Triplet Model of Elementary Particles
The model of a fundamental triplet of fractionally charged fermions* (quarks) has been remarkably successful in producing many numbers of direct experimental significance. In this model pseudoscalar and vector SU3 octets and singulets are pictured as quar
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I. Introduction
The model of a fundamental triplet of fractionally charged fermions* (quarks) has been remarkably successful in producing many numbers of direct experimental significance. In this model pseudoscalar and vector SU 3 octets and singulets are pictured as quark-antiquark bound in an s-state. The baryon oc~et and decuplet are three quarks in an s-state and the forces which hold the quarks together appear to be to a large extent independent of spin and unitary spin. In this SU 6-approximations the above mentioned bosons belong to the 35 and 1 rep-
*
t
Their quantum numbers are: T
T
(N = Baryon number
N
Q
y
p
1 /3
2/3
1/3
2/3
1 /2
1 /2
Y
Hypercharge
n
1/3
-1/3
1/3
-1/3
-1/2
1/2
Q
Charge
A
1 /3
-1/3
-2/3
-1/3
0
II
ll/llq
3
0
= Magnetic moment)
Lecture given at V. Internationalen Universitätswochen für Kernphysik, Schladming, 24 February - 9 March 1966.
P. Urban (ed.), Elementary Particle Theories © Springer-Verlag GmbH Wien 1966
295
resentations and the baryons to the 56 representation. Their quark content lS as follows
spins are antiparallel
l2.1
P
+
p p
+
, TI
0
, TI
l.
n·l
0
= np = pn
K*+ ,K +
1 = 72(pp-nn)
K*- ,K -
PA
-*0 -0 K ,K
nA
AP
K*o , KO
=
An
1 = 72(pp+nn)
w. l ~
, TI
=U 1 2U-pp-nn) = n(
The vector particles correspond to spin parallel and the pseudoscalar particles to spin antiparallel.
2§.1
p
ppn
- *- =
N
pnn
,,*0
= pU
L:+
PPA
y*-
nnA
L: 0
pnA
y*o
pnA
L:
nnA
y*+
AO
pnA
N*-
pU
N*o
-
nU
N*+
npp
rl
AU
N*++
ppp
,,0
=
nAA
(2)
PPA nnn
=
nnp
. 1 / 2 + parHere in 3/2+ particles all spins are parallel and ln
ticles one pair of quark spins is antiparallel. The total spin-
296 unitary spin wave function is totally symmetric~. We added a subscript i to some of these bosons since these ideal configurations are mixed by SU 6 breaking terms. Assuming that these are mainly a higher mass for A than for p and n we see that to first order this induces an equal spacing in the baryon octet and decuplet. The vector meson nonet also has equal spacing whereas the pseudoscalar octet satisfies the Gell-Mann Okubo mass formula. A more exact theory goes as follows. heavier by 2ß than pp and un. If m
8
AA is
and mare the octet and 1
singulet masses for perfect symmetry we find the following masses 11
m
K ,K:
m
p,
..
For the T
8
8
+ ß
=
Y
=
representation)
m
+
8
4
3'
0 states we have the mass matrix (in thel88 81 18 1 1
2/2"
-3- I ß
ß
(4) 2/2"
-3- I ß
m
2
+ - ß 3
1
if I is the overlap integral of the 35 and 1 wave functions.
(4) are
The eigenvalues of m +m 8
2
J
+ ß
±
and the eigenvectors ~+
= ~8cosa + ~lsina
~
=
-
~lcosa
-
~
8
sina
.. These wave-functions are written out in full in W. Thirring, Acta Physica Austriaca, Suppl. 11, 1965.
297 with
212 I
tga. =
mS~ml
+ % +
/:"/3
[(mS~ml
(6)
~
+ %)2 +
/:,.2 1 2]1/2
For the pseudoscalar particles m1 -m S »/:" and there is not much octet-singulet mixing. One finds from the observed (masses)2 mg
=
140, m 1
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