14. Quark model
1
14. QUARK MODEL
Revised September 2009 by C. Amsler (University of Z¨urich), T. DeGrand (University of Colorado,
Boulder), and B. Krusche (University of Basel).
14.1. Quantum numbers of the quarks
Quarks are strongly interacting fermions with spin 1/2 and, by convention, positive parity.
Antiquarks have negative parity. Quarks have the additive baryon number 1/3, antiquarks 1/3.
Table 14.1 gives the other additive quantum numbers (ﬂavors) for the three generations of quarks.
They are related to the charge
Q
(in units of the elementary charge
e
) through the generalized
GellMannNishijima formula
Q
=
I
z
+
B
+
S
+
C
+
B
+
T
2
,
(14
.
1)
where
B
is the baryon number. The convention is that the
favor
of a quark (
I
z
,
S
,
C
,
B
,or
T
)has
thesames
ignasits
charge
Q
. With this convention, any ﬂavor carried by a charged meson has the
same sign as its charge,
e.g.
, the strangeness of the
K
+
is +1, the bottomness of the
B
+
is +1,
and the charm and strangeness of the
D
−
s
are each
−
1. Antiquarks have the opposite ﬂavor signs.
Table 14.1:
Additive quantum numbers of the quarks.
Property

Quark
d
u
s
c
b
t
Q
– electric charge
−
1
3
+
2
3
−
1
3
+
2
3
−
1
3
+
2
3
I
– isospin
1
2
1
2
0
0
0
0
I
z
– isospin
z
component
−
1
2
+
1
2
0
0
0
0
S
– strangeness
0
0
−
1
0
0
0
C
–charm
0
0
0
+1
0
0
B
– bottomness
0
0
0
0
−
1
0
T
– topness
0
0
0
0
0
+1
14.2. Mesons
Mesons have baryon number
B
= 0. In the quark model, they are
q
q
±
bound states of quarks
q
and antiquarks
q
±
(the ﬂavors of
q
and
q
±
may be diFerent). If the orbital angular momentum of
the
q
q
±
state is
±
, then the parity
P
is (
−
1)
±
+1
. The meson spin
J
is given by the usual relation

±
−
s
≤
J
≤
±
+
s

,where
s
is 0 (antiparallel quark spins) or 1 (parallel quark spins). The charge
conjugation, or
C
parity
C
=(
−
1)
±
+
s
, is de±ned only for the
q
¯
q
states made of quarks and their
own antiquarks. The
C
parity can be generalized to the
G
parity
G
−
1)
I
+
±
+
s
for mesons
made of quarks and their own antiquarks (isospin
I
z
= 0), and for the charged
u
¯
d
and
d
¯
u
states
(isospin
I
=1)
.
K. Nakamura
et al.
,JPG
37
, 075021 (2010) (http://pdg.lbl.gov)
July 30, 2010
14:36