J. TOWE 553

quark and the muon’s neutrino are regarded as I3 = +1/2

partners in the moderately heavy generation.

3

1

2

I

The mass of expression (13) motivates the association

of (13) with the composite, spin-2ħ field

LR

or eS

LR

, where SR and Se

S respectively represent the RH

strange quark and the LH anti-strange, and where

e

and

e respectively represent the RH electron and the

LH anti-electron. The strange quark and the right-hand-

ed electron are (in the proposed model) regarded as I3

partners in the light generation.

3

1

2

I

30I

The mass of expression (14) motivates the association

of (14) with the average mass of the two spin-2ħ states

e

LR

U

and

LR

, where UL and DL respectively

represent the LH up quark and LH down quark, where

De

represents a mass-less LH spin-2ħ field and where

e

and

e respectively represent the LH electron’s

neutrino and the LH electron. The up quark and the LH

electron’s neutrino are regarded as I3 = +1/2 partners in

the light generation, and the down quark and LH electron

are regarded as I3 = −1/2 partners in the light generation.

Note that the masses described by expressions (11), (12),

(13) and (14) are approximately equal to those deter-

mined by observation [7,8].

To interpret the mass that is described by expression

(10), it is first observed that the LH muon

is not

included in the earlier discussion. Accordingly, the mass

that is described by (10) is interpreted as the spin-2ħ

composite 7

LR

or 7

LR

. Paralleling the earlier

discussion, the composites 7

LR

and 7

LR

are

interpreted as lepto-quark states (which consist of conju-

gates that form composites with spin-2ħ fields

), the

constituents of which share an I3 classification and a

generational classification. Thus the 7L is interpreted as

an unobserved LH quark that is characterized by I3 =

−1/2 and is regarded as an element of the moderately

heavy generation. Finally, since the mass of the

is

relatively negligible, the mass of the newly predicted

quark that is associated with expression (10) will be des-

ignated as approximately 30 GeV/c2.

The spin-2ħ composites (9) through (14) are associated

with three generations of I3 generators. These elements

are therefore interpreted as constituting an SU(3) sym-

metry, the preservation of which is regarded as equiva-

lent to the conservation of I3 and generation:

Referring to Figure 2, the counterclockwise sequence

beginning at 180 GeV/c2 indicates, in order of occurrence,

the masses that are described by expressions (9) through

(14). Again the mass 0.25 GeV/c2 and the associated I3

value of I3 = 0 represent the averages of the masses and I3

numbers of the up quark (together with its I3 lepton part-

ner) and the down quark (together with its I3 lepton part-

ner).

Note that the Figure 2 symmetry is partially broken

because the vertices represent a variety of masses. Note

however that an appropriate realization of the SUGRA

Figure 2. World symmetry.

e

LR

U

RRR

TU

LR

T

e

RR

e

RRR

TU

LR

U

t

LR

T

Figure 3. A pure SUGRA GUT interaction.

GUT interaction can preserve the partially broken sym-

metry that is depicted in Figure 2 by beginning and ter-

minating at a single vertex. Specifically, the Figure 2 sym-

metry is preserved by the SUGRA GUT interaction.

Note that preservation of the Figure 2 symmetry by

the Figure 3 interaction is indeed equivalent to the con-

servation of I3 and generation by the Figure 3 interac-

tion.

4. Conclusion

The proposed model is geometrically characterized by

Ricci flatness (all curvature is identified with the ana-

logues (7) of Weyl curvature) and by the SU(3) symme-

try that is described by Figure 2. This model appears to

represent an increment of progress because it is charac-

terized by a uniqueness that is established by gauge in-

variance and because significant physical consequences

and predictions emerge.

5. Acknowledgements

Figures designed by R. James Towe.

Copyright © 2013 SciRes. JMP