higgs - page 28

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!
, and Refs. 11 and 15
therein.
~
A
!
D. Composite quarks and leptons
Families of quarks and leptons appear to be replicas of one
another
~
see Table V
!
, aside from their differing masses and
weak couplings. Attempts have been made to explain this
regularity in terms of a composite structure, much as the
periodic table of the elements reflects their underlying
atomic structure. A set of guidelines for this program was
laid down by ’t Hooft.
236
For an example of a recent effort,
see Ref. 237.
236.
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!
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!
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E. Grand unification and extended gauge groups
An early point in favor of quark–lepton unification was
the anomaly cancellation
182–184
mentioned in Sec. IX E. The
idea that lepton number could be regarded as a fourth
‘‘color,’’ leading to an extended gauge group embracing both
electroweak and strong interactions, was proposed by Pati
and Salam.
238
The strong and electroweak coupling constants are ex-
pected to approach one another at very small distance
~
large
momentum
!
scales,
239
suggesting
grand unified theories
based on symmetry groups such as SU
~
5
!
,
240
SO
~
10
!
,
241
and
E
6
.
242
~
For an early popular article on this program see Ref.
114.
!
These theories typically predict that the proton will
decay,
115–117
and some of them entail additional observable
gauge bosons besides those of the SU
~
3
!
3
SU
~
2
!
3
U
~
1
!
stan-
dard model.
71
Some useful group-theoretic techniques for
model-building are described in Ref. 56.
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; see also ‘‘Is Baryon Number Conserved?’’, J. C. Pati and
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!
; ‘‘Lepton Number as
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!
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,’’ F. Gu¨ rsey, P.
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F. Strong
CP
problem and axions
In a non-Abelian gauge theory such as SU
~
3
!
there can
arise nontrivial gauge configurations that prevent terms in
the Lagrangian proportional to Tr (
G
m
n
m
n
) from being ig-
nored as pure divergences. Such terms can lead to strong
CP
violation. Their coefficient, a parameter conventionally
called
u
, must be of order 10
2
10
or smaller in order not to
conflict with limits on the electric dipole moment of the
neutron.
243
Several proposals have been advanced for why
u
is so small.
40,244
In one of the most interesting,
u
is promoted
to the status of a dynamical variable that can relax to a natu-
ral value of zero. As a consequence, there arises a nearly
massless particle known as the
axion
, whose properties
~
and
the search for which
!
are well-described in Refs. 40, 244.
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G. String theory
A truly unified theory of interactions must include gravity.
The leading candidate for such a theory is
string theory
,
which originated in pre-QCD attempts to explain the strong
interactions
245–248
by replacing the space–time points of
quantum field theories with extended objects
~
‘‘strings’’
!
. In
1974 it was realized that string theories necessarily entailed a
massless spin-2 particle, for which the graviton was an ideal
candidate.
249
While it appeared that such theories required
space–time to be 26-dimensional
~
or 10-dimensional in the
presence of supersymmetry
!
, these extra dimensions were
interpreted in the 1980s as a source of the internal degrees of
freedom characterizing particle quantum numbers
~
see. e.g.,
Refs. 250–252
!
. A typical scenario whereby string theory
might yield predictions for the quark and lepton spectrum is
described in Ref. 253.
Early results on string theory are described in the textbook
by Green, Schwarz, and Witten.
41,42
Later texts are Refs. 43,
44. Descriptions for the non-specialist are given by Green,
122
Duff,
123
Greene,
100
and Weinberg.
132
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~
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!
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!
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313
313
Am. J. Phys., Vol. 71, No. 4, April 2003
Jonathan L. Rosner
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