Announcements

1. Announcements • Recap of important material today & Monday. • Review sheet will be handed out on Monday (4/22) • Video on Wednesday (4/24), with questions to answer. • Friday (4/26) is a pure Q&A session. • HW solutions due last Wednesday (4/17) will be postedtoday. • Next Wednesday’s HW will be posted that evening. • HW’s handed in late will be greatly reduced in credit, or not accepted.

2. Putting it all together

3. What IS Matter ? • Matter is all the “stuff” around you ! • Here’s the picture we’ve uncovered Matter Hadrons Leptons Forces Baryons Mesons Charged Neutrinos Gravity Strong Weak EM Quarks Anti-Quarks

4. The Quarks • Each quark has a corresponding antiquark. • Antiquarks have opposite charge to their quark. • Huge variation in the masses, from 5 [MeV/c2] to 175,000 [MeV/c2].

5. The Leptons • Each lepton has a corresponding anti-lepton. • Antileptons have opposite charge to their lepton. • Huge variation in the masses, from 0.5 [MeV/c2] to 1,780 [MeV/c2].

6. Forces • Forces are the due to the exchange of force carriers. • For each fundamental force, there is a force carrier (or set of them). • The force carriers only “talk-to” or “couple to”particles which carry the proper charge. Electromagnetic: the photon (g)Strong: the gluon (g)Weak: the W+, W- & Z0 Electric Charge (+, -)Color Charge (r,g,b) Weak Charge

7. Particles & Forces quarks Charged leptons(e,m,t) Neutral leptons(n) ColorCharge ? Y N N EMCharge ? N Y Y WeakCharge ? Y Y Y • Quarks can participate in Strong, EM & Weak Interactions ! • All quarks & all leptons carry weak charge

8. In other words… • Since quarks have color charge, EM charge & weak charge, they can engage in all 3 types of interactions ! • Charged leptons (e,m,t) carry EM and weak charge, but no strong charge. Therefore, they can participate in the EM & weak interaction, but they cannot participate in the strong interaction. • Neutrinos only carry weak charge, and therefore they onlyparticipate in the weak interaction they can pass through the earth like it wasn’t even there !

9. Why should we believe that forces are the result of force carriers? • The Standard Model (SM) which I have describe to you is just that, it’s a model, or better yet, a theory. • All forces are described by exchange of force carriers, period ! • It’s is an extremely successful theory. • It explains all subatomic phenomenon to extraordinary precision! One example is in a quantity referred to as the electron’s “g-factor” “g” from experiment: 2.0023193043768 “g” from theory (SM): 2.0023193043070 They agree to better than 1 part in 10 billion ! Coincidence ?

10. Particle or Wave? Two benchmark experiments established the foundation for theparticle nature of light 1. Photoelectric Effect2. Compton Effect Both experiments indicated that light was acting like a particlewith energy and momentum given by: Usesc = ln E = hn = hc / l p = E / c = (hc / l) / c = h/ l • This light particle has energy and momentum, but no mass !!! • It’s energy & momentum are inversely proportional to the wavelength

11. What if we try this ? Vary wavelength, fixed amplitude electrons emitted ? No No Yes, withlow KE No Yes, withhigh KE No No Photoelectric Effect “Classical” Method Increase energy by increasing amplitude electrons emitted ? No electrons were emitteduntil the frequency of the light exceeded a critical frequency, at which point electrons were emitted from the surface! (Recall: small l large n)

12. The Electromagnetic Spectrum Shortest wavelengths (Most energetic photons) E = hn = hc/l h = 6.6x10-34 [J*sec](Planck’s constant) Longest wavelengths (Least energetic photons)

13. The EM force and the Photon • The photon is the carrier of the EM force. • It can only “talk-to” particles which have electric charge. • A photon does NOT have electric charge, and therefore it cannot interact with other photons • While the photon is massless, it does carry both momentum & energy given by:p = h / l E = pc = hc / l = hn • When charged particles exchange photons, they are exchangingthis momentum. One particle emits the photon & the other absorbs it ! • Can also have particle-antiparticle annihilation into a photon.

14. Electromagnetic Force Quark PairProduction Detectablehadrons,such asp+, p-, p0,p, n, etc q e+ g e-

15. hadrons e e e e e e- e- u hadrons g u This the Feynman diagram for anelectron scattering off an up quark ! d u u Electron – Proton Collision ! u Proton u d

16. Actual e+e- Collision at Cornell’s Collider E ~ 5 [GeV] forthe e+ and e- Hadrons which are chargedand are “bent”by a magneticfield Eventis notbalanced… Side view ofDetector n ? Probably a n in this interaction

17. Another e+ e- Collision at CERN E ~ 103 [GeV] forthe e+ and e- LOTSMOREHADRONS !!!

18. t How much energy is needed to produce a t t pair via an e+e- Collision ? t e+ Me = 0.5 MeV/c2 Mt = 175 GeV/c2 e- What minimum energy is needed by each incoming particle to produce the top and antitop quark?A) 175 MeVB) 350 GeVC) 175 GeVD) 350 MeV

19. q What maximum mass particle canbe produced? particle q Ee = 115 GeV (each) antiparticle What maximum mass particle can be created in this collision ?A) 115 MeV/c2 B) 230 GeV/c2 C) 115 GeV/c2 D) 230 MeV/c2

20. Strong Force and the Gluon • The gluon is the carrier of the strong force. • Unlike the EM force, it gets stronger as quarks separate ! • It can only “talk-to” particles which have color charge (quarks). • Since gluons do have color charge, they can interact with other gluons ! • The gluon is also massless. • When quarks exchange gluons, they are exchanging color charge. One quark emits the gluon & the other absorbs it ! • Quarks and antiquarks can annihilate into a gluon!

21. Color (or Color charge) • Like electric charge, quarks have an internal property which allows gluons to interact with them (i.e., couple to them). • This property is called color. Quarks can have one of three colors:red, green, or blue. • Antiquarks have anticolor: antired, antigreen or antiblue. • Gluons also carry color (rb, bg, gr, etc ), and therefore caninteract among themselves !!! This is the most striking differencebetween gluons & photons! • FYI, it is the fact that gluons have color which leads to confinement

22. Hadrons • Because of the strong force, quarks are bound into hadrons. • Hadrons are simply particles which interact via the strong force. • Our inability to directly observe the color of hadrons have lead us to believe that all hadrons are colorless • There are two types of hadrons:Baryons: bound state of any 3 quarks (except the top quark) ( 1 red + 1 green + 1 blue == colorless ) Mesons: bound state of a quark and antiquark (except t) one color + one anticolor ( r r, g g, or b b ) == colorless ) • Antibaryons contain 3 antiquarks

23. hadrons u u u d u u d u u d d d d hadrons u u u u d u u d u u u d u u u u hadrons u u u u d d d hadrons Proton-Proton Collision The up & downquarks have exchangeda gluon, and henceunderwent an interaction!

24. d u u d u u Quark-Quark Interaction tohadrons tohadrons u u g d d tohadrons tohadrons

25. d u u d u u Quark-Gluon Interaction tohadrons tohadrons g g g tohadrons d d tohadrons

26. Hadrons! As quarks move apart, the potentialenergy associated with the “spring”increases, until its large enough, toconvert into mass energy (qq pairs) K- s K+ u u d p- d d d d p0 d Hadronization In this way, you can see that quarksare always confined inside hadrons(that’s CONFINEMENT) !

27. p p  t t from Fermilab Jet = sprayof particleswhen a quarkundergoeshadronization4 jets  4 quarksemerging from the interaction.

28. Putting it all together

29. The Carriers of the Weak Force • Three force carriers for the weak force: W+, W- and Z0 • The W+ and W- are the ones I have emphasized, and their rolein the decay of heavy quarks to lighter quarks. • The W+ and W- carry both electrical and weak charge. • They “connect” the +2/3 charge quarks with the –1/3 chargequarks (a change in charge of 1 unit). • These range of the weakforce is very short !! It’s about 10-18 [m],which is about 10,000 times smaller than the range of the strong force

30. quarks Charged leptons(e,m,t) Neutral leptons(n) Y Strong N N Electro-Magnetic N Y Y Y Y Y Weak Particles & Forces Quarks carry strong, weak & EM charge !!!!!

31. Weak Force • They W and Z particles can only“talk-to” particles which have weak charge (the leptons and the quarks !). • Heavy quark decay to lighter quarks via emission of a W+ or W-. • The weak force is also responsible for neutron decay. • Because the weak force is sooo weak, neutrinos can passthrough matter (like the earth) as if it wasn’t there ! • Quarks and leptons can interact by exchanging a W or Zforce carrier…

32. + W- W- + e- + + n p e - Proton Neutron But in fact, what’s really going on is this: u u + + d u e - d d u d Neutron Decay (cont)

33. 0 m- -1 W- b c -1/3 +2/3 Notice: Here, the W- decays to a m- and nm,could have also been a e-ne, or t-nt What about the decay of a b-quark?b  c + m- + nm

34. W- d b c b-quark decay at the hadron level Decay of a B- Meson Could end up as:B- D0p-B- D0p-p0B- D0p- p+ p-etc to hadrons B- D0 • Additional particles are created when the strong force produces morequark-antiquark pairs. They then combine to form hadrons! • Notice that the charge of the particles other than the D0 add up to the charge of the W- (Q = -1), as they must!

35. Hadrons! p0 u uu pair produced by convertingenergy stored in the “stretched spring” into mass energy… d d p- d d Hadronization – Producing hadrons! In this way, you can see that quarksare always confined inside hadrons(that’s CONFINEMENT) !

36. Conservation Laws • Conservation of Total Energy • Conservation of Total Momentum • Conservation of Electric Charge • Conservation of Baryon Number • Conservation of Lepton Number (Le, Lm, and Lt)

37. Energy conservation means: Energy of particle “A” + Energy of particle “B” =Energy of particle “C” + Energy of particle “D” • Or, in simpler notation, EA + EB= EC + ED Energy Conservation (I) A + B C + D If you knew any 3 of the energies, you could compute the fourth!  So, in such a reaction, you only need to measure 3 particles, andenergy conservation allows you to compute the fourth!

38. B D A A This canhappen A B D EB=MBc2 EA=MAc2 ED=MDc2 Energy Conservation (II) Decay Process: A  B + D If particle A has non-zero mass (mA> 0), then: mB < mA mD < mA This is a consequence of energy conservation (see lecture 24) ! This can’thappen ifMB>MA, orMD>MA

39. p0 n p+ p p0 Boom p p p p - n p0 p p Interaction – Conversion of KE to Mass Notice that the total mass of the particles after the interaction islarger than the incoming masses (2 proton masses) !This is OK, as long as the incoming protons have enough kineticenergy to produce all these particles

40. Well, according to me, this neutron is at rest ! So, ha !Therefore it cannot decayto something heavier!!That would violate energyconservation ! n Now, if the neutron is zipping along, and it has a lot of KE, why can’t it decay to something heavier by converting some of its KE into mass ??? Then why can’t this happen in decays?

41. e+ e- Bam Momentum Conservation (I) (I) If this electron & positron have equal & opposite velocity, whatcan be said about their total momentum?A) It’s twice as large B) It’s zero C) It’s negative D) It’s positive (II) What can be said about the total momentum of all the particles which are produced in this collision at top?A) It’s positive B) It’s negative C) It’s same as in (I) D) It’s 0.5 [MeV/c]

42. n This is precisely what lead to the conjecture that there must bean undetected particle, called the neutrino! Momentum Conservation (II) neutron at rest appears todecay to a proton + electron p n mP me e Since both the electron and proton are both moving off to theright, their total momentum cannot be zero.  In other words, this reaction, as shown cannot occur, since it would violate momentum conservation.

43. Consider the process: p+ + p  n + p0 Can it occur? What about this one ? What about this one ? p+ + n  p + p0 p+ + p  p0 + p0 Charge Conservation Total charge on left has to equal total charge on right in order forcharge to be conserved! The process could still be forbidden to occur if it violates some other conservation law !

44. Y N p + p  p + p+ + n + p0 p+ + p  p0 + p0 p + p  n + n + p+ + p- n  p + p Baryon Number Conservation Rules of the game: For each baryon, assign B = +1 For each antibaryon, assign B = -1Compare total Baryon number on left side to right side… X X X n  p0 + p0 X X

45. < 940 [MeV/c2] + 0.51 [MeV/c2] + ~0[MeV/c2] Why can’t the proton decay ? p  ? + ? + ? Since baryon number must be conserved , there MUST BE abaryon among the “?” decay products.But, the proton is the lowest mass baryon (938 [MeV/c2]).So there is nowhere it can go ! It CANNOT decay into something heavier, as this would violateenergy conservation ! p  n + e+ + ne 938 [MeV/c2]

46. Lepton Number Conservation A + B C + D At it’s heart, it’s just: Total lepton number on LHS = Total lepton number on RHSAll leptons get assigned: L = +1 All antileptons get assigned: L = -1But, it’s more powerful than that ! It can be applied for “electron-type”, “muon-type” and “tau-type”objects separately!

47. X X LeLm 0 0 -1 0 0 1 Example Photon Conversion: g e+ + m- Lepton Antilepton • If we don’t distinguish between “electron-type” and “muon-type”objects, we would conclude that this process can occur, sincewe have a lepton and anti-lepton on the RHS ! • If we require both Le and Lm conserved separately, we see thatthis process violates both cannot occur ! And, in fact this process is never observed… g e+ + m-

48. n  p + e+ + nm 938 [MeV/c2] 0.51 [MeV/c2] ~0[MeV/c2] -1 +1 0 -1 0 0 0 -1 0 0 0 +1 Example II Energy(Checkmass) 940 [MeV/c2] Charge 0 BaryonNumber -1 Le 0 Lm 0

49. The Big Bang !Everything that could have possibly existed, did exist ! And ???

50. Matter today • Today, the universe is a relatively cold place (rememberthe 3o microwave background… that’s –270 oC) • Nearly all heavy quarks have decayed through the weak interaction into up & down quarks. t  b  c  s  u  d • The up & down quarks which are the lightest of the quarks are thelightest, and have combined to form protons & neutrons • The protons and neutrons have combined with electrons to formour atomic elements…and hence, US ! • The heavy quarks are produced in cosmic rays or at large acceleratorlaboratories, like Fermilab..