1. Matter & Forces Matter Hadrons Leptons Forces
Baryons
Mesons
Quarks
Anti-Quarks
Leptons
Forces
Charged
Neutrinos
Gravity
Strong
Weak EM
Exam 3: April 28th: Will cover Lecture 26 through the end of semester.

2. A Sense of Scale q e
<1x [m]
~5x10-6 [m]
~2x10-9 [m]
~2x10-8 [m]
~5x [m]
~1.5x [m]
Quarks and leptons are the most elementary particles we know about at this time. They are no larger than [cm]

3. The Standard Model
Quarks and leptons are the most fundamental particles of nature that we know about.
Up & down quarks and electrons are the constituents of ordinary matter.
The other quarks and leptons can be produced in cosmic ray showers or in high energy particle accelerators.
Each particle has a corresponding antiparticle.

4. The cast of quarks & leptons
Family
Quarks
Antiquarks
Q = +2/3
Q = -1/3
Q = -2/3
Q = +1/3 1 u d 2 c s 3 t b
Family
Leptons
Antileptons
Q = -1
Q = 0
Q = +1 1 e- e e+ 2    3   

5. Quarks versus Leptons
What are the primary differences between quarks and leptons?
Ultimately, what differentiates the quarks & leptons from one another are the forces which each may exhibit.
We therefore now embark on the concept of forces.

6. The Four Fundamental Forces
Weaker
Stronger
Gravity
Weak Force
Electromagnetic force
Strong Force
Doesn’t that look like George W. ?
All other forces you know about can be attributed to one of these!

7. Gravity
Gravity is the weakest of the 4 forces. The gravitational force between two objects of masses m1 and m2, separated by a distance d is:
F = Gm1m2/d2
G = gravitational constant = 6.7x10-11[N*m2/kg2]
d = distance from center-to-center
The units of each are:
[Force] = [Newton] = [N] [mass] = [kg] [distance] = [meters]
Gravity is only an attractive force

8. The Electric Force
In the old days, we believed that “force” was transmitted more or less instantaneously by a “field of force”.
Lines of force p p p p p
The proton to the right is repelled by the “electric field” created by the one on the left (electrical repulsion).

9. The New Concept of Force
In the 1960’s, a new theory of interactions was developed. At the heart of it is the concept that:
Richard Feynman, Nobel Prize in Physics
Forces are the result of the exchange of “force carriers” between the two particles involved in the interaction.
Shown is a photon of Richard Feynman. He was one of the chief architects in constructing the most successful theory known, quantum electrodynamics, or just QED.
QED describes all electric and magentic (or just electromagnetic for short) phenomenon to stunning accuracy. Built into QED, is the notion of force carriers being responsible for all interactions between particles.
The force carrier of the electromagnetic force is the photon ()

10. The Photon () Property Value Mass Charge
Charge
The photon is the “mediator” of the electromagnetic interaction
The photon can only interact with objects which have electric charge !!!!!
From Merriam-Webster dictinary:
Quantum: any of the very small increments or parcels into which many forms
of energy are subdivided

11. As we go through these slides, note that all particles involved (other than the photon) carry electrical charge!

12. Electron-Positron Scattering
e e  e e- e+ e- e+ e- e- e+ e+ e- e+ e- e+ e- e+ e-
Another process which can occur when an electron and a positron approach each other is the following. When the electron and positron get close enough, the positron emits a photon. Because this photon carries energy and momentum, the positron’s momentum is altered (I.e., it is scattered). The photon is subsequently absorbed by the electron, and in doing so, absorbs the photon’s momentum. Because the electron absorbs the photon’s momentum, it too is scattered (ie., deflected). The net result is the same. An electron and a positron in, and an electron and positron out.
However, this process, and the previous one (annihilation) are 2 very distinct processes, both which occur in nature.
Don’t worry about memorizing the name “Compton Scattering”.

13. Electron-Positron Scattering
e e  e e- e+ e+ e+ e- e+ e+ e+
Another process which can occur when an electron and a positron approach each other is the following. When the electron and positron get close enough, the positron emits a photon. Because this photon carries energy and momentum, the positron’s momentum is altered (I.e., it is scattered). The photon is subsequently absorbed by the electron, and in doing so, absorbs the photon’s momentum. Because the electron absorbs the photon’s momentum, it too is scattered (ie., deflected). The net result is the same. An electron and a positron in, and an electron and positron out.
However, this process, and the previous one (annihilation) are 2 very distinct processes, both which occur in nature.
Don’t worry about memorizing the name “Compton Scattering”. e- e- e- e- e- e-

14. Electron-Positron Annihilation
e e  e e- e+ e- e+ e- e- e+ e+ e- e+ e- e- e+ e+ e- e+ e-  
The electron and positron collide and produce a photon. Since both the electron and positron have equal and opposite electric charge, this can happen. All of the energy of the electrons goes into the energy of the photon. That is, all the kinetic and mass energy of the electrons are converted into pure radiation (I.e., a photon)
Then, the photon converts into an electron positron pair. In this case, pure energy in the form of radiation (a photon) is converted into mass energy plus kinetic energy!
You may not believe it, but it really happens!!

15. Electron-Positron Annihilation
e e  e e- e+ e- e- e+ e+ e- e+ e- e+ e- e+ e- e- e+   e+ e-
The electron and positron collide and produce a photon. Since both the electron and positron have equal and opposite electric charge, this can happen. All of the energy of the electrons goes into the energy of the photon. That is, all the kinetic and mass energy of the electrons are converted into pure radiation (I.e., a photon)
Then, the photon converts into an electron positron pair. In this case, pure energy in the form of radiation (a photon) is converted into mass energy plus kinetic energy!
You may not believe it, but it really happens!!

16. Quark Pair Production e+ + e-  q + q e+ e- e+ e- e+ e- q q e- e+ q 
The electron and positron collide and produce a photon. Since both the electron and positron have electric charge, this can happen. Then, the photon converts into a quark-antiquark pair. Again, this is possible, because the quarks also have electric charge (2/3 or 1/3)!
Note that the quark and antiquark must have opposite charge. You cannot produce a charge 2/3 quark and a charge 1/3 antiquark (charge conservation would be violated!)
* Note: Two completely different particles in the “final state”. Since quarks have electric charge, this can in fact happen!

17. Quark Pair Production e+ + e-  q + q e+ q e+ q e+ q e+ q e-  e- q q
The electron and positron collide and produce a photon. Since both the electron and positron have electric charge, this can happen. Then, the photon converts into a quark-antiquark pair. Again, this is possible, because the quarks also have electric charge (2/3 or 1/3)!
Note that the quark and antiquark must have opposite charge. You cannot produce a charge 2/3 quark and a charge 1/3 antiquark (charge conservation would be violated!) q q e-
* Note: Two completely different particles in the “final state”

18. Example
In the preceding example, assume that the incoming electron and positron each have energy of 5 GeV.
1. What is the energy of the photon after the electron & positron annihilate? A) 5 GeV B) 10 GeV C) 0 GeV D) None of these
2. Assuming that the final state electron & positron have equal energy, what is the energy of the emergent electron ? A) 5 GeV B) 10 GeV C) 0 GeV D) None of these
Once the photon is produced, it may split into any particle-antiparticle pair which is permissible by energy conservation. For each of these, tell whether the photon can produce the final state particles: a) u and u (Mu~0.005 GeV) Y or N b) d and d (Md ~ GeV) Y or N c) s and s (MS ~ 0.20 GeV) Y or N d) c and c (MC ~ 1.5 GeV) Y or N e) b and b (Mb ~ 4.8 GeV) Y or N f) t and t (Mt ~ 175 GeV) Y or N

19. Photon Conversion   e+ + e- e- e+ e+ e- e+ e-     e+ e- 
Note that lepton number is conserved. This is very similar to the annihilation animation. To realize this, just chop off the front part of the annihilation diagram, and you will arrive at this process.
Here a photon, travelling through some medium, could be air, can spontaneously convert its energy into an electron and positron. The electron and positron carry away all the energy and momentum of the original photon.

20. Photon Conversion   e+ + e- e+ e+ e+    e+ e-   e- e- e-
Note that lepton number is conserved. This is very similar to the annihilation animation. To realize this, just chop off the front part of the annihilation diagram, and you will arrive at this process.
Here a photon, travelling through some medium, could be air, can spontaneously convert its energy into an electron and positron. The electron and positron carry away all the energy and momentum of the original photon.   e- e- e-

21. Quark Antiquark Annihilation
q q  e e- q q e- e+ q e+ e- e- q e+ e- e+ e-  
The quark and antiquark collide and produce a photon. Since both the quarks have electric charge (+2/3 and –2/3, or +1/3 and –1/3), this can happen. Note that the quark and antiquark must have opposite charge. You cannot have a charge 2/3 quark annihilate with a charge 1/3 antiquark (charge conservation would be violated).
Then, the photon converts into a electron-positron pair. Again, this is possible, because they have electric charge (+1 and -1)!
* Note: Reverse process to quark pair production!

22. Quark Antiquark Annihilation
q q  e e - q e+ q e+ q e+ e- q e+ e- 
The quark and antiquark collide and produce a photon. Since both the quarks have electric charge (+2/3 and –2/3, or +1/3 and –1/3), this can happen. Note that the quark and antiquark must have opposite charge. You cannot have a charge 2/3 quark annihilate with a charge 1/3 antiquark (charge conservation would be violated).
Then, the photon converts into a electron-positron pair. Again, this is possible, because they have electric charge (+1 and -1)! e- e- e-
* Note: Reverse process to quark pair production!

23. Feynman Diagrams
A great simplification which allows us to represent these physical processes are facilitated by Feynman Diagrams.
It turns out, they can also be used to calculate the probability for the process to occur (Beyond the scope of this module though).
We will use them more in a qualitative sense to visualize various processes.

24. Feynman Diagrams e+ e- Electron-Positron Annihilation  e+ Position
Electron-Positron Scattering
time
Position
It is usually understood that time runs along the X-axis, and position along the Y-axis. From now on, I will not draw it.

25. Photon Conversion and Emission e- e+
Photon Conversion  e-
Photon Emission

26. Quark Antiquark Annihilation to Electron & Positron
More Feynman Diagrams
Quark Pair Production e+ q
“q” can be any quark, as long as there is enough energy to create 2 of ‘em!  e-
Quark Antiquark Annihilation to Electron & Positron q
Note that energy and momentum is conserved both at the point of annihilation and at the point where the new particles are created. e+  e-