Elementary Particles
371
small compared to the baryonic masses). If these differences in masses are
ignored, an extra degeneracy exists between the states with different I, which is
equivalent to having the same mass for u, d and s quarks. This is reminiscent of
the accidental degeneracy of the hydrogenic levels where the states with different
l have the same energy. The interaction between the quarks is approximately
invariant under transformations which mix u, d and s. As in Eq. (10.5), these
transformations retain orthonormality and satisfy the phase condition for the
determinant. This invariance gives rise to what is called the SU (3) symmetry.
The multiplets of this symmetry which transform among themselves, have
dimensions 1, 8, 8, 10 for the three-quark system, 1 and 8 for the quark-antiquark
system etc. The observed multiplets are the baryon octet [shown in Fig. (10.1)],
the pseudoscalar meson octet, the baryon decuplet with spin 3/2 and positive
parity, etc. It should be mentioned that the symmetries not only imply the equality
of the masses of the components of each multiplet, but also relate many of their
other properties such as the magnetic dipole moment, the interaction strengths.
etc. With the addition of charmed, top and bottom quarks, the symmetry can be
extended to SU (6) symmetry, which implies symmetry under transformations
which involve all the six quarks.
– 2
– 1
0
1
2
2
1
0
– 1
– 2
N
P
S
–
S
+
S
o
X
–
X
0
L
Y = S + B
I z
Fig. 10.1 The baryon octet shown in terms of I z and Y = S + B
(Y is called the hypercharge).
It may be noted that processes which involve only strong interaction conserve
charge, I z , I, strangeness, charm, etc. Indeed, it appears that even the constituently
quarks retain these properties. An interesting example of this was the discovery
of a group of spin 1 particles called Ψ, Ψ′, etc. which have masses greater than
3 × 10
3
MeV but very long lifetimes (about 10
4
times the lifetime of other
vector mesons such as the ρ, etc.). They have a net charm of zero, but are made
371
small compared to the baryonic masses). If these differences in masses are
ignored, an extra degeneracy exists between the states with different I, which is
equivalent to having the same mass for u, d and s quarks. This is reminiscent of
the accidental degeneracy of the hydrogenic levels where the states with different
l have the same energy. The interaction between the quarks is approximately
invariant under transformations which mix u, d and s. As in Eq. (10.5), these
transformations retain orthonormality and satisfy the phase condition for the
determinant. This invariance gives rise to what is called the SU (3) symmetry.
The multiplets of this symmetry which transform among themselves, have
dimensions 1, 8, 8, 10 for the three-quark system, 1 and 8 for the quark-antiquark
system etc. The observed multiplets are the baryon octet [shown in Fig. (10.1)],
the pseudoscalar meson octet, the baryon decuplet with spin 3/2 and positive
parity, etc. It should be mentioned that the symmetries not only imply the equality
of the masses of the components of each multiplet, but also relate many of their
other properties such as the magnetic dipole moment, the interaction strengths.
etc. With the addition of charmed, top and bottom quarks, the symmetry can be
extended to SU (6) symmetry, which implies symmetry under transformations
which involve all the six quarks.
– 2
– 1
0
1
2
2
1
0
– 1
– 2
N
P
S
–
S
+
S
o
X
–
X
0
L
Y = S + B
I z
Fig. 10.1 The baryon octet shown in terms of I z and Y = S + B
(Y is called the hypercharge).
It may be noted that processes which involve only strong interaction conserve
charge, I z , I, strangeness, charm, etc. Indeed, it appears that even the constituently
quarks retain these properties. An interesting example of this was the discovery
of a group of spin 1 particles called Ψ, Ψ′, etc. which have masses greater than
3 × 10
3
MeV but very long lifetimes (about 10
4
times the lifetime of other
vector mesons such as the ρ, etc.). They have a net charm of zero, but are made