Quark Soup
Elementary Particles?? (circa 1960)
p(pions), l, r, w, y, h
K, , etc
proton neutron
D0 S+ X0 L, Lc, Lb,
Etc
www-pnp.physics.ox.ac.uk/~huffman/
Long before the discovery of quantum
mechanics, the Periodic table of the Elements
gave chemists a testable model with enough
predictive power to search for the missing ones.
Examples of Similarities among
‘elementary’ particles
Total Spin 1/2: p+ n  938, 939 (all masses in MeV)
0  1116
+ 0 -  1189,1192, 1197
0 -  1315, 1321
D++, D+, D0, D-  1231, 1235, 1234, 1235(?)
Total Spin 0:  0  139, 134 (all masses in MeV)
0  547
K K0L K0S  494, 497
’ 0  958
These similarities are what has
D D0 1869, 1864
led to the quark model of
c0  2980
particle bound states.
Quark Model Botany lessons:
Quarks:
up
down
charm
strange
top
bottom
Hadrons: Everything that is a bound state of the quarks which are
spin 1/2 (Fermions).
Held together by the strong nuclear force.
Hadrons split into two sub-classes:
Meson
Mesons: bound quark- antiquark pairs.
Bosons; none are stable; copiously produced in
interactions involving nuclear particles.
Baryons: bound groups of 3 quarks or 3 antiquarks.
Baryon
Fermions; proton is stable; neutron is almost stable;
copiously produced in interactions involving
nuclear particles.
Conservation of Baryon number  conservation of quark number
More Botany lessons:
Leptons: electron
ne
muon
nm
tau
nt  neutrinos
Each individual Lepton number is conserved exactly in all interactions
electron number, muon number, and tau number are all conserved.
(But New Discovery of Neutrino oscillations at SNO!)
You will learn about this later in the course.
Leptons do not form any stable bound states with
themselves, only with hadrons (in atoms).
Since Leptons also do not interact with the strong nuclear force,
we will not discuss them much further in this part of the course.
The Fermions of the Standard Model
• The Hadrons composite structures
• The Leptons ‘elementary’
• What does ‘elementary’
mean?
• ANS: an exact
geometric point in
space.
• Are the quarks and
leptons black holes?
• ANS: Beats me!
What Makes a Theory “Good”?
Any theory … not just a theory of
matter and Energy.
Falsifiable!
Baryon Octet:
The only Example 
There is also a complete octet where
L = 1 but you will never see it.
JP = 1/2+
S
n p
uud
udd
0
-1
S   S 0  S + 1190
L0
uds
dds
uss
dss
-2
X   X 0 1320
uus
Notes:
U+D-S = 3
for all Baryon states.
I3
-1
-1/2
0
1/2
1
Quark compositions are NOT
the same as quark wave functions
Baryon Decuplet:
The only Example 
S
D  D0  D+  D+ +
uuu
uud
udd
ddd
JP = 3/2+
0
S   S0  S + 1385
dds
-1
dss
-2
uus
uds
X   X 0 1530
  1673
uss
-3
sss
I3
-3/2
-1
-1/2
0
1/2
1
3/2
Examples
Meson Nonets:
S
ds
Pseudoscalars
JP = 0 K0  K+
h
p p0 p+
h
us
1
K  K0
0
u u, d d, s s
du
ud
Vector Mesons
JP = 1 -
K 0*  K +*
-1
Q=1
su
sd
Q=0
Q = -1
I3
-1
-1/2
0
1/2
1
w0
r  r0  r+

K *  K 0*
Much Ado about Isospin
(apologies for revealing my bias)
Talk about ad hoc!
First we make ‘upness’ and ‘downness’ and then proceed to make
this Isospin quantum number, the ‘z’ component of which is really
just 1/2 times up-ness or down-ness.
Legitimate question:
Is this useful at all?
Why is there no uuu or ddd state in the spin 1/2 Baryon chart?
Before we get much deeper into Isospin though, it would be a
good idea to divert somewhat and revision on spin 1/2 particles
and introduce the Special Unitary group in Two dimensions (the
infamous SU(2)).
1/2 x 1/2
1
+1
+1/2 +1/2
1
+1/2 -1/2
-1/2 +1/2
J
M
Notation:
1
0
1/2
1/2
-1/2
0
0
1/2 1
- 1/2 - 1
-1/2 1
m1
m1
.
.
m2
m2
.
.
J
M
coefficient
1 x 1/2
3/2
+3/2 3/2
1/2
+1 +1/2
1 +1/2 + 1/2
+1 -1/2
1/3
2/3 3/2 1/2
0 +1/2
2/3 -1/3 -1/2 -1/2
0
-1/2 2/3 1/3 3/2
-1
+1/2 1/3 -2/3 -3/2
-1 -1/2
1
Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).
3/2 x 1
5/2
+5/2 5/2
3/2
+3/2 +1
1 +3/2 +3/2
+3/2
0 2/5 3/5
+1/2 +1 3/5 -2/5
+3/2 -1
+1/2 0
-1/2 +1
J
M
Notation:
5/2
3/2 1/2
+1/2 +1/2 +1/2
1/10 2/5
1/2
3/5 1/15 -1/3
5/2
3/10 -8/15 1/6 -1/2
+1/2 -1 3/10
-1/2 0
3/5
-3/2 +1 1/10
m1
m1
.
.
m2
m2
.
.
J
M
coefficient
3/2 1/2
-1/2 -1/2
8/15 1/6
-1/15 -1/3 5/2 3/2
-2/5 1/2 -3/2 -3/2
-1/2 -1 3/5 2/5 5/2
-3/2
0
2/5 -3/5 -5/2
-3/2 -1 1
Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).