Lec35 EM Interactions
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Transcript of Lec35 EM Interactions
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The Four Fundamental Forces
1. Gravity
2. Weak Force
3. Electromagnetic force
4. Strong Force
Weaker
Stronger
All other forces you know about can be attributed to one of these!
Announcements
1. Exam#3 next Monday.
2. HW10 will be posted today.Solutions will be posted
Sat. afternoon or Sunday AM.
(Im not collecting HW#10)
3. Q&A session on Sunday at 5 pm.
4. Tentative course grades will beposted by Tuesday evening.
5. You can do no worse than
this grade if you skip the
final (but you could do
better if you take it)6. Final Exam, Friday, May 2
10:1512:15 in Stolkin.
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The Photon (g)Property Value
Mass 0
Charge 0
The photon is the mediator of the
electromagnetic interaction
The photon can only interact with objects which
have electric charge
So, the photon can mediate interactions between
quarks and charged leptons.
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Feynman Diagram fore+e- Scattering
g
e+ e+
e- e-
Electron-Positron
Scattering
time
The photon may be emitted (absorbed) by either the e+ (e-) or the e- (e+).
In this interaction (scattering), the incoming particles are deflected but the
electron & positron in the final state are the same ones as the initial state.
After emission or absorption of the photon, the charge of the e+ cannot
be replaced by an e- since the emission (or absorption) of a photon (Q=0)cannot produce a change in electric charge.
Important Points
Initial (e+e-) Final (e+e-)
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Feynman Diagram fore+e- Annihilation
g
e+ e-
e- e+
Electron-Positron
Annihilation
The electron and positron annihilate into pure energy in the form of a photon
The photons energy is equal to the sum of the electron & positron energies. In this process, the photon must break back into a particle & its antiparticle.
The combined energy of the particle and anti-particle must be equal to the
energy of the photon.
You can flip the arrangement of the e+ ore- in the initial or final state, but
you must have one e+ and one e- on each side of the photon.
Important Points
Initial (e+e-) Final (e+e-)
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Conservation LawsIn any physical process, total energy and total charge is always
conserved throughout.
e+
e-
e+ e-
e- e+
Initial (e+e-) Final (e+e-)
g
e-
e+
Energy Q
e+ 5 GeV +1
e- 5 GeV -1
Total 10 GeV 0
Energy Q
g 10 GeV 0
Energy Q
e+ 5 GeV +1
e- 5 GeV -1
Total 10 GeV 0
Notice that total energy and
total charge never changed !!!
- Conservation Laws are Key !
- They allow you to predict
things!
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Example 1Suppose you collide a 4 [GeV] electron into a 4 [GeV] positron and
they annihilate.
What is the energy of the produced photon?
A) 8 [GeV] B) 4 [GeV] C) 16 [GeV] D) 0 [GeV]
If the photon splits into an up quark and a second particle, which ofthe following is true?
A) The other particle is an electron
B) The other particle is a positron.
C) The other particle is a d quark.D) The other particle is an anti-up quark.
E) The other particle is an anti-down quark.
What is the heaviest quark which can be produced ?
A) c (1.5 GeV/c2) B)b (4.7 GeV /c2) C) t (175 GeV /c2) D) s (0.2 GeV /c2)
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e+e-qq
Initial (e+e-) Final (uu)
g
e+ q
e- q
Energy Q
e+ 5 GeV +1
e- 5 GeV -1
Total 10 GeV 0
Energy Q
g 10 GeV 0
q/q
Total
Energy
(GeV)
Mass
Energy
(GeV)
Kinetic
Energy
(GeV)Q
u 5 GeV 0.005 4.995 +2/3
u 5 GeV 0.005 4.995 -2/3
d 5 GeV 0.01 4.99 -1/3
d 5 GeV 0.01 4.99 +1/3
c 5 GeV 1.5 3.5 +2/3
c
5 GeV 1.5 3.5 -2/3
b 5 GeV 4.7 0.3 -1/3
b 5 GeV 4.7 0.3 +1/3
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Example 2
g
e+ q
e- q
Suppose you wanted to have a top quark and top antiquark in the
final state. Which of the following choices are capable of producing
this final state with reference to this figure?
(mass of top quark is 175 GeV/c2)?
A) Energy(electron) = 175 [GeV] and Energy(positron) = 0 [GeV]
B) Energy(electron) = 300 [GeV] and Energy(positron) = 50 [GeV]
C) Energy(electron) = 175 [GeV] and Energy(positron) = 175 [GeV]
D) Energy(electron) = 200 [GeV] and Energy(positron) = 200 [GeV]
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Example 3
g
e+ t+
e- t-
Assume the energy of the electron
and positron are each 3 [GeV].
Suppose you wanted to have a
t+ and t- lepton in the final state
(mass oft lepton is ~1.8 [GeV/c2])?
1) How much kinetic energy does the t+ have after the collision?
A) 3 [GeV] B) 1.8 [GeV] C) 1.2 [GeV] D) 0 [GeV]
2) If the leptons were a pair of muons (m~0.1 [GeV]), how muchtotal energy would each have?
A) 0.1 [GeV] B) 3.0 [GeV] C) 2.9 [GeV] D) 6 [GeV]
3) What property is it that quarks, e, m, and t have that allow the
photon to produce them?
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Hmmm, Ive got a few question,
Mister!
1. Where did you get the quarks and antiquarks in
the first place ? (Not at Wal-Mart, I can assure you)!
g
e+q
e-
Quark Antiquark
Annihilation
q
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Where do we get quark and
anti quarks from?
u
u
d
Hmmm
Introducing, the
PROTON
u
u
dAnd,
antiquarks?Introducing, the
humble antiparticle
of the proton, the
ANTIPROTON
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Proton-Antiproton
Collisions
u
u
du
u
du
u
du
u
d
At high energies, the collisions actually occur
between the quarks in the protons and the
antiquarks in the antiproton!
That is, quark-antiquark collisions !
u
u
du
u
d
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Summary of EM Interactions1. The Photon is the mediator of the EM Interaction.
- This means that EM interactions occur via photons.
2. The photon is massless and has no electrical charge.
3. Photon can convert into pairs ofoppositely-charged,
like-type leptons or quarks.ge+e-, m+m -, t+tguu, dd, ss, cc, bb, tt(Nature does not makeg uc, db, etc)
4. Feynman diagrams are a pictorial method for expressing a
type of interaction.
5. You can apply energy and momentum conservation to all
these interactions !
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The Need for a Strong Force
Why do protons stay together in the nucleus, despite
the fact that they have the same electric charge?
They should repel since they have like charge
Why do protons and neutrons in the nucleus bind
together?
Since the neutron is electrically neutral, there shouldbe no EM binding between protons and neutrons.
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The Strong ForceFor the EM interactions, we learned that:
The photon mediates the interaction between objectswhich carry electrical charge
For the Strong Interactions, we conjecture that:
Quarks have an additional charge called color charge
or just color for short.A force carrier, called the gluon mediates the interaction
between objects which carry color charge (that is, the
quarks)
The most striking difference between the gluon and the
photon is:
The gluon carries color charge, but the photondoes not
carry electric charge.
Gluons can interact with other gluons !!!!
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Comparison
Strong and EM force
Property EM Strong
Force Carrier Photon (g) Gluon (g)Mass 0 0
Charge ? None Yes, color charge
Charge types +, - red, green, blueMediates interaction
between:
All objects with
electrical charge
All objects with
color charge
Range Infinite ( 1/d2
)
10-14 [m](inside hadrons)
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Color Charge of Quarks
Recall, we stated, without much explanation, that quarks come in3 colors.
color charge strong-force as
electrical charge EM force.
Experiments show that there are 3 colors; not 2, not 4, but 3.
Again, this does not mean that if you could see quarks, you
would see them as being colored. This color that we refer to is
an intr insic property and color is just a nice way to visualize it.
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Color of Hadrons (II)
q1 q2
q3
RED + BLUE + GREEN = WHITE
or COLORLESS
BARYONS
GREEN + ANTIGREEN = COLORLESS
RED + ANTIRED = COLORLESSBLUE + ANTIBLUE = COLORLESS
MESONS
q
q
q
q
q
q
Hadrons observed in nature are colorless (but there constituents are not)