Physics Notes: The Standard Model
Lecture 1: Jan 11, 2010 Back to PHY30
Renormalization
Analogy: Assume that one has a pair of charges (+ and -) placed in water. Water molecules are dipoles and will tend to line up along field lines. The positive ends of the molecules will be closer to the negative charge. If one draws a sphere around the negative charge at a distance, then you would find that the total charge in the sphere is reduced because of molecules straddling the boundary of the sphere. The dipoles ÒshieldÓ the bare charge. As the distance to a charge drops below the size of water molecules the shielding effect disappears and the bare charge becomes visible.
Electron positron pairs are created with a distribution of separations around charges. These pairs have a similar shielding effect. As one approaches a charge to less than the Compton wavelength then the shielding effect begins to reduce.
As one approaches closer, the observed charge of the electron rises to infinity. Renormalization then consists of picking a length scale at which the observable charge of the electron is known and then describing the theory in terms of that charge value. This avoids the infinity.
Electron charge is a ÒrunningÓ parameter – depends on length scale.
Pretty obviously, all Feynman diagrams, not just electron positron pairs created from photons are involved in the shielding effect.
Particles-Fields-Forces
Different ways of describing same physics
Consider 2 particles with fields
Field Energy of P1 = 
Field Energy of P2 = 
Field Energy of P1 and P2
Which gives us an extra energy term from the combination of fields
This term could be positive or negative, but the magnitude
will depend on the distance between the charges.
The energy of the electrons can also be raised or lowered via particle
exchanges.
How is not clear yet. Total energy should be
conserved. Emission of
a photon should lower the energy of one particle and when captured by the
other, it should raise its energy.
The Particle Zoo
|
Name |
Sym |
Sym-Field |
Ferm/ Bos |
Spin |
Charge |
Baryon# |
eV |
Comment |
|
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|
Photon |
γ |
A |
B |
1 |
0 |
0 |
0 |
|
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|
|
|
Electron/ Positron |
e-/e+ |
|
F |
1/2 |
-1/+1 |
0 |
0.51M |
0.510 |
|
|
|
|
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|
|
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|
|
Quarks |
q |
|
F |
1/2 |
|
1/3 |
|
|
|
Down |
d |
|
F |
1/2 |
-1/3 |
1/3 |
10M/3.5-6M |
|
|
Up |
u |
|
F |
1/2 |
+2/3 |
1/3 |
5M/1.5-3.3M |
|
|
Strange |
s |
|
F |
1/2 |
-1/3 |
1/3 |
100/70-130M |
|
|
Charm |
c |
|
F |
1/2 |
+2/3 |
1/3 |
1.16-1.34G |
|
|
Bottom |
b |
|
F |
1/2 |
-1/3 |
1/3 |
4.13-4.37G |
|
|
Top |
t |
|
F |
½ |
+2/3 |
1/3 |
169-173G |
|
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Pions |
|
|
B |
|
|
|
500/140M |
|
|
|
|
|
B |
0 |
+1 |
|
140/135M |
|
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|
B |
0 |
-1 |
|
140/135M |
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Kaon |
|
|
|
|
-1 |
|
896M |
|
|
Kaon |
|
|
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|
+1 |
|
497M |
|
|
Kaon |
|
|
|
|
0 |
|
892M? |
|
|
Kaon |
|
|
|
|
0 |
|
493M? |
|
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0 |
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Probably more were added in class 2. When I list two sets of
numbers for eV, the first is from lecture and the second from Wikipedia. ÒBareÓ masses are difficult
anyway. The 
form and others
seem to appear in reference material as a superposition like instead of
individually, like the 
case. The reason for this appears in class
4. There is a fun iPhone
application called the ÒParticle ZooÓ that categorizes all the ÒfundamentalÓ
and ÒcompositeÓ particles.