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The Four Fundamental Forces

Weaker. Stronger. The Four Fundamental Forces. Announcements Exam#3 next Monday. HW10 will be posted today. Solutions will be posted Sat. afternoon or Sunday AM. (I’m not collecting HW#10) Q&A session on Sunday at 5 pm. Tentative course grades will be posted by Tuesday evening.

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The Four Fundamental Forces

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  1. Weaker Stronger The Four Fundamental Forces • Announcements • Exam#3 next Monday. • HW10 will be posted today. Solutions will be posted Sat. afternoon or Sunday AM.(I’m not collecting HW#10) • Q&A session on Sunday at 5 pm. • Tentative course grades will be posted by Tuesday evening. • You can do no worse than this grade if you skip the final (but you could do better if you take it) • Final Exam, Friday, May 210:15 – 12:15 in Stolkin. • Gravity • Weak Force • Electromagnetic force • Strong Force All other forces you know about can be attributed to one of these!

  2. The Photon (g) • 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 betweenquarks and charged leptons.

  3. e+ e+ Position Electron-PositronScattering g e- e- time Feynman Diagram for e+e- Scattering Initial (e+e-) Final (e+e-) Important Points • 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+ cannotbe replaced by an e- since the emission (or absorption) of a photon (Q=0) cannot produce a change in electric charge.

  4. Electron-PositronAnnihilation e+ e- g e- e+ Feynman Diagram for e+e- Annihilation Initial (e+e-) Final (e+e-) Important Points • 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 theenergy 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.

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

  6. Example 1 Suppose you collide a 4 [GeV] electron into a 4 [GeV] positron andthey 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. e+ q g e- q e+e- qq Initial (e+e-)

  8. e+ q g e- q Example 2 Suppose you wanted to have a top quark and top antiquark in thefinal 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. Example 3 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 of t lepton is ~1.8 [GeV/c2])? g t - e- 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 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, m, and t have that allow thephoton to produce them?

  10. Quark AntiquarkAnnihilation q e+ g e- 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)!

  11. u d u u d u Where do we get quark and anti quarks from? Hmmm… Introducing, thePROTON… And, antiquarks?… Introducing, thehumble antiparticleof the proton, theANTIPROTON…

  12. u u u d d d u u u u u u d d d u u u Proton-Antiproton Collisions 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 !

  13. Summary of EM Interactions • The Photon is the mediator of the EM Interaction.- This means that EM interactions occur via photons. • The photon is massless and has no electrical charge. • Photon can convert into pairs of oppositely-charged, like-type leptons or quarks.g  e+e-, m+m -, t+t—g  uu, dd, ss, cc, bb, tt (Nature does not make g  uc, db, etc) • Feynman diagrams are a pictorial method for expressing atype of interaction. • You can apply energy and momentum conservation to allthese interactions !

  14. 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. The Strong Force • For the EM interactions, we learned that:The photonmediates 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 gluonmediates the interaction between objects which carry color charge(that is, the quarks) • The most striking difference between the gluon and thephoton is:The gluon carries color charge, but the photondoes notcarry electric charge. Gluons can interact with other gluons !!!!

  16. Comparison Strong and EM force

  17. 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 isan “intrinsic property” and color is just a nice way to visualize it.

  18. BARYONS q1 q2 RED + BLUE + GREEN = “WHITE” or “COLORLESS” q3 MESONS q q q GREEN + ANTIGREEN = “COLORLESS”RED + ANTIRED = “COLORLESS” BLUE + ANTIBLUE = “COLORLESS” Color of Hadrons (II) Hadrons observed in nature are colorless (but there constituents are not)

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