Download SLAC-PUB-2310 April 1979 (T/E) A SCHEMATIC MODEL OF

SLAC-PUB-2310
April 1979
(T/E)
A SCHEMATICMODELOF QUARKSAND LEPTONS*
**
Haim Harari
Stanford Linear Accelerator
Center
Stanford University,
Stanford,
California
94305
ABSTRACT
We consider
a scheme in which all
of only two types of fundamental
l/3
level
and 0.
The concepts
of the composite
nect only composite
for several
states,
regularities
objects
and flavor
with
acquire
are composites
electric
charges
meaning only at the
Gauge bosons such as W' or gluons con-
and are not fundamental.
of the observed pattern
However, we cannot offer
questions
spin l/2
of color
systems.
quarks and leptons
any convincing
dynamics,
The scheme accounts
of quarks and leptons.
leaving
many important
unanswered.
Submitted
to Physics Letters
*
Work supported
N-76-C-03-0515.
**
On leave of absence from the Weizmann Institute
ISRAEL.
by the Department
of Energy under contract
of Science,
number
Rehovot,
The discovery
in three
colors,
of at least
raise
of matter
It
there
unlikely
they consist
indicated
charge quantizations
for
charges of quarks and leptons
ve, e-, u, d).
Additional
motivation
each generation,
generation
the masses.
It
combinations
create
all
is possible
all
construction
SO(N) groups.
motivation
structure
of its
is offered
by the
Here we have
within
predecessors,
some fundamental
of quarks and leptons,
excitations
fundamental
interactions,
including
of a class
of extended
supergravity
such theory
except for
entities
while
whose
the next
of the same system.
is much more speculative.
The largest
in each "genera-
appear in an analogous way and each
to envisage
one generation
fact,
scheme, is the
at a common substructure:
the properties
are simply higher-order
Our final
to unify
both hinting
would arise
empirical
of quarks and leptons.
quarks and leptons
reproduces
generations
for an underlying
of "generations"
facts,
by a successful
from
connection
A related
vanishing
(e.g.,
that,
and quarks.
Such a connection
explained
two independent
some
by the relation-
a mysterious
of the same objects.
sum of electric
suggests
leptons
which should be naturally
observed pattern
conceal
are constructed
This is particularly
between the charges of quarks and leptons.
tion"
six)
that more than 20 building
of the Hydrogen atom reflects
if
(and probably
these particles
both types of particles
ship between the electric
naturally
five
between quarks and leptons
entities.
The neutrality
each appearing
are fundamental.
is a substructure,
the same basic
that
is simply
The observed similarity
if
of quarks,
of at least
the possibility
substructure.1
blocks
flavors
and the observation
types of leptons,
further
five
Ambitious
gravity,
theories,
attempts
have led to the
3
based on the
which accommodates the J= 2
-3graviton
without
28 vector
fail
introducing
J= 5/2 fields
bosons and 56 fermions.
However, even these large
to accommodate the W'-bosons
overall
unification
is carried
quarks and leptons,
out at the level
scheme.
possibly
multiplets
3
and the u, T and b fermions.
allowing
In such a model,
fermions
for
If
the
of the substructure
the number of fundamental
would be much smaller,
supergravity
is based on SO(8), yielding
of
and vector
a more realistic
bosons
extended
p, 't, b and even W" would not be
fundamental.
Several
different
arguments lead us to believe
substructure
may be observed
only at extremely
respondingly
large
The well-known
behavior
momenta.
of leptons
correspond
and quarks indicates
to distances
well
of deep inelastic
correct
like"
value)
functions
second-generation
fermions
u*e+y,
s-td-i-y
the tiny
radii
present
tic
course,
on the rate
involved
model,
and the approximate
that
leptons
The details
scaling
(and
and quarks are "point-
of the same bound
transitions
indicates
be much smaller
of QED
constancy
but suppressed by factors
for u+e+y
must
accuracy
the approximate
fermions,
may actually
below 10-24 cm.
the "point-like"
The present
of such systems or the heavy constituent
upper limit
distances
probably
might be allowed,
for
and cor-
such a substructure
are excitations
system which forms the first-generation
distances
evidence
below 10-16 cm.
of R
all indicate
e+e- '
down to 10-16 cm.
at least
If
structure
short
that
the success of the Weinberg-Salam
tests,
that any possible
such as
representing
masses.
that
The
the characteris-
than 10-16 cm, and
of such calculations
depend, of
on the unknown dynamics.
Finally,
if
baryon and lepton
quarks and leptons
number violations
are "made" of the same objects,
are very likely.
The present
limit
-4on the proton's
with
gravity
hints,
Having realized
are many orders
is different
that
of magnitude
for
example,
are sufficient
for
tical
blocks.
building
below our present
presently
explaining
happen only
Uni-
leptons
should somehow reproduce
dynamics
It would be premature
established
ideas of gauge theories
of the new hypothe-
dynamics at very short
and is likely
to involve
However, when viewed at present
in which quarks,
which
and intui-
the relevant
the interactions
different,
distances
understanding
that
the correct
In fact,
new principles.
it
the possibility
that
fully
must involve
we have seen, so far.
may be radically
distances,
like",
can probably
at the Planck mass, corresponding
any substructure
from anything
to insist,
entirely
this
of course,
we should not exclude
distances
that
around 10-34cm .
to distances
tion,
indicates
below 10-2gcm , or momenta somewhere above 10 15 GeV.4
at distances
fication
lifetime
and ordinary
some
energies
and
gauge bosons are "point-
currently
accepted
theories
such as
discussed
possible
substructures.
SU(2) x U(1) and QCD.
Several
All
published
blocks
authors1
have already
were assigned
either
color
from these ideas in both respects.
may be generated
through
blocks,
and cannot be attributed
further
suggest that
W' and the gluons)
fundamental.
fundamental?
If
or flavor
and the standard
We wish to consider
remained fundamental.
flavor
the fundamental
schemes have two common features:
at least
one accepts
combinations
both color
and
of the fundamental
to the building
some of our present
a composite
gauge bosons
here a scheme which differs
We suggest that
act only on composite
building
states
electron,
blocks
building
themselves.
We
gauge bosons (such as
and are therefore
not
why should W' remain
'
-5In a composite model of quarks and leptons,
charge must, presumably,
economical
charged
be one third
set of building
(Q=1/3)
our scheme.
blocks
of the electron
consists
and one neutral.
charge.
of two J=1/2
This is precisely
We denote the charged particle
We name these particles
the fundamental
"Rishons".
5
Their
electric
The most
objects:
the full
content
by T and the neutral
antiparticles
one
of
one by V.
are T(.Q=-l/3)
and a(Q=O).
The simplest
composite
There are eight
can be constructed
This is a Q=+l
TTT.
(ii)
TTV, TVT, VTT.
fermion.
We identify
These form three Q=+2/3
the dynamics is such that
We identify
these states
other
from three
rishons.
combinations:
0)
that
fermion
it
fermions.
the three
states
them as the three
color-states
are degenerate,
we may clearly
three orthogonal
combinations
as the positron
e+.
We suggest
are degenerate.
of the u-quark.
replace
If
them by any
and we have an overall
"color"
SU(3) symmetry among them.
(iii)
Three degenerate
TW, VTV, WT.
the three
(iv)
WV.
A neutral
Note that
lepton
color-states
clearly:
the three-rishon
;,(.e);
rishons
in a quark.
allowed
arrangement
assigned
color
identified
states
create
relates
as
a
are
e-(.!?T).
internal
arrangements
of
because they have only one
The rishons
(TTT or VW).
an antiquark,
of the above states
to different
Leptons have no color
because there
a quark,
~(~~,~~~,~~~);
degrees of freedom.
than two or four)
identified
as ve.
The antiparticles
d(~T,~?!?,T~);
The concept of color
fermions,
of the 8-antiquark.
fermion,
and an antilepton.
Q=+1/3
themselves
Quarks have three
cannot be
colors
are three ways to arrange
(rather
three
rishons
-6in a quark
(and because two rishons
In the limit
in which the net number of T's and V's are conserved,
we have two additive
quantum numbers:
n(T)1 - n(T)
=
34
n(V) - n(v)
=
34 - 3($-L)
where Q,B,L are the usual electric
ber.
We immediately
but their
mixing,
see that
difference
is conserved.
cannot make a fermion).
charge,
baryon number and lepton
baryon and lepton
is conserved,
number are not conserved,
as long as the net number of rishons
However, we may wish to consider
in which case, B-L will
Baryon-number
violating
num-
parity
not be exactly
processes
violating
V-v
conserved.
are allowed.
An important
example is:
u+u
or,
equivalently:
3 f e+
+
(TTV) + (TTV) -t (TW)+
process which is responsible
for proton
(TTT).
This is precisely
the
decay in grand unification
schemes6 such as SU(5).
The relation
scheme.
between quark and lepton
The empirical
observation
charges is natural
concerning
charges of ve, e-, u, d is now explained
the vanishing
by the assertion
them (ye, u) contain
rishons
while
The total
content
of ve, e-, u, d includes
rishons.
rishons
and antirishons
of electric
charges.
for each generation
aware of this
simple regularity.
antimatter
is interesting
(d,e-)
guaranteeing
The same argument correctly
of B-L values
It
the two others
(6T+6V+6T+6@,
also vanishes.
to note that,
may be equally
in this
at the level
abundant in the universe.
sum of
that
contain
two of
anti-
equal numbers of
a vanishing
predicts
that
sum
the sum
We were not previously
of rishons,
matter
A hydrogen atom
and
-7contains
an equal number of rishons
The second and third
ably constructed
generation
generations
must contain
of the energy levels
rates
unit
between single
states.
rishon
quantum numbers of W+ (Q=l
will
yield
nect only composite
and universality
and quarks,
energy values.
masses) and of
the role
played by the usual gauge bosons.
of electric
charge is l/3,
In fact,
; B-L=O)
a state
the simplest
corresponds
on a fermion
of three rishons,
W+[K>
=
ITTT >
W+ 1 ET>
=
IVTT >
provided
ie+e+,
d+u,
the \? cannot act
boson with
to a state
the
of the form
which consists
of three
e.g.:
The We-+v e' as required.
-----the quantum numbers of (TTTWV).
Both W+ and W- can con-
Thus W+ can convert
color
(quark and lepton
Such a boson, when acting
boson carries
at higher
Each
among them, depend on the unknown dynamics.
Since the fundamental
antirishons,
are presum-
generation.
the same set of states,
We now proceed to discuss
(TTTVVV).
of quarks and leptons
in an analogous way to the first
The calculation
transition
and antirishons.
The W'-bosons
states.
is likely
that
u-t;,
to hold for
their
Gluons change a VTT state
couplings
into
quarks assumed in grand unification
quantum numbers of a six-rishon
their
couplings
under
to leptons
They rearrange
states.
theories6
state.
singlets
are symmetric between T and V.
TVT, etc.
in a quark and can act only on composite
quark of Su(5) corresponds
are presumably
the rishons
Some of the lepto-
are also carrying
For instance,
the
the Q= 4/3 lepto-
to (TTTTW).
If W' (and Z) are composite,
sets of W's and Z's may exist.
it
Parity
is reasonable
to guess that
may be violated
several
at the short
dis-
-8tances relevant
it
to our scheme (perhaps
may be conserved at small distances
80-90 GeV masses predicted
for
No symmetry principle
prevents
Such transitions
between ground and excited
Their
relative
strengths
processes,
define
we can offer
Assuming that
x SUWR
xU(1)
J
em
about their
We presumably
understanding
inte-
speculation
generalizations.
violation
concerning
in weak
the Weinberg
dynamics somehow leads to an
Bw is defined
generators
of these neutral
effective
of SU(Z)h,
by:
currents
couplings
carry
SU(2)R and U(l),
no net charges,
to our fundamental
have
W's couple
B is right-left
of parity
say, TeV energies,
at,
J em = &
Since all
by small overlap
sin fjw(Wl + Wi) + 4~0s 2ew B
Since all
we may talk
state
but they are not forbidden.
the short-distance
=
say, the ground
--of WT (namely,
the Cabibbo angle and its
where Wl, gR and B are the neutral
respectively.
to an excited
only a wild
theory
at larger
weak bosons above the
W' from connecting,
states,
In the absence of a clear
sumL
and broken spontaneously
may be suppressed
grals
Alternatively,
the usual W and Z.
the u-quark)
of TTV (namely,
the s-quark).
angle.
V-v mixing)..
In both cases we may have additional
distances.
state
through
(T,Y,TL
symmetrically
+ TRYvT~)
to T and V we must have:
3 =
WL
&
(TLr,TL
w; = $j
(TRYpTR +
symmetric
and orthogonal
B =: + (?,v,TL
+
‘Ryp‘R)
tow;, w;. Hence:
+ TRYuTR - VLYgJL
- v~ yp 'R)
objects.
-9Substituting
these expressions
into
the defining
equation
for
Bw we find
1
sin28 w = -z
This pleasant
understand
presently
result
should be taken seriously
the transition
only when and if
from the unknown dynamics of our scheme to the
accepted gauge theory
of electroweak
interactions.
Needless to say, we have major difficults,
of a dynmaical
(1)
A full
theory
low-lying
must explain
The question
consist
3T+3V,
but not free
is still
TTV? All
Why do we have
observed particles
in
(e.g.,
p is 3T+TT+2e).
between generations
splittings
are extremely
which consist
Is there a mass-generating
electric
charge?
equally
mysterious.
to puzzle
by returning
small when com-
to the relevant
radii.
solely
distances?
However, neutrinos
of neutral
mechanism of parity
to our original
scheme proposed here is extremely
us.
How
rishons.
mechanism which is somehow linked
The detailed
economical.
The
remains unexplained.
of order GeV at such short
masses continue
are the only particles
We conclude
open.
of TTT, TT, VW, w
pared to momenta which are conjugate
The neutrino
why we do not have
and what is the quantum number
The mass spectrum of quarks and leptons
do we generate
fermions
why the three different
only of combinations
mass splittings
(.iv>
to the lack
between generations.
of quark confinement
free TTT states
(iii)
and one antirishon,
of TTV are degenerate,
which distinguishes
a+is
relating
why we do not have low-lying
J= 3/2 quarks and leptons,
arrangement
nature
all
theory.
composed of two rishons
(ii)
we fully
list
It
violation
that
is
The
of motivations.
suggests
with
all
of
-lOmatter
consists
of only two fundamental
zation
of quark and lepton
generation
appears naturally
obtained.
The concepts
level
of composite
supergravity
six vector
(T,V,'?,v)
vincing
charges is explained,
and the similarity
of color
states.
(charges
&l/3,
dynamics to offer,
leaving
We thank L. F. Abbott,
Freedman, F. J. Gilman,
with
The related
the contents
are meaningful
of each
that
is
only at the
an SO(4) extended
one graviton,
four gravitinos,
_+1/3, 0, O), four J=1/2
Finally,
quanti-
between generations
We may even speculate
and two J= 0 particles.
discussions.
and flavor
7
scheme may be considered
particles
entities.
rishons,
we do not yet have any con-
many, many open questions.
R. M. Barnett,
J. D. Bjorken,
E. Cohen, D. Z.
G. L. Kane, H. R. Quinn and P. Ramond for helpful
-ll-
REFERENCES
1.
For an earlier
consideration
of a substructure,
see e.g.:
and A. Salam, Phys. Rev. DlO (1974) 275; H. Terazawa,
J. C. Pati
Y. Chikashige
and K. Akama, Phys. Rev. D15 (1977) 480; S. L. Glashow, Harvard
Preprint
HLJTP-77/A005, unpublished;
(1979) 69; G. 't Hooft,
Symposium, Jerusalem
building
blocks
Y. Ne'eman, Phys. Lett.
Proceedings
(1979),
of the Einstein
to be published.
in these papers are called,
Centennial
The fundamental
respectively,
(or preons),
subquarks,
2.
For a review
see e.g.,
H. Harari,
3.
For a review
see e.g.,
D. Z. Freedman, Proceedings
International
82B
prequarks
maons, alphons and quinks.
Conference
Phys. Reports
42C (1978) 235.
on High Energy Physics,
of the 19th
Tokyo, p. 535
(1978).
4.
H. Georgi,
H. R. Quinn and S. Weinberg,
Phys. Rev. Lett.
33 (1974)
451.
5.
"Rishon"
means first,
from Genesis &2
everything
was "Tohu va-Vohu"
while
The choice of T and V
(in Hebrew).
originates
reader might
6.
primary
where before
the creation
(unformed and void;
simply remember that
of matter
chaos).
The
the charge of T is one Third
the charge of V Vanishes.
H. Georgi and S. L. Glashow, Phys. Rev. Lett
original
suggestion
of baryon non-conservation
theories
is due to J. C. Pati
32 (1974) 438.
The
in grand-unification
and A. Salam, Phys. Rev. -D8 (1973)
1240.
7.
Phys. B127 (-1977) 259; E. Cremmer,
E. Cremmer and J. Scherk,
Nucl.
J. Scherk and S. Ferrara,
Phys. Lett.
74B (1978) 61.