Final Exam: Mon. May 8, 2:45-4:45 pm, 2241 Cham. Exam is cmlative, coverin all material 40 qestions, 2 note sheets allowe Review Particle Physics Particles an fiels: a new pictre Qarks an leptons The weak interaction Unification an mass The approach of strin theory Particle physics an the bi ban Particles an fiels Think abot electrons an photons Moern view is that both are excitations of qantm fiels that permeate all state. Photon is an excitation of the photon fiel. Electron is an excitation of the electron fiel. Bt there is a ifference: Electron is a matter particle Photon is a force particle Phy107 Lectre 41 1 Phy107 Lectre 41 2 Qantm Electroynamics: QED Normal electromanetic force comes abot from exchane of photons. Qestion An electron an anti-electron (positron) can annihilate, so that the particles vanish. What is left after the annihilation? Electromanetic replsion via emission of a photon electron photon A. nothin B. qarks C. photons D. netrinos electron Phy107 Lectre 41 3 Phy107 Lectre 41 4 Pair proction, annihilation Electron an positron can annihilate to form two photons. Photon can isappear to form electron-positron pair. Relativity: Mass an enery are the same Go from electron mass to electromanetic/photon enery Seein antiparticles Photons shot into a tank of liqi hyroen in a manetic fiel. Electrons an positrons ben in opposite irections an, losin enery to ionization, spiral to rest. Phy107 Lectre 41 5 Phy107 Lectre 41 6 1
The story so far Electromanetic force an electrons are both fiels. The fiels have qanta: photon an electrons. The Qantm fiel theory QED explains how they interact. Very sccessfl theory: explains perfectly all the interactions between electrons an photons Preicte a few thins we in t expect: Antiparticles - the positron. Electrons an positions can be annihilate to photons an vice versa. Phy107 Lectre 41 7 Creatin more particles All that is neee to create particles is enery. Enery can be provie by hih-enery collision of particles. An example: Electron an positron annihilate to form a photon. This can then create particles with mc 2 <photon enery. e- e-,µe+ µ, Mon mass: 100MeV/c 2, electron mass 0.5 MeV/c 2 e+,µ+ First new particle fon this way Phy107 Lectre 41 8 All the leptons Six ifferent leptons: cats an fleas The cats have an electrical chare of -e The fleas (netrinos) have zero chare (netral). Three lepton enerations Each electron-like particle an netrino paire in a eneration. Generation I Generation II Generation III e µ τ ν e ν µ ν τ Phy107 Lectre 41 9 Phy107 Lectre 41 10 Qestion The ifference between the ifferent enerations of leptons is A. their chare B. their mass C. their color D. their spin Qarks Six ifferent kin of qarks, analoos to the six leptons All qarks have an electric chare, they cople to photon fiel. Bt they also have a color chare, an they cople to the lon fiel. Coplin of qarks to the lon fiel is the stron interaction Phy107 Lectre 41 11 Phy107 Lectre 41 12 2
Three qark enerations Six ifferent qarks, bt two per eneration Jst like the leptons Generation I Generation II Generation III Chare c s t b +2/3-1/3 Phy107 Lectre 41 13 Qarks & leptons: matter particles Three enerations ifferentiate primarily by mass (enery). First eneration One pair of leptons, one pair of qarks Leptons: Electron, electron-netrino. Qarks: Up, own. All 3 enerations seen Phy107 Lectre 41 14 Protons/Netrons are composite Qestion A netron is a composite particle consistin of three qarks (p=chare +2/3e, an own = chare -1/3e). Which is the strctre of the netron. A. p, p, p B. p, p, ow C. p, own, own Total chare: +2e +e 0 Netron has zero total chare Phy107 Lectre 41 15 Phy107 Lectre 41 16 More Baryons Qark p own strane Q +2/3-1/3-1/3 Mass ~5 [MeV/c 2 ] ~10 [MeV/c 2 ] ~200 [MeV/c 2 ] s s s Mesons They are forme when a qark an an anti-qark bin toether. So far we ve only seen 3 qark combinations. There are also 2 qark combinations. The harons: 2 qarks, meson an 3 qarks, baryon. s Lamba (Λ) Q = 0 M=1116 MeV/c 2 Excite state - Hiher enery/mass s Sima (Σ + ) Q = +1 M=1189 MeV/c 2 s Sima (Σ 0 ) Q = 0 M=1192 MeV/c 2 s Sima (Σ ) Q = -1 M=1197 MeV/c 2 Phy107 Lectre 41 17 What s the chare of this particle? Q=+1, an it s calle a π + c What s the chare of this particle? Q= -1, an this charm Q= 0, this strane meson is calle a D - meson is calle a K 0 Phy107 Lectre 41 18 s What s the chare of this particle? 3
For interactions The for fnamental interactions all have associate fiels an meiatin particles. Talke abot EM interaction between electrically chare particles by exchane of photons Stron interaction between color chare particles by lon exchane Phy107 Lectre 41 19 Exchane bosons Each interaction has one or more associate particles that meiate the interaction. The exchane particles are associate with the known interactions Interaction Meiatin particle(s) Nmber Electro- photon (1) manetic Weak W +, W - an Z o (3) Stron lons (8) Gravity raviton (1) These all have inteer spins ( bosons ) Phy107 Lectre 41 20 Qestion The Stanar Moel Which of the followin particles is not a matter particle A. Electron B. Qark C. Glon D. Netrino 6 leptons 6 qarks 4 interactions Electromanetic, Gravitational, Stron, Weak meiate by 13 exchane bosons, which are excitations of the corresponin fiels. Phy107 Lectre 41 21 Phy107 Lectre 41 22 EM interaction Chare particles interact via the electromanetic (EM) interaction A chare particle coples to the photon fiel It excites a photon (excite state of photon fiel) an loses enery. Another chare particle can absorb the enery from the photon fiel (photon isappears). Only particles with an electric chare cople to the photon fiel. Matter particles & their interactions Three enerations of leptons an qarks All feel the weak force. Chare leptons feel weak & EM forces Qarks feel weak, EM, & stron Phy107 Lectre 41 23 Phy107 Lectre 41 24 4
Chare These are the exchane bosons. What are they exchane between? Or on what are the corresponin forces exerte? Example: When a photon is exchane between two particles, there is a electromanetic or Colomb force. We know that only particles with electrical chare interact via the Colomb force Zero chare -> zero Colomb interaction Many Chares A particle with electrical chare coples to the photon fiel Particle with mass chare coples to rav. fiel Particle with weak chare coples to weak int. fiel Particle with color chare coples to lon fiel Phy107 Lectre 41 25 Phy107 Lectre 41 26 Electromanetic Force In the Stanar Moel particles are often classifie by which forces they can participate in. Which of these particle oes not interact via the electromanetic force: A. electron B. mon C. photon D. qark The weak interaction Weak interaction is not stron, bt is important. It can chane one particle into another! Mon, ta, can trn into netrinos! Qarks can trn into other qarks Particles with a weak chare (qarks an leptons) cople to the weak fiel Excitations of the weak fiel are the Z an W bosons. Phy107 Lectre 41 27 Phy107 Lectre 41 28 Qestion The Weak Force Qarks interact only via the A. weak force B. stron force C. ravitational force D. all of the above EM STRONG WEAK Phy107 Lectre 41 29 Phy107 Lectre 41 30 5
Carriers of the weak force Like the Electromanetic & Stron forces, the Weak force is also meiate by force carriers. For the weak force, there are three force carriers: W + W - Z 0 These weak force carriers carry electric chare also! This weak force carrier is electrically netral The chare of the weak interaction is calle weak chare Phy107 Lectre 41 31 Drin raioactive beta ecay, a netron chanes to a proton insie a ncles by one of the internal qarks ecayin into a ifferent qark. What particle meiates the qark ecay? A. photon B. lon C. Z D. W E. W + Phy107 Lectre 41 32 Similar to nclear beta ecay Interaction via the W explains nclear beta ecay. Lepton ecay Flavor chane can occr spontaneosly if the particle is heavy enoh. n W - _ ν e e - p time s qark emits a W-, chanin flavor into a qark. W ecays to an electron an anti-electron netrino. The ncleon then has two ps an one own qark, which is a proton. Similar to the rotate Feynman iaram we sties with the electromanetic force Generation I e ν e Electron is stable Generation II µ ν µ Emit W - 2x10-6 secons Generation III τ ν τ Emit W - 3x10-13 secons Chare -1 0 Phy107 Lectre 41 33 Phy107 Lectre 41 34 Qarks an the weak force Qarks have color chare, electric chare, an weak chare other interactions swamp the weak interaction Bt similar to leptons, qarks can chane their flavor (ecay) via the weak force, by emittin a W particle. Flavor chane between enerations Bt for qarks, not limite to within a eneration! Generation I Generation II Generation III Chare Generation I Generation II Generation III Chare c t +2/3 c t +2/3 s b -1/3 s b -1/3 Emit W + 2x10-12 secons Emit W + 10-23 secons Emit W - 10-12 secons Emit W - 10-12 secons Phy107 Lectre 41 35 Phy107 Lectre 41 36 6
Qarks an leptons have mltiple chares. Some of the bosons have chares. Electric, flavor, color, mass Flavor Electric, flavor, mass A little complicate Phy107 Lectre 41 37 Color None Electric, mass Key Points Differences between particles connecte to how they interact, what chares they have. Qarks have all the chares. Color chare: Qarks form composite states harons via the stron force. Flavor chare: Heavy qarks ecay to lihter qarks via the weak force. Leptons have no color chane. Don t form any composite states. Netrinos only interact via the weak force which means they rarely interact at all. Phy107 Lectre 41 38 Key Points Cont. Properties of the force carriers etermine the aspects of that force. Glons an the stron force. Glon can interact with other lons. Limits the rane of that force. W, Z an the weak force. Force carriers are massive. Limits the rane they can travel an makes the force weaker. Photon an the electromanetic force. Happy mile ron between stron an weak. Phy107 Lectre 41 39 The His boson If the His fiel were not present, particles A. wol not have ifferent chares. B. wol not interact with each other. C. wol not be confine. D. wol not have antiparticles E. wol not have mass. Phy107 Lectre 41 40 Particle masses Mass in the SM In the stanar moel (SM), particles have mass becase they interact with somethin that pervaes the niverse. This somethin is the His fiel Particles hit the His fiel when yo try to accelerate them Mass = (chance of hit) x (His ensity) Coplin constant Phy107 Lectre 41 41 Phy107 Lectre 41 42 7
Unification Details of weak interaction sest that Different qarks are iff. orientations of the same particle. Different leptons are iff. orientations of the same particle. Weak an EM interactions are ifferent parts of a sinle electroweak force. Electroweak interaction le to the introction of the His Boson Gran Unifie Theories (GUTs) Will combine leptons an qarks Unify stron an electroweak interactions More Unifications? Phy107 Lectre 41 43 Phy107 Lectre 41 44 Strin theory In strin theory, ifferent fnamental particles appear as a. ifferent qantm vibrations of strins. b. ifferent qantm interactions between strins. c. qantm strins with ifferent spin.. qantm strins of ifferent lenth. e. qantm strins of ifferent velocity. Strin theory A strin is a fnamental qantm mechanical object that has a small bt nonzero spatial extent. Jst like a particle has a mass, a strin has a tension that characterizes its behavior. Qantm mechanical vibrations of the strin correspon to the particles we observe Can incle Kalza Klein theory an Spersymmetry. Phy107 Lectre 41 45 Phy107 Lectre 41 46 The niverse is expanin In the beinnin Jst after bi ban, the niverse was Very ense Very hot Very hih enery Forces nifie? Strin theory? Hbble s reat iscovery Phy107 Lectre 41 47 Phy107 Lectre 41 48 8
Inflation Phy107 Lectre 41 49 Phy107 Lectre 41 50 The beinnin of time? Phy107 Lectre 41 51 Phy107 Lectre 41 52 Kalza-Klein: EM & ravity Connect electromanetism an ravity in a classical relativistic theory. Kalza an Klein fon a theory in five imensions (for space & one time) with one interaction (5-imensional ravity). When one of the imensions was compactifie, two interactions reslte: ravity an electromanetism. What appears to s as two istinct interactions oriinate from only one. Kalza & Klein, 1920 Only nifies ravity. Can t be qantize. Doesn t answer all the other qestions! Phy107 Lectre 41 53 Qestion Which of the followin particles cannot interact with a particle that carries only the weak chare? A. Qark B. Netrino C. Electron D. All of them can Phy107 Lectre 41 54 9
Spersymmetry (SSy) The Stanar Moel Sperpartners (compare to anti-particles) Every fermion has a boson partner an vice versa Phy107 Lectre 41 55 6 leptons 6 qarks 4 interactions Electromanetic, Gravitational, Stron, Weak meiate by 13 exchane bosons, which are excitations of the corresponin fiels. Phy107 Lectre 41 56 Fnamental Matter Particles Three enerations of leptons an qarks All feel the weak force. Chare leptons feel weak & EM forces Qarks feel weak, EM, & stron Phy107 Lectre 41 57 Mass an the His fiel Now a poplar person enters the room, attractin a clster of haners-on that impee her motion As she moves she attracts the people she comes close to- the ones she has left retrn to their even spacin. Imaine a party in a room packe fll of people. Noboy is movin aron mch, jst stanin an talkin. Her motion is impee - she has become more massive. Phy107 Lectre 41 58 Spersymmetry Sccesses Desine to explain behavior at very hih enery Forces mere in SUSY Same strenth at hih enery. Lihtest SUSY particles on t ecay. Dark Matter Doesn t nifies ravity. Can t explain many of the other qestions! Checklist Strin Theory Unify all the forces: stron force - ravity Qantize the forces - QFT very sccessfl Unify the particles: qarks lepton - 3 enerations Explain all the ifferent masses an strenths Explain ark matter Explain why niverse is mostly matter Explain physics at very hih enery - bi ban Phy107 Lectre 41 59 Phy107 Lectre 41 60 10
CERN (Switzerlan) 27 km CERN, Geneva Switzerlan LHC accelerator 14TeV Enoh enery to see SUSY or KK More enery neee to see Strins Unification an New Physics Stanar moel has many nanswere qestions. Several theories propose to explain these qestions. Goal is to nerstan all physics from the beinnin of the niverse till toay. LHC: Will soon have a new experiment that miht ncover some of the answers. Phy107 Lectre 41 61 Phy107 Lectre 41 62 What have we learne? Matter is mae of atoms Electroweak Unification W + ν ν e W - e νe ν e Atoms are mae of leptons an qarks Atoms are mae of leptons an qarks Leptons ν e Qarks e Interact via ifferent forces carrie by particles, photons, simple except for the mon Phy107 Lectre 41 63 Netral weak Zero chare Mass=91 GeV/c 2 Rane ~ 10-18 m Electromanetic Zero chare Mass=0 GeV/c 2 Rane ~ inf. These two both exchane netral bosons Neither boson chanes the lepton flavor (remains electron) Have the same strenth at hih enery! Pos. weak Pos. chare Mass=80 GeV/c 2 Rane ~ 10-18 m Ne. weak Ne. chare Mass=80 GeV/c 2 Rane ~ 10-18 m These two both exchane chare bosons. Both bosons chane the lepton flavor Come from one sorce. Electroweak force Phy107 Lectre 41 64 How can we see the His? The His boson nees to be create in orer to see it. E = mc 2 Not fon yet m H > 114GeV m H < 186GeV e- Z o e+ Z o H Phy107 Lectre 41 65 Interactions throh Exchane of Color Chare r r r Initially Emission of Glon After lon emission RED RED-ANTIBLUE + BLUE (qark) (lon) (qark) Re-absorption of Glon Before lon absorption After lon absorption RED-ANTIBLUE + BLUE RED (lon) (qark) (qark) Phy107 Lectre 41 66 11
Feynman Diarams (Qark Scatterin) Qark-qark Scatterin Col also be Qark-antiqark Scatterin or Antiqark-antiqark Scatterin Qark-antiqark Annihilation Position Phy107 Lectre 41 67 time Glon interactions Since lons carry color chare, they can interact with each other! (Photons can t o that) Glon-lon Scatterin Glon-lon Fsion Phy107 Lectre 41 68 Qark flavors Each qark has a ifferent "flavor." For instance, the flavor of an p qark is simply "p. Up qark chanin to own qark is chanin flavor. A eneric way of referrin to ifferences between qarks. Leptons also have a flavor Netrino chanin into a mon is chanin flavor Phy107 Lectre 41 69 Rane of the interaction Electron oesn t have enoh enery to create Z o. Z o only present e to ncertainty relation (Enery ncertainty)x(time ncertainty)~planck cnst It can only exist for a time etermine by Planck cnst Time ncertainty ~ Particle mass Farthest it can travel in that time is Planck cnst Rane ~(Liht Spee)x Particle Mass ~ 10-18 m Phy107 Lectre 41 70 Particles & their Interactions (Smmary) Color Chare? EM Chare? Weak Chare? qarks Y Y Y Chare leptons (e,µ,τ) Y Netral leptons (ν) Qarks can participate in Stron, EM & Weak Interactions. All qarks & all leptons carry weak chare. N Y N N Y Comparison of the Force Carriers Force Carrier Chare of force carrier Coples to: Particles w/color chare (Qarks,lons) <10-14 m (insie harons) W +, W - Particles w/weak chare (Qarks, leptons) W,Z) < 2x10-18 m Netrinos only carry weak Phy107 chare. Lectre 41 71 Phy107 Lectre 41 72 Rane EM Photon (γ) None Particles w/elect. chare Infinite (1/ 2 ) Stron Glon () Color Electric Weak Z 0 None Particles w/weak chare (Qarks, leptons W,Z) < 2x10-18 m 12
Enery ncertainty To make a very short plse in time, nee to combine a rane of freqencies. Freqency relate to qantm enery by E=hf. Heisenber ncertainty relation can also be state (Enery ncertainty)x(time ncertainty) ~ (Planck s constant) In other wors, if a particle of enery E only exists for a time less than h/e, it oesn t reqire any enery to create it! Liht Heavier Heaviest The enerations Phy107 Lectre 41 73 Phy107 Lectre 41 74 Scatterin from qarks in a ncles What Ice Cbe looks for is netrinos emerin from collisions as mons. n ν µ W + µ - p time The netrino interacts with qarks bon insie ncleons in the ncles. Netrino emits W +, chanin flavor into mon. Down qark bon in a netron absorbs W +, chanin into a p qark. The ncleon then has two ps an one own qark, which is a proton. Checklist for a theory of everythin Unify all the forces: stron force - ravity Qantize the forces - QFT very sccessfl Unify the particles: qarks lepton - 3 enerations Explain all the ifferent masses an strenths Explain ark matter Explain why niverse is mostly matter Explain physics at very hih enery - bi ban Phy107 Lectre 41 75 Phy107 Lectre 41 76 13