Quark Soup

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Quark Soup
U C T
d S b
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/huffma
n/
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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.
Result Discovery of Ge and Ga (among others)
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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 D? D0
?1869, 1864 ?c0 ? 2980
These similarities are what has led to the quark
model of particle bound states.
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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
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More Botany lessons
Leptons electron muon tau ne nm
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.
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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!

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What Makes a Theory Good?

• Any theory not just a theory of matter and
  Energy.

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Falsifiable!
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Baryon Octet
The only Example ? There is also a complete octet
where L 1 but you will never see it.
JP 1/2
S
0
-1
-2
Notes UD-S 3 for all Baryon states. Quark
compositions are NOT the same as quark wave
functions
I3
0
-1
1
1/2
-1/2
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Baryon Decuplet
The only Example ?
JP 3/2
S
-3
I3
0
1
-3/2
3/2
1/2
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Meson Nonets
Examples?
Pseudoscalars JP 0-
Vector Mesons JP 1-
Q 1
Q 0
Q -1
I3
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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)).
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Clebsch-Gordan Coefficients
J J
M M m1 m2 m1 m2 . . .
.
Notation
1/2 x 1/2
coefficient
1 x 1/2
Note A square-root sign is to be understood over
every coefficient, e.g., for -8/15, read -?(8/15).
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Clebsch-Gordan Coefficients
3/2 x 1
Note A square-root sign is to be understood over
every coefficient, e.g., for -8/15, read -?(8/15).