of its constituent two charged *T*-rishons.

The above is a qualitative description of the mass hierarchy of the three generations of leptons and quarks, based on the degree of localization of their constituent rishons and/or antirishons. However, in principle, it should be possible to calculate the actual masses of the leptons and quarks by carrying out QCD-type computations, analogous to those employed for determining the masses of the proton and other baryons within the framework of the SM (Butler *et al.*, 1993; Aoki *et al.*, 2000; Davies *et al.*, 2004).

#### **4.3 Origin of gravity**

Robson (2009) proposed that the residual interaction, arising from the incomplete cancellation of the inter-fermion color interactions acting between the rishons and/or antirishons of one colorless particle and those of another colorless particle, may be identified with the usual gravitational interaction, since it has several properties associated with that interaction: universality, infinite range and very weak strength. Based upon this earlier conjecture, Robson (2011a) has presented a quantum theory of gravity, described below, leading approximately to Newton's law of universal gravitation.

The mass of a body of ordinary matter is essentially the total mass of its constituent electrons, protons and neutrons. It should be noted that these masses will depend upon the environment in which the particle exists: e.g. the mass of a proton in an atom of helium will differ slightly from that of a proton in an atom of lead. In the CGM, each of these three particles is considered 20 Will-be-set-by-IN-TECH

antirishons, so that the lepton has a significantly larger mass than its corresponding first

Each quark of the *second* generation has a similar structure to that of the corresponding quark of the first generation, with the additional colorless rishon-antirishon pair, (*VU*¯ ) or (*UV*¯ ), attached quantum mechanically so that the whole rishon structure is essentially a linear distribution of the constituent rishons and antirishons. This structure is expected to be less localized, leading to a larger mass relative to that of the corresponding quark of the first generation, with the charmed quark having a greater mass than the strange quark, arising

Each lepton of the *third* generation is considered to basically exist in an antisymmetric three-particle color state, which physically assumes a quantum mechanical triangular distribution of the three differently colored identical rishons (or antirishons), as for the corresponding leptons of the first and second generations. The two additional colorless rishon-antirishon pairs, (*VU*¯ )(*VU*¯ ), (*VU*¯ )(*UV*¯ ) or (*UV*¯ )(*UV*¯ ), are expected to be attached externally to this triangular distribution, leading to a considerably less localized quantum mechanical distribution of the constituent rishons and/or antirishons, so that the lepton has a

Each quark of the *third* generation has a similar structure to that of the first generation, with the additional two rishon-antirishon pairs (*VU*¯ ) and/or (*UV*¯ ) attached quantum mechanically so that the whole rishon structure is essentially a linear distribution of the constituent rishons and antirishons. This structure is expected to be even less localized, leading to a larger mass relative to that of the corresponding quark of the second generation, with the top quark having a greater mass than the bottom quark, arising from the electromagnetic repulsion of

The above is a qualitative description of the mass hierarchy of the three generations of leptons and quarks, based on the degree of localization of their constituent rishons and/or antirishons. However, in principle, it should be possible to calculate the actual masses of the leptons and quarks by carrying out QCD-type computations, analogous to those employed for determining the masses of the proton and other baryons within the framework of the SM

Robson (2009) proposed that the residual interaction, arising from the incomplete cancellation of the inter-fermion color interactions acting between the rishons and/or antirishons of one colorless particle and those of another colorless particle, may be identified with the usual gravitational interaction, since it has several properties associated with that interaction: universality, infinite range and very weak strength. Based upon this earlier conjecture, Robson (2011a) has presented a quantum theory of gravity, described below, leading approximately

The mass of a body of ordinary matter is essentially the total mass of its constituent electrons, protons and neutrons. It should be noted that these masses will depend upon the environment in which the particle exists: e.g. the mass of a proton in an atom of helium will differ slightly from that of a proton in an atom of lead. In the CGM, each of these three particles is considered

from the electromagnetic repulsion of its constituent two charged *T*-rishons.

significantly larger mass than its corresponding second generation lepton.

its constituent two charged *T*-rishons.

to Newton's law of universal gravitation.

**4.3 Origin of gravity**

(Butler *et al.*, 1993; Aoki *et al.*, 2000; Davies *et al.*, 2004).

generation lepton.

to be colorless. The electron is composed of three *T*¯-antirishons, each carrying a different anticolor charge, antired, antigreen or antiblue. Both the proton and neutron are envisaged (as in the SM) to be composed of three quarks, each carrying a different color charge, red, green or blue. All three particles are assumed to be essentially in a three-color antisymmetric state, so that their behavior with respect to the strong color interactions is expected basically to be the same. This similar behavior suggests that the proposed residual interaction has several properties associated with the usual gravitational interaction.

Firstly, the residual interaction between any two of the above colorless particles, arising from the inter-fermion color interactions, is predicted to be of a *universal* character.

Secondly, assuming that the strong color fields are almost completely cancelled at large distances, it seems plausible that the residual interaction, mediated by massless hypergluons, should have an infinite range, and tend to zero as 1/*r*2. These properties may be attributed to the fact that the constituents of each colorless particle are very strongly localized so that the strength of the residual interaction is *extremely weak*, and consequently the hypergluon self-interactions are also practically negligible. This means that one may consider the color interactions using a perturbation approach: the residual color interaction is the sum of all the two-particle color charge interactions, each of which may be treated perturbatively, i.e. as a single hypergluon exchange. Using the color factors (Halzen and Martin, 1984) appropriate for the *SU*(3) gauge field, one finds that the residual color interactions between any two colorless particles (electron, neutron or proton) are each *attractive*.

Since the mass of a body of ordinary matter is essentially the total mass of its constituent electrons, neutrons and protons, the total interaction between two bodies of masses, *m*<sup>1</sup> and *m*2, will be the sum of all the two-particle contributions so that the total interaction will be proportional to the product of these two masses, *m*1*m*2, provided that each two-particle interaction contribution is also proportional to the product of the masses of the two particles.

This latter requirement may be understood if each electron, neutron or proton is considered physically to be essentially a quantum mechanical triangular distribution of three differently colored rishons or antirishons. In this case, each particle may be viewed as a distribution of three color charges throughout a small volume of space with each color charge having a certain probability of being at a particular point, determined by its corresponding color wave function. The total residual interaction between two colorless particles will then be the sum of all the intrinsic interactions acting between a particular triangular distribution of one particle with that of the other particle.

Now the mass *m* of each colorless particle is considered to be given by *m* = *E*/*c*2, where *E* is a characteristic energy, determined by the degree of localization of its constituent rishons and/or antirishons. Thus the significant volume of space occupied by the triangular distribution of the three differently colored rishons or antirishons is larger the greater the mass of the particle. Moreover, due to antiscreening effects (Gross and Wilczek, 1973; Politzer, 1973) of the strong color fields, the average strength of the color charge within each unit volume of the larger localized volume of space will be increased. If one assumes that the mass of a particle is proportional to the integrated sum of the intra-fermion interactions within the significant volume of space occupied by the triangular distribution, then the total residual interaction between two such colorless particles will be proportional to the product of their masses.

both parity (P) and charge-conjugation (C) (Lee and Yang, 1956; Wu *et al.*, 1957; Garwin *et al.*, 1957; Friedman and Telegdi, 1957) and later combined CP conservation (Christenson *et al.*, 1964). Recently, Robson (2011b) has demonstrated that this experiment is also compatible with the mixed-parity nature of the *π*<sup>−</sup> predicted by the CGM: ≈ (0.95*Pd* + 0.05*Ps*), with *Pd* = −1 and *Ps* = +1. This implies that the original determination of the parity of the negatively charged pion is *not* conclusive, if the pion has a complex substructure as in the CGM. Similarly, Robson (2011c) has shown that the recent determination (Abouzaid *et al.*, 2008) of the parity of the neutral pion, using the double Dalitz decay *<sup>π</sup>*<sup>0</sup> <sup>→</sup> *<sup>e</sup>*+*e*−*e*+*e*<sup>−</sup> is also compatible with the

The Generation Model of Particle Physics 23

This new concept of mixed-parity states in hadrons, based upon the existence of weak eigenstate quarks in hadrons and the composite nature of the mass eigenstate quarks, leads to an understanding of CP symmetry in nature. This is discussed in the following subsection.

Gell-Mann and Pais (1955) considered the behavior of neutral particles under the charge-conjugation operator C. In particular they considered the *K*<sup>0</sup> meson and realized that unlike the photon and the neutral pion, which transform into themselves under the C operator so that they are their own antiparticles, the antiparticle of the *K*<sup>0</sup> meson (strangeness *S* = +1), *<sup>K</sup>*¯ 0, was a distinct particle, since it had a different strangeness quantum number (*<sup>S</sup>* <sup>=</sup> <sup>−</sup>1). They concluded that the two neutral mesons, *K*<sup>0</sup> and *K*¯ 0, are degenerate particles that exhibit unusual properties, since they can transform into each other via weak interactions such as

In order to treat this novel situation, Gell-Mann and Pais suggested that it was more convenient to employ different particle states, rather than *K*<sup>0</sup> and *K*¯ 0, to describe neutral kaon

and concluded that these particle states must have different decay modes and lifetimes. In

a longer lifetime and more complex decay modes. This conclusion was based upon the

The particle-mixing theory of Gell-Mann and Pais was confirmed in 1957 by experiment, in spite of the incorrect assumption of C invariance in weak interaction processes. Following the discovery in 1957 of both C and P violation in weak interaction processes, the particle-mixing theory led to a suggestion by Landau (1957) that the weak interactions may be invariant under

Landau's suggestion implied that the Gell-Mann–Pais model of neutral kaons would still

respectively. Since the charged pions were considered to have intrinsic parity *P<sup>π</sup>* = −1, it

The suggestion of Landau was accepted for several years since it nicely restored some degree of symmetry in weak interaction processes. However, the surprising discovery (Christenson

√ 2 , *K*<sup>0</sup>

*K*<sup>0</sup> *π*+*π*<sup>−</sup> *K*¯ 0. (42)

√

<sup>2</sup>, were eigenstates of CP with eigenvalues +1 and −1,

<sup>1</sup> state could decay to two charged pions, if CP was conserved.

2 , (43)

<sup>1</sup> and the *<sup>π</sup>*+*π*<sup>−</sup> system are even

<sup>2</sup> would have

<sup>2</sup> = (*K*<sup>0</sup> <sup>−</sup> *<sup>K</sup>*¯ <sup>0</sup>)/

<sup>1</sup> could decay to two charged pions, while *<sup>K</sup>*<sup>0</sup>

mixed-parity nature of the neutral pion predicted by the CGM.

decay. They suggested the following representative states:

<sup>1</sup> = (*K*<sup>0</sup> <sup>+</sup> *<sup>K</sup>*¯ <sup>0</sup>)/

conservation of C in the weak interaction processes: both *K*<sup>0</sup>

<sup>1</sup> and *<sup>K</sup>*<sup>0</sup>

*K*0

particular they concluded that *K*<sup>0</sup>

(i.e. *C* = +1) under the C operation.

the combined operation CP.

apply if the states, *K*<sup>0</sup>

was clear that only the *K*<sup>0</sup>

**4.5 CP violation in the** *<sup>K</sup>***<sup>0</sup>** <sup>−</sup> *<sup>K</sup>***¯ <sup>0</sup> system**

Thus the residual color interaction between two colorless bodies of masses, *m*<sup>1</sup> and *m*2, is proportional to the product of these masses and moreover is expected to depend *approximately* as the inverse square of their distance of separation *r*, i.e. as 1/*r*2, in accordance with Newton's law of universal gravitation. The approximate dependence on the inverse square law is expected to arise from the effect of hypergluon self-interactions, especially for large separations. Such deviations from an inverse square law do not occur for electromagnetic interactions, since there are no corresponding photon self-interactions.

### **4.4 Mixed-quark states in hadrons**

As discussed in Subsection 3.2 the GM postulates that hadrons are composed of weak eigenstate quarks rather than mass eigenstate quarks as in the SM. This gives rise to several important consequences (Evans and Robson, 2006; Morrison and Robson, 2009; Robson, 2011b; 2011c).

Firstly, hadrons composed of mixed-quark states might seem to suggest that the electromagnetic and strong interaction processes between mass eigenstate hadron components are not consistent with the fact that weak interaction processes occur between weak eigenstate quarks. However, since the electromagnetic and strong interactions are flavor independent: the down, strange and bottom quarks carry the same electric and color charges so that the weak eigenstate quarks have the same magnitude of electric and color charge as the mass eigenstate quarks. Consequently, the weak interaction is the *only* interaction in which the quark-mixing phenomenon can be detected.

Secondly, the occurrence of mixed-quark states in hadrons implies the existence of higher generation quarks in hadrons. In particular, the GM predicts that the proton contains ≈ 1.7% of strange quarks, while the neutron having two *d*� -quarks contains ≈ 3.4% of strange quarks. Recent experiments (Maas *et al.*, 2005; Armstrong *et al*, 2005) have provided some evidence for the existence of strange quarks in the proton. However, to date the experimental data are compatible with the predictions of both the GM and the SM (� 1.7%).

Thirdly, the presence of strange quarks in nucleons explains why the mass of the neutron is greater than the mass of a proton, so that the proton is stable. This arises because the mass of the weak eigenstate *d*� -quark is larger than the mass of the *u*-quark, although the mass eigenstate *d*-quark is expected to be smaller than that of the *u*-quark, as discussed in the previous section.

Another consequence of the presence of mixed-quark states in hadrons is that mixed-quark states may have mixed parity. In the CGM the constituents of quarks are rishons and/or antirishons. If one assumes the simple convention that all rishons have positive parity and all their antiparticles have negative parity, one finds that the down and strange quarks have opposite intrinsic parities, according to the proposed structures of these quarks in the CGM: the *d*-quark (see Table 5) consists of two rishons and one antirishon (*Pd* = −1), while the *s*-quark (see Table 6) consists of three rishons and two antirishons (*Ps* = +1). The *u*-quark consists of two rishons and one antirishon so that *Pu* = −1, and the antiparicles of these three quarks have the corresponding opposite parities: *P*¯*<sup>d</sup>* = +1, *Ps*¯ = −1 and *Pu*¯ = +1.

In the SM the intrinsic parity of the charged pions is assumed to be *P<sup>π</sup>* = −1. This result was established by Chinowsky and Steinberger (1954), using the capture of negatively charged pions in deuterium to form two neutrons, and led to the overthrow of the conservation of 22 Will-be-set-by-IN-TECH

Thus the residual color interaction between two colorless bodies of masses, *m*<sup>1</sup> and *m*2, is proportional to the product of these masses and moreover is expected to depend *approximately* as the inverse square of their distance of separation *r*, i.e. as 1/*r*2, in accordance with Newton's law of universal gravitation. The approximate dependence on the inverse square law is expected to arise from the effect of hypergluon self-interactions, especially for large separations. Such deviations from an inverse square law do not occur for electromagnetic

As discussed in Subsection 3.2 the GM postulates that hadrons are composed of weak eigenstate quarks rather than mass eigenstate quarks as in the SM. This gives rise to several important consequences (Evans and Robson, 2006; Morrison and Robson, 2009; Robson,

Firstly, hadrons composed of mixed-quark states might seem to suggest that the electromagnetic and strong interaction processes between mass eigenstate hadron components are not consistent with the fact that weak interaction processes occur between weak eigenstate quarks. However, since the electromagnetic and strong interactions are flavor independent: the down, strange and bottom quarks carry the same electric and color charges so that the weak eigenstate quarks have the same magnitude of electric and color charge as the mass eigenstate quarks. Consequently, the weak interaction is the *only* interaction in which

Secondly, the occurrence of mixed-quark states in hadrons implies the existence of higher generation quarks in hadrons. In particular, the GM predicts that the proton contains ≈ 1.7%

Recent experiments (Maas *et al.*, 2005; Armstrong *et al*, 2005) have provided some evidence for the existence of strange quarks in the proton. However, to date the experimental data are

Thirdly, the presence of strange quarks in nucleons explains why the mass of the neutron is greater than the mass of a proton, so that the proton is stable. This arises because the

mass eigenstate *d*-quark is expected to be smaller than that of the *u*-quark, as discussed in the

Another consequence of the presence of mixed-quark states in hadrons is that mixed-quark states may have mixed parity. In the CGM the constituents of quarks are rishons and/or antirishons. If one assumes the simple convention that all rishons have positive parity and all their antiparticles have negative parity, one finds that the down and strange quarks have opposite intrinsic parities, according to the proposed structures of these quarks in the CGM: the *d*-quark (see Table 5) consists of two rishons and one antirishon (*Pd* = −1), while the *s*-quark (see Table 6) consists of three rishons and two antirishons (*Ps* = +1). The *u*-quark consists of two rishons and one antirishon so that *Pu* = −1, and the antiparicles of these three

In the SM the intrinsic parity of the charged pions is assumed to be *P<sup>π</sup>* = −1. This result was established by Chinowsky and Steinberger (1954), using the capture of negatively charged pions in deuterium to form two neutrons, and led to the overthrow of the conservation of

quarks have the corresponding opposite parities: *P*¯*<sup>d</sup>* = +1, *Ps*¯ = −1 and *Pu*¯ = +1.



interactions, since there are no corresponding photon self-interactions.

**4.4 Mixed-quark states in hadrons**

the quark-mixing phenomenon can be detected.

of strange quarks, while the neutron having two *d*�

mass of the weak eigenstate *d*�

previous section.

compatible with the predictions of both the GM and the SM (� 1.7%).

2011b; 2011c).

both parity (P) and charge-conjugation (C) (Lee and Yang, 1956; Wu *et al.*, 1957; Garwin *et al.*, 1957; Friedman and Telegdi, 1957) and later combined CP conservation (Christenson *et al.*, 1964). Recently, Robson (2011b) has demonstrated that this experiment is also compatible with the mixed-parity nature of the *π*<sup>−</sup> predicted by the CGM: ≈ (0.95*Pd* + 0.05*Ps*), with *Pd* = −1 and *Ps* = +1. This implies that the original determination of the parity of the negatively charged pion is *not* conclusive, if the pion has a complex substructure as in the CGM. Similarly, Robson (2011c) has shown that the recent determination (Abouzaid *et al.*, 2008) of the parity of the neutral pion, using the double Dalitz decay *<sup>π</sup>*<sup>0</sup> <sup>→</sup> *<sup>e</sup>*+*e*−*e*+*e*<sup>−</sup> is also compatible with the mixed-parity nature of the neutral pion predicted by the CGM.

This new concept of mixed-parity states in hadrons, based upon the existence of weak eigenstate quarks in hadrons and the composite nature of the mass eigenstate quarks, leads to an understanding of CP symmetry in nature. This is discussed in the following subsection.
