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all fundamental with no underlying structure Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 No QM theory for gr

all fundamental with no underlying structure Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 No QM theory for gravity Higher generations have larger mass. When/where discovered. Nobel Prize?. g Mostly Europe 1895-1920 Roentgen (sort of)1901

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all fundamental with no underlying structure Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 No QM theory for gr

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  1. all fundamental with no underlying structure • Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 • No QM theory for gravity • Higher generations have larger mass P461 - particles I

  2. When/where discovered Nobel Prize? g Mostly Europe 1895-1920 Roentgen (sort of)1901 W/Z CERN 1983 Rubbia/vanderMeer1984 gluon DESY 1979 NO electron Europe 1895-1905 Thomson 1906 muon Harvard 1937 No tau SLAC 1975 Perl 1995 ne US 1953 Reines/Cowan 1995 nm BNL 1962 Schwartz/Lederman/Steinberger 1988 nt FNAL 2000 NO u,d SLAC 1960s Friedman/Kendall/Taylor 1990 s mostly US 1950s NO c SLAC/BNL 1974 Richter/Ting 1976 b FNAL 1978 NO (Lederman) t FNAL 1995 NO muon – Street+Stevenson had “evidence” but Piccione often gets credit in the 1940s as measured lifetime P461 - particles I

  3. Couplings and Charges • All charged particles interact electromagnetically • All particles except gamma and gluon interact weakly (have nonzero “weak” charge) (partially semantics on photon as mixing defined in this way) A WWZ vertex exists • Only quarks and gluons interact strongly; have non-zero “strong” charge (called color). This has been tested by: magnetic moment electron and muon H energy levels (Lamb shift) “muonic” atoms. Substitute muon for electron pi-mu atoms • EM charge just electric charge q • Weak charge – “weak” isospin in i=1/2 doublets used for charged (W) and have I3-Aq for neutral current (Z) • Strong charge – color charge triplet “red” “green” “blue” P461 - particles I

  4. Pi-mu coupling P461 - particles I

  5. Strong Force and Hadrons • p + p -> p + N* • N* are excited states of proton or neutron (all of which are baryons) • P = uud n = udd (bound by gluons) where u = up quark (charge 2/3) and d = down quark (charge -1/3) • About 20 N states spin ½ mass 938 – 2700 MeV • About 20 D states spin 3/2 • Charges = uuu(2) uud(1) udd(0) ddd(-1) • N,D decay by strong interaction N  p/n + p with lifetimes of 10-23 sec (pion is quark-antiquark meson). Identify by looking at the invariant mass and other kinematic distributions P461 - particles I

  6. ISOSPIN • Assume the strong force is ~identical between baryons (p,n,N*) and between three pions • Introduce concept of Isospin with (p,n) forming an isopsin doublet I=1/2 and pions in an isopsin triplet I=1, and quarks (u,d) in a I=1/2 doublet • Isospin isn’t spin but has the same group algebra SU(2) as spin and so same quantum numbers and addition rules P461 - particles I

  7. Baryons and Mesons • 3 quark combinations (like uud) are called baryons. Historically first understood for u,d,s quarks • “plotted” in isospin vs strangeness. Have a group of 8 for spin ½ (octet) and 10 (decuplet) for spin 3/2. Fermions and so need antisymmetric wavefunction (and have some duplication of quark flavor like p = uud) • Gell-Mann tried to explain using SU(3) but badly broken (seen in different masses) but did point out underlying quarks • Mesons are quark-antiquark combinations and so spin 0 or 1. Bosons and need symmetric wavefunction (“simpler” as not duplicating quark flavor) • Spin 0 (or spin 1) come in a group of 8 (octet) and a group of 1 (singlet). Again SU(3) sort of explains if there are 3 quarks but badly broken as seen in both the mass variations and the mixing between the singlet and octet P461 - particles I

  8. Baryons and Mesons • Use group theory to understand: -what states are allowed - “mixing” (how decay) - state changes (step-up/down) - magnetic moments of • as masses are so different this only partially works – broken • SU(2) Isospin –very good (u/d quark same mass) SU(3) for s-quark – good with caveats SU(4) with c-quark – not so good P461 - particles I

  9. Baryons D0 also P461 - particles I

  10. Baryon Wave Functions • Totally Antisymmetric as 3 s=1/2 quarks - Fermions • S=3/2. spin part must be symmetric (all “aligned”). There are some states which are quark symmetric (uuu,ddd,sss). As all members of the same multiplet have the same symmetries  quark and spin are both symmetric • to be antisymmetric, obey Pauli exclusion, need a new quantum number “color” which comes in 3 (at least) indices. Color wavefunctions: P461 - particles I

  11. Baryon Wave Functions • S=1/2. color part is like S=3/2. So spin*quark flavor = symmetric. Adding 3 spin = ½ to give S=1/2 produces “mixed” spin symmetry. • First combine two quarks giving symmetric 1<->2 • Add on third quark to get first term • Cycle 1  2  3  1 8 more terms. And then multiply by 6 color terms from S=3/2 page (4*9*6=216 terms) • Why no charge 2 or charge -1particles like the proton or neutron exist  the need for an antisymmetric wavefunction makes the proton the lightest baryon (which is a good thing for us) P461 - particles I

  12. Meson Wave Functions • quark antiquark combinations. Governed by SU(2) (spin) and strangenessSU(3) (SU(4)) for c-quark). But broken symmetries • pions have no s quarks. The h’s (or the w+f) mix to find real particles  break SU(3) meson mass Decay p 135,140 no s h 550 little s h’ 958 mostly s r 770 no s w 782 little s f 1019 85% KK, 15% ppp P461 - particles I

  13. Hadron + Quark masses • Mass of hadron = mass of constituent quarks plus binding energy. As gluons have F=kx, increase in energy with separationpositive “binding” energy • Bare quark masses: u = 1-5 MeV d = 3-9 MeV s = 75-170 MeV c = 1.15 – 1.35 GeV b = 4.0–4.4 GeV t = 169-179 GeV • Top quark decay so quickly it never binds into a hadron. No binding energy correction and so best determined mass value (though < 300 t quark decays observed) • Other quark masses determined from measured hadron masses and binding energy model pion = “2 u/d quarks” = 135 Mev proton = “3 u/d quarks” = 940 MeV kaon = “1 s and 1 u/d” = 500 MeV Omega = “3 s quarks” = 1672 MeV • High energy p-p interactions really q-q (or quark-gluon or gluon-gluon). “partons” emerge but then hadronize. Called “jets” whose energy and momentum are mostly original quark or gluon P461 - particles I

  14. Hadrons, Partons and Jets • The quarks and gluons which make up a hadron are called partons (Feynman, Field, Bjorken) • Proton consists of: -3 valence quarks (about 40% of momentum) -gluons (about 50% opf the momentum) -“sea” quark-antiquark pairs • The sea quarks are constantly being made/annihilated from gluons and can include heavier quarks (s,c,b) with probability mass-dependent • X = p/p(total) is the momentum fraction and each type of particle has a probability to have a given X (parton distribution function or pdf) • PDFs mostly measured in experiments using nu,e,mu,p etc. Some theoretical modeling • Even at highest energy collisions, quarks still pointlike particles (no structure) as distances of 0.002 F (G. Blazey et al) • single quark produces other gluons and quarks  jet. Have similar fragmentation function P461 - particles I

  15. u,d,s Fragmentation functions p c fraction of energy which quark (or gluon) has for either particle or jet b P461 - particles I

  16. Lepton and Baryon Conservation • Strong and EM conserve particle type. Weak can change but always leptonlepton or quarkquark • So number of quarks (#quarks-#antiquarks) conserved. Sometimes called baryon conservation B. • Number of each type (e,mu,tau) conserved L conservation • Can always create particle-antiparticle pair • But universe breaks B,L conservation as there is more matter than antimatter • At small time after big bang #baryons = #antibaryons = #leptons = #antileptons (modulo spin/color/etc) = ~#photons (as can convert to particle-antiparticle pairs) • Now baryon/photon ratio 10-10 P461 - particles I

  17. Hadron production + Decay • Allowed production channels are simply quark counting • Can make/destroy quark-antiquark pairs with the total “flavor” (upness = #up-#antiup, downness, etc) staying the same • All decays allowed by mass conservation occur quickly (<10-21 sec) with a few decaying by EM with lifetimes of ~10-16 sec) Those forbidden are long-lived and decay weakly and do not conserve flavor. P461 - particles I

  18. Hadrons and QCD • Hadrons are made from quarks bound together by gluons • EM force QuantumElectroDynamics QED strong is QuantumChromoDynamics QCD • Strong force “color” is equivalent to electric charge except three different (identical) charges red-green-blue. Each type of quark has electric charge (2/3 up -1/3 down, etc) and either r g b (or antired, antiblue, antigreen) color charge • Unlike charge=0 photon, gluons can have color charge. 8 such charges (like blue-antigreen) combos, 2 are colorless. Gluon exchange usually color exchange. Can have gluon-gluon interaction P461 - particles I

  19. quark-gluon coupling • why q-qbar and qqq combinations are stable • 8 gluons each with color and anticolor. All “orthogonal”. 2 are colorless gluons • coupling gluon-quark = +c coupling gluon-antiquark = -c r b vertex 1 +c r vertex 2 +c b vertex 2 -c P461 - particles I

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  21. Group Theory • W/Z bosons and gluons carry weak charge and color charge (respectively)Bosons couple to Bosons • SU(2) and SU(3) which have 3 and 8 “base” vectors can be used to represent weak and strong forces. The base vectors are the W+,W-,Z and the 8 gluons. Exact (non-broken) symmetry • The group algebra tells us about boson interaction. So for W/Z use • SU(2) used for 3D rotations angular momentum (orbital and spin) isospin (hadrons – broken) weak interactions  weak “isospin” P461 - particles I

  22. Group Theory – SU(3) • 3x3 unitary matrices with det=1. 2n2-n2-1=8 parameters. Have group algebra • and representation of generators • and 3 color states P461 - particles I

  23. Pions • Use as strong interaction example • Produce in strong interactions • Measure pion spin. Mirror reactions have same matrix element but different phase space/kinematics term. “easy” part of phase space is just the 2s+1 spin degeneracy term • Find S=0 for pions P461 - particles I

  24. More Pions • Useful to think of pions as I=1 isospin triplet and p,n is I=1/2 doublet (from quark plots) • Look at reactions: • p p -> d pi+ Total I ½ ½ 0 1 1 Iz ½ ½ 0 1 1 p n -> d pi0 Total I ½ ½ 0 1 0 or 1 Iz ½ - ½ 0 0 0 • in the past we combined 2 spin ½ states to form S=0 or 1 P461 - particles I

  25. More Pions • Reverse this and say eigentstate |p,n> is combination of I=1 and I=0 • reactions: • then take the “dot product” between |p,n> and |d,pi0> brings in a 1/sqrt(2) (the Clebsch-Gordon coefficient) • Square to get A/B cross section ratio of 1/2 P461 - particles I

  26. EM Decay of Hadrons u g • If a photon is involved in a decay (either final state or virtual) then the decay is at least partially electromagnetic • Can’t have u-ubar quark go to a single photon as have to conserve energy and momentum (and angular momentum) • Rate is less than a strong decay as have coupling of 1/137 compared to strong of about 0.2. Also have 2 vertices in pi decay and so (1/137)2 • EM decays always proceed if allowed but usually only small contribution if strong also allowed g ubar P461 - particles I

  27. c-cbar and b-bbar Mesons • Similar to u-ubar, d-dbar, and s-sbar • “excited” states similar to atoms 1S, 2S, 3S…1P, 2P…photon emitted in transitions. Mass spectrum can be modeled by QCD • If mass > 2*meson mass can decay strongly • But if mass <2*meson decays EM. “easiest” way is through virtual photons (suppressed for pions due to spin) m+ c g m- cbar P461 - particles I

  28. c-cbar and b-bbar Meson EM-Decays • Can be any particle-antiparticle pair whose pass is less than psi or upsilon: electron-positron, u-ubar, d-dbar, s-sbar • rate into each channel depends on charge2(EM coupling) and mass (phase space) • Some of the decays into hadrons proceed through virtual photon and some through a virtual (colorless) gluon) c g cbar P461 - particles I

  29. Electromagnetic production of Hadrons • Same matrix element as decay. Electron-positron pair make a virtual photon which then “decays” to quark-antiquark pairs. (or mu+-mu-, etc) • electron-positron pair has a given invariant mass which the virtual photon acquires. Any quark-antiquark pair lighter than this can be produced • The q-qbar pair can acquire other quark pairs from the available energy to make hadrons. Any combination which conserves quark counting, energy and angular momentum OK q e+ g qbar e- P461 - particles I

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  31. Weak Decays • If no strong or EM decays are allowed, hadrons decay weakly (except for stable proton) • Exactly the same as lepton decays. Exactly the same as beta decays • Charge current Weak interactions proceed be exchange of W+ or W-. Couples to 2 members of weak doublets (provided enough energy) U d d u d u W e n P461 - particles I

  32. Decays of Leptons • Transition leptonneutrino emits virtual W which then “decays” to all kinematically available doublet pairs • For taus, mass=1800 MeV and W can decay into e+n,m+n, and u+d (s by mixing). 3 colors for quarks and so rate ~3 times higher. W e P461 - particles I

  33. Weak Decays of Hadrons • Can have “beta” decay with same number of quarks in final state (semileptonic) • or quark-antiquark combine (leptonic) • or can have purely hadronic decays • Rates will be different: 2-body vs 3-body phase space; different spin factors W e P461 - particles I

  34. Top Quark Decay • Simplest weak decay (and hadronic). • M(top)>>Mw (175 GeV vs 81 GeV) and so W is real (not virtual) and there is no suppression of different final states due to phase space • the t quark decays before it becomes a hadron. The outgoing b/c/s/u/d quarks are seen as jets t b W c u P461 - particles I

  35. Top Quark Decay • Very small rate of ts or td • the quark states have a color factor of 3 t b W P461 - particles I

  36. How to Discover the Top Quark • make sure it wasn’t discovered before you start collecting data (CDF run 88-89 top mass too heavy) • build detector with good detection of electrons, muons, jets, “missing energy”, and some B-ID (D0 Run I bm) • have detector work from Day 1. D0 Run I: 3 inner detectors severe problems, muon detector some problems but good enough. U-LA cal perfect • collect enough data with right kinematics so statistically can’t be background. mostly W+>2 jets • Total: 17 events in data collected from 1992-1995 with estimated background of 3.8 events P461 - particles I

  37. The First Top Quark Event muon electron P461 - particles I

  38. The First Top Quark Event jet P461 - particles I

  39. Another Top Quark Event jets electron P461 - particles I

  40. Decay Rates: Pions u dbar • Look at pion branching fractions (BF) • The Beta decay is the easiest. ~Same as neutron beta decay • Q= 4.1 MeV. Assume FT=1600 s. LogF=3.2 (from plot) F= 1600 • for just this decay gives “partial” T=1600/F=1 sec or partial width = 1 sec-1 P461 - particles I

  41. Pi Decay to e-nu vs mu-nu nu L+ • Depends on phase space and spin factors • in pion rest frame pion has S=0 • 2 spin=1/2 combine to give S=0. Nominally can either be both right-handed or both left-handed • But parity violated in weak interactions. If m=0  all S=1/2 particles are LH and all S=1/2 antiparticles are RH • neutrino mass = 0  LH • electron and muon mass not = 0 and so can have some “wrong” helicity. Antparticles which are LH.But easier for muon as heavier mass P461 - particles I

  42. Polarization of Spin 1/2 Particles • Obtain through Dirac equation and polarization operators. Polarization defined • the degree of polarization then depends on velocity. The fraction in the “right” and “wrong” helicity states are: • fraction “wrong” = 0 if m=0 and v=c • for a given energy, electron has higher velocity than muon and so less likely to have “wrong” helicity P461 - particles I

  43. Pion Decay Kinematics • 2 Body decay. Conserve energy and momentum • can then calculate the velocity of the electron or muon • look at the fraction in the “wrong” helicity to get relative spin suppression of decay to electrons P461 - particles I

  44. Pion Decay Phase Space • Lorentz invariant phase space plus energy and momentum conservation • gives the 2-body phase space factor (partially a computational trick) • as the electron is lighter, more phase space (3.3 times the muon) • Branching Fraction ratio is spin suppression times phase space P461 - particles I

  45. Muon Decay • Almost 100% of the time muons decay by • Q(muon decay) > Q(pionmuon decay) but there is significant spin suppression and so muon’s lifetime ~100 longer than pions • spin 1/2 muon  1/2 mostly LH (e) plus 1/2 all LH( nu) plus 1/2 all RH (antinu) • 3 body phase space and some areas of Dalitz plot suppressed as S=3/2 • electron tends to follow muon direction and “remember” the muon polarization. Dirac equation plus a spin rotation matrix can give the angular distribution of the electron relative to the muon direction/polarization P461 - particles I

  46. Jm Jn p+ n m+ Jn Je Jm n e+ m+ n Jn Detecting Parity Violation in muon decay • Massless neutrinos are fully polarized, P=-1 for neutrino and P=+1 for antineutrino (defines helicity) • Consider + + e+ decay. Since neutrinos are left-handed PH=-1, muons should also be polarised with polarisation P=-v/c (muons are non-relativistic, so both helicity states are allowed). • If muons conserve polarization when they come to rest, the electrons from muon decay should also be polarized and have an angular dependence: p+ m+ + nm m+e+ + ne +nm P461 - particles I

  47. Parity violation in + + e+ decay • Experiment by Garwin, Lederman, Weinrich aimed to confirm parity violation through the measurements of I(q) for positrons. • 85 MeV pion beam (+ ) from cyclotron. • 10% of muons in the beam: need to be separated from pions. • Pions were stopped in the carbon absorber (20 cm thick) • Counters 1-2 were used to separate muons • Muons were stopped in the carbon target below counter 2. P461 - particles I

  48. Parity violation in + + e+ decay • Positrons from muon decay were detected by a telescope 3-4, which required particles of range >8 g/cm2 (25 MeV positrons). • Events: concidence between counters 1-2 (muon) plus coincidence between counters 3-4 (positron) delayed by 0.75-2.0 ms. • Goal: to measure I(q) for positrons. • Conventional way: move detecting system (telescope 3-4) around carbon target measuring intensities at various q. But very complicated. • More sophisticated method: precession of muon spin in magnetic field. Vertical magnetic field in a shielded box around the target. • The intensity distribution in angle was carried around with the muon spin. P461 - particles I

  49. Results of the experiment by Garwin et al. • Changing the field (the magnetising current), they could change the rate (frequency) of the spin precession, which will be reflected in the angular distribution of the emitted positrons. • Garwin et al. plotted the positron rate as a function of magnetising current (magnetic field) and compared it to the expected distribution: P461 - particles I

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