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. (I’m not collecting HW#10) 3.Q&A session on Sunday at 5 pm. 4.Tentative course grades will be posted 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 10:15 – 12:15 in Stolkin.

The Photon (  ) PropertyValue Mass0 Charge0  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.  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.

Feynman Diagram for e + e - Scattering  e+e+ e+e+ e-e- e-e- Electron-Positron Scattering time Position  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 - )

Feynman Diagram for e + e - Annihilation  e+e+ e-e- e-e- e+e+ Electron-Positron Annihilation  The electron and positron annihilate into pure energy in the form of a photon  The photon’s 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 + or e - 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 - )

Conservation Laws In any physical process, total energy and total charge is always conserved throughout. e+e+ e-e-  e+e+ e-e- e-e- e+e+ Initial (e + e - )Final (e + e - )  e-e- e+e+ Energy Q e+e+ 5 GeV +1 e-e- 5 GeV Total10 GeV 0 Energy Q  10 GeV 0 Energy Q e+e+ 5 GeV +1 e-e- 5 GeV Total10 GeV 0 Notice that total energy and total charge never changed !!! - Conservation Laws are Key ! - They allow you to predict things!

Example 1 Suppose 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 of the 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/c 2 ) B) b (4.7 GeV /c 2 ) C) t (175 GeV /c 2 ) D) s (0.2 GeV /c 2 )

e + e -  qq Initial (e + e - )  e+e+ q e-e- q Energy Q e+e+ 5 GeV +1 e-e- 5 GeV Total10 GeV 0 Energy Q  10 GeV 0 q/q Total Energy (GeV) Mass Energy (GeV) Kinetic Energy (GeV) Q u 5 GeV /3 u 5 GeV /3 d 5 GeV /3 d 5 GeV /3 c 5 GeV /3 c 5 GeV /3 b 5 GeV /3 b 5 GeV /3

Example 2  e+e+ q e-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/c 2 )? 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]

Example 3  e+e+  e-e-  - Assume the energy of the electron and positron are each 3 [GeV]. Suppose you wanted to have a  + and  - lepton in the final state (mass of  lepton is ~1.8 [GeV/c 2 ])? 1) How much kinetic energy does the  + 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 much total 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, , and  have that allow the photon to produce them?

Hmmm, I’ve 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)!  e+e+ q e-e- Quark Antiquark Annihilation

Where do we get quark and anti quarks from? u u d Hmmm… Introducing, the PROTON… u u d And, antiquarks?… Introducing, the humble antiparticle of the proton, the ANTIPROTON…

Proton-Antiproton Collisions u u d u u d u u d u u d BOOM ! At high energies, the collisions actually occur between the quarks in the protons and the antiquarks in the antiproton! That is, quark-antiquark collisions ! 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 d u u d

Summary of EM Interactions 1.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 of oppositely-charged, like-type leptons or quarks.   e + e -,  +  -,  +  —   uu, dd, ss, cc, bb, tt (Nature does not make   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 ! 1.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 of oppositely-charged, like-type leptons or quarks.   e + e -,  +  -,  +  —   uu, dd, ss, cc, bb, tt (Nature does not make   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 !

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 should be no EM binding between protons and neutrons.

The Strong Force  For the EM interactions, we learned that: The photon mediates the interaction between objects which 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 photon does not carry electric charge.  Gluons can interact with other gluons !!!!

Comparison Strong and EM force PropertyEMStrong Force Carrier Photon (  ) Gluon (g) Mass 00 Charge ? NoneYes, color charge Charge types +, -red, green, blue Mediates interaction between: All objects with electrical charge All objects with color charge Range Infinite (  1/d 2 )  [m] (inside hadrons)

Color Charge of Quarks  Recall, we stated, without much explanation, that quarks come in 3 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 “intrinsic property” and color is just a nice way to visualize it.

Color of Hadrons (II) q1q2 q3 RED + BLUE + GREEN = “WHITE” or “COLORLESS” BARYONS GREEN + ANTIGREEN = “COLORLESS” RED + ANTIRED = “COLORLESS” BLUE + ANTIBLUE = “COLORLESS” MESONS qqq Hadrons observed in nature are colorless (but there constituents are not)