Subatomic Physics

476 Quark Models of Mesons and Baryons
Table 15.2: Some Properties of Constituent Quarks.
Quark Charge (e) Spin I I3 S C B T Mass (MeV/c 2 ) †
u 2/3 1/2 1/2 1/2 0 0 0 0 330
d −1/3 1/2 1/2 −1/2 0 0 0 0 336
s −1/3 1/2 0 0 −1 0 0 0 540
c 2/3 1/2 0 0 0 1 0 0 1,550
b −1/3 1/2 0 0 0 0 −1 0 4,800
t 2/3 1/2 0 0 0 0 0 1 178, 000
† The masses cannot be measured directly; they are model-dependent, and hence approxi-
mate.
Table 15.3: Reordering the qq States According to
Strangeness and Isospin Component I3.
⎧
⎪⎨ 1
S
⎪⎩
0
−1
I3 = −1 −1/2 0 1/2 1
ds
us
du
uu, dd, ss
ud
su
sd
(color singlets). Quarks of all three colors and three anticolors must appear with
equal probability so that, for instance, the product uu should really be written as
urur + ugug + ubub
√ , (15.3)
3
where the subscripts denote the colors.
The matrix, (15.2), implies the existence of nine different mesons, in agreement
with the numbers listed in Table 15.1. However, the arrangement in Eq. (15.2) is
not made according to quantum numbers, and comparison with the experimentally
observed mesons is thus not obvious. In Table 15.3, the nine combinations are
reordered according to the values of the strangeness S and the isospin component
I3. Table 15.2 is helpful in such rearrangements. The states in Table 15.3 can
now be compared with the nine pseudoscalar and the nine vector mesons. For the
pseudoscalar mesons, arranging these in the same scheme gives
and for the vector mesons
K 0 K +
π − π 0 η 0 η ′ π +
K − K 0
K ∗0 K ∗+
ρ − ρ 0 ω 0 φ 0 ρ +
K ∗− K ∗0
(15.4)
. (15.5)