To understand how these quark substructures work, let us specifically examine the proton, neutron, and the two pions pictured in Figure 1 before moving on to more general considerations. First, the proton p is composed of the three quarks uud, so that its total charge is +23qe+23qe−13qe=qe+23qe+23qe−13qe=qe size 12{+ left ( { {2} over {3} } right )q rSub { size 8{e} } + left ( { {2} over {3} } right )q rSub { size 8{e} }  left ( { {1} over {3} } right )q rSub { size 8{e} } =q rSub { size 8{e} } } {}, as expected. With the spins aligned as in the figure, the proton’s intrinsic spin is +12+12−12=12+12+12−12=12 size 12{+ left ( { {1} over {2} } right )+ left ( { {1} over {2} } right )  left ( { {1} over {2} } right )= left ( { {1} over {2} } right )} {}, also as expected. Note that the spins of the up quarks are aligned, so that they would be in the same state except that they have different colors (another quantum number to be elaborated upon a little later). Quarks obey the Pauli exclusion principle. Similar comments apply to the neutron n, which is composed of the three quarks udd. Note also that the neutron is made of charges that add to zero but move internally, producing its wellknown magnetic moment. When the neutron β−β− size 12{β rSup { size 8{  {}} } } {} decays, it does so by changing the flavor of one of its quarks. Writing neutron β−β− size 12{β rSup { size 8{  {}} } } {} decay in terms of quarks,
n→p+β−+ve becomes udd→uud+β−+ve.n→p+β−+ve size 12{n rightarrow p+β rSup { size 8{  {}} } + { bar {v}} rSub { size 8{e} } } {} becomes udd→uud+β−+ve size 12{ ital "udd" rightarrow ital "uud"+β rSup { size 8{  {}} } + { bar {v}} rSub { size 8{e} } } {}.
(1)We see that this is equivalent to a down quark changing flavor to become an up quark:
d
→
u
+
β
−
+
v

e
d
→
u
+
β
−
+
v

e
size 12{d rightarrow u+β rSup { size 8{  {}} } + { bar {v}} rSub { size 8{e} } } {}
(2)Table 1: Quarks and Antiquarks
Name

Symbol

Antiparticle

Spin

Charge

B
B
size 12{B} {}

S
S
size 12{S} {}

c
c
size 12{c} {}

b
b
size 12{b} {}

t
t
size 12{t} {}

Mass
(
GeV
/
c
2
)
(GeV/
c
2
)

Up 
u
u
size 12{u} {}

u

u

size 12{ { bar {u}}} {}

1/2 
±
2
3
q
e
±
2
3
q
e
size 12{ + { {2} over {3} } q rSub { size 8{e} } } {}

±
1
3
±
1
3
size 12{ + { {1} over {3} } } {}

0 
0 
0 
0 
0.005 
Down 
d
d
size 12{d} {}

d

d

size 12{ { bar {d}}} {}

1/2 
∓
1
3
q
e
∓
1
3
q
e
size 12{ + { {1} over {3} } q rSub { size 8{e} } } {}

±
1
3
±
1
3
size 12{ + { {1} over {3} } } {}

0 
0 
0 
0 
0.008 

Strange 
s
s
size 12{s} {}

s

s

size 12{ { bar {s}}} {}

1/2 
∓
1
3
q
e
∓
1
3
q
e
size 12{ + { {1} over {3} } q rSub { size 8{e} } } {}

±
1
3
±
1
3
size 12{ + { {1} over {3} } } {}

∓
1
∓
1
size 12{ + 1} {}

0 
0 
0 
0.50 
Charmed 
c
c
size 12{c} {}

c

c

size 12{ { bar {c}}} {}

1/2 
±
2
3
q
e
±
2
3
q
e
size 12{ + { {2} over {3} } q rSub { size 8{e} } } {}

±
1
3
±
1
3
size 12{ + { {1} over {3} } } {}

0 
±
1
±
1
size 12{ + 1} {}

0 
0 
1.6 

Bottom 
b
b
size 12{b} {}

b

b

size 12{ { bar {b}}} {}

1/2 
∓
1
3
q
e
∓
1
3
q
e
size 12{ + { {1} over {3} } q rSub { size 8{e} } } {}

±
1
3
±
1
3
size 12{ + { {1} over {3} } } {}

0 
0 
∓
1
∓
1
size 12{ + 1} {}

0 
5 
Top 
t
t
size 12{t} {}

t

t

size 12{ { bar {t}}} {}

1/2 
±
2
3
q
e
±
2
3
q
e
size 12{ + { {2} over {3} } q rSub { size 8{e} } } {}

±
1
3
±
1
3
size 12{ + { {1} over {3} } } {}

0 
0 
0 
±
1
±
1
size 12{ + 1} {}

173 
Table 2: Quark Composition of Selected Hadrons
Particle

Quark Composition

Mesons

π
+
π
+
size 12{π rSup { size 8{+{}} } } {}

u
d

u
d

size 12{u { bar {d}}} {}

π
−
π
−
size 12{π rSup { size 8{  {}} } } {}

u

d
u

d
size 12{ { bar {u}}d} {}

π
0
π
0
size 12{π rSup { size 8{0} } } {}

uuuu size 12{u { bar {u}}} {}, dddd size 12{d { bar {d}}} {} mixture 
η
0
η
0
size 12{η rSup { size 8{0} } } {}

uuuu size 12{u { bar {u}}} {}, dddd size 12{d { bar {d}}} {} mixture 
K
0
K
0
size 12{K rSup { size 8{0} } } {}

d
s

d
s

size 12{d { bar {s}}} {}

K

0
K

0
size 12{ { bar {K}} rSup { size 8{0} } } {}

d

s
d

s
size 12{ { bar {d}}s} {}

K
+
K
+
size 12{K rSup { size 8{+{}} } } {}

u
s

u
s

size 12{u { bar {s}}} {}

K
−
K
−
size 12{K rSup { size 8{  {}} } } {}

u

s
u

s
size 12{ { bar {u}}s} {}

J
/
ψ
J
/
ψ
size 12{J/ψ} {}

c
c

c
c

size 12{c { bar {c}}} {}

ϒ
ϒ 
b
b

b
b

size 12{b { bar {b}}} {}

Baryons,

p
p
size 12{p} {}

uud
uud
size 12{ ital "uud"} {}

n
n
size 12{n} {}

udd
udd
size 12{ ital "uud"} {}

Δ
0
Δ
0
size 12{Δ rSup { size 8{0} } } {}

udd
udd
size 12{ ital "uud"} {}

Δ
+
Δ
+
size 12{Δ rSup { size 8{+{}} } } {}

uud
uud
size 12{ ital "uud"} {}

Δ
−
Δ
−
size 12{Δ rSup { size 8{  {}} } } {}

ddd
ddd
size 12{ ital "ddd"} {}

Δ
++
Δ
++
size 12{Δ rSup { size 8{"++"} } } {}

uuu
uuu
size 12{ ital "uuu"} {}

Λ
0
Λ
0
size 12{Λ rSup { size 8{0} } } {}

uds
uds
size 12{ ital "uds"} {}

Σ
0
Σ
0
size 12{Σ rSup { size 8{0} } } {}

uds
uds
size 12{ ital "uds"} {}

Σ
+
Σ
+
size 12{Σ rSup { size 8{+{}} } } {}

uus
uus
size 12{ ital "uus"} {}

Σ
−
Σ
−
size 12{Σ rSup { size 8{  {}} } } {}

dds
dds
size 12{ ital "dds"} {}

Ξ
0
Ξ
0
size 12{Ξ rSup { size 8{0} } } {}

uss
uss
size 12{ ital "uss"} {}

Ξ
−
Ξ
−
size 12{Ξ rSup { size 8{  {}} } } {}

dss
dss
size 12{ ital "dss"} {}

Ω
−
Ω
−
size 12{ %OMEGA rSup { size 8{  {}} } } {}

sss
sss
size 12{ ital "sss"} {}

This is an example of the general fact that the weak nuclear force can change the flavor of a quark. By general, we mean that any quark can be converted to any other (change flavor) by the weak nuclear force. Not only can we get d→ud→u size 12{d rightarrow u} {}, we can also get u→du→d size 12{u rightarrow d} {}. Furthermore, the strange quark can be changed by the weak force, too, making s→us→u size 12{s rightarrow u} {} and s→ds→d size 12{s rightarrow d} {} possible. This explains the violation of the conservation of strangeness by the weak force noted in the preceding section. Another general fact is that the strong nuclear force cannot change the flavor of a quark.
Again, from Figure 1, we see that the π+π+ size 12{π rSup { size 8{+{}} } } {} meson (one of the three pions) is composed of an up quark plus an antidown quark, or udud size 12{u { bar {d}}} {}. Its total charge is thus +23qe+13qe=qe+23qe+13qe=qe size 12{+ left ( { {2} over {3} } right )q rSub { size 8{e} } + left ( { {1} over {3} } right )q rSub { size 8{e} } =q rSub { size 8{e} } } {}, as expected. Its baryon number is 0, since it has a quark and an antiquark with baryon numbers +13−13=0+13−13=0 size 12{+ left ( { {1} over {3} } right )  left ( { {1} over {3} } right )=0} {}. The π+π+ size 12{π rSup { size 8{+{}} } } {} halflife is relatively long since, although it is composed of matter and antimatter, the quarks are different flavors and the weak force should cause the decay by changing the flavor of one into that of the other. The spins of the uu size 12{u} {} and dd size 12{ { bar {d}}} {} quarks are antiparallel, enabling the pion to have spin zero, as observed experimentally. Finally, the π−π− size 12{π rSup { size 8{  {}} } } {} meson shown in Figure 1 is the antiparticle of the π+π+ size 12{π rSup { size 8{+{}} } } {} meson, and it is composed of the corresponding quark antiparticles. That is, the π+π+ size 12{π rSup { size 8{+{}} } } {} meson is udud size 12{u { bar {d}}} {}, while the π−π− size 12{π rSup { size 8{  {}} } } {} meson is udud size 12{ { bar {u}}d} {}. These two pions annihilate each other quickly, because their constituent quarks are each other’s antiparticles.
Two general rules for combining quarks to form hadrons are:
 Baryons are composed of three quarks, and antibaryons are composed of three antiquarks.
 Mesons are combinations of a quark and an antiquark.
One of the clever things about this scheme is that only integral charges result, even though the quarks have fractional charge.
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