Lec35 EM Interactions

7/27/2019 Lec35 EM Interactions

1/18

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.


2/18

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.


3/18

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-)


4/18

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



5/18

Conservation LawsIn any physical process, total energy and total charge is always

conserved throughout.

e+

e-

e+ e-

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!


6/18

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)


7/18

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


8/18

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]


9/18

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?


10/18

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


11/18

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


12/18

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


13/18

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 !


14/18

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.


15/18

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 !!!!


16/18

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)


17/18

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.


18/18

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)

Lec35 EM Interactions

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