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