Quark Soup
Elementary Particles?? (circa 1960)(pions),K, , etc
proton neutron c,b,Etc
www-pnp.physics.ox.ac.uk/~huffman/
Long before the discovery of quantum
m
echanics, the Periodic table of the E
lements
gave chemists a testable m
odel with enough
predictive power to search for the m
issing ones.
Re su
l t:D
is c ov e r y of Ge a n
d G
a(am
ong o th
e r s)
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
++, +, 0, - 1231, 1235, 1234, 1235(?)
Total Spin 0: 0 139, 134 (all masses in MeV) 0 547
K K0L
K0S
494, 497 ’ 0 958 D D0 1869, 1864 c
0 2980
These similarities are what has led to the quark model of particle bound states.
Quark Model Botany lessons:
Quarks: up charm top down strange 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: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. Fermions; proton is stable; neutron is almost stable;
copiously produced in interactions involving nuclear particles.
Conservation of Baryon number conservation of quark number
Meson
Baryon
More Botany lessons:
Leptons: electron muon tau e neutrinos
Each individual Lepton number is conserved exactly in all interactionselectron 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:
I3
JP = 1/2+The only Example There is also a complete octet where L = 1 but you will never see it.
pn
0
0 1190
13200
0
S
0 1/2-1/2-1 1
-2
-1
udd uud
udsdds uus
dss uss
Notes:U+D-S = 3for all Baryon states.
Quark compositions are NOTthe same as quark wave functions
Baryon Decuplet:
I3
JP = 3/2+The only Example
0
15300
S
0
0 1/2-1/2 1
-1
udd
-2
-1
-3
-3/2 3/2
ddd uud uuu
dds uds uus
dss uss
sss
13850
1673
Meson Nonets:
I3
1
S
0 1/2-1/2-1 1
-1
0
Pseudoscalars JP = 0-
Vector Mesons JP = 1-
Q = 0
Q = 1
Q = -1
Examples
ssdduu ,,
sd su
us ds
ud du
KK 0
0
0KK
*0* KK
**0 KK
0
0
Much Ado about Isospin(apologies for revealing my bias)
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)).
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?
1/2 x 1/2
1 x 1/2
1 +1 1 0+1/2 +1/2 1 0 0 +1/2 -1/2 1/2 1/2 1 -1/2 +1/2 1/2 - 1/2 - 1 -1/2 -1/2 1 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).
Notation: J J M Mm1 m2
m1 m2
. . . .
coefficient
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 5/2 3/2 1/2 +1/2 +1 3/5 -2/5 +1/2 +1/2 +1/2 +3/2 -1 1/10 2/5 1/2 +1/2 0 3/5 1/15 -1/3 5/2 3/2 1/2 -1/2 +1 3/10 -8/15 1/6 -1/2 -1/2 -1/2 +1/2 -1 3/10 8/15 1/6 -1/2 0 3/5 -1/15 -1/3 5/2 3/2 -3/2 +1 1/10 -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
J J M Mm1 m2
m1 m2
. . . .
Notation:
coefficient
Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).