Elementary Particle Physics Summer 2001
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R. D. Field Summer 2001 Elementary Particle Physics Summer 2001 “Hard” Scattering Outgoing Parton PT(hard) Proton AntiProton Underlying Event Underlying Event Initial-State Radiation Final-State Radiation Outgoing Parton Books: • • • • Introduction to Elementary Particles, David Griffiths. Modern Elementary Particle Physics, Gordon Kane. An Introduction to High Energy Physics, Donald Perkins. Quarks & Leptons: An Introductory Course in Modern Particle Physics, F. Halzen and A. D. Martin. • Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, Chris Quigg. • Applications of Perturbative QCD, R. D. Field. University of Florida Page 1 of 39 R. D. Field Summer 2001 The Simple Structure of our Universe Elementary Particle: Indivisible piece of matter without internal structure and without detectable size or shape . . Mass and chage located inside sphere of radius zero! • Four Forces: • Gravity (Solar Systems, Galaxies, Curved Space-Time , Black Holes) • Electromagnetism (Atoms & Molecules, Chemical Reactions) • Weak (Neutron Decay, Beta Radioactivity) • Strong (Atomic Nuclei, Fission & Fusion) • Two Classes of Elementary Particles: • Leptons: Do not interact with the strong force (but may interact with weak, EM and gravity). • Quarks: Do interact with the strong force (may also interact with weak, EM and gravity). • Quarks and Leptons have very different properties: 1. Weak and EM forces much weaker that strong force. 2. Quarks have fractional electric charge. 3. Quarks are found only as constituents of composite particles called hadrons (baryons have B not 0, mesons have B = 0). Leptons exist as free particles. Baryon Number • Gauge Particles are the carriers (or mediators) of the forces: • • • • Electromagnetism – Photon γ (massless) Weak – Weak Vector Bosons W+, W-, Z (massive) Gravity – Graviton Strong – 8 Gluons (massless) University of Florida Page 2 of 39 R. D. Field Summer 2001 Labeling the Particles – Quantum Numbers Elementary particles and hadrons are labeled by their quantum numbers. These labels characterize the properties of the particles. Symbol Name M J C P G B Qem QU1 Qweak Qcolor Y S Ch Bo To I Iz Le Lµ Lτ L Mass Spin Angular Momentum Charge Conjugation Parity G-Parity Baryon Number Electric Charge Q = Y/2 + Iz Q = Qweak + QU1 U1 Charge Weak Charge Strong Charge Hypercharge Y = B + S + Ch + Bo + To Strangness Charmness Bottomness Topness Isospin 3rd component of Isospin Electron Lepton Number Muon Lepton Number Tau Lepton Number Overall Lepton Number L = Le +Lµ +Lτ Additive Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Not all particles carry every label. The particles are only labeled by the quantum numbers that are conserved for that particle. • Particles with integral spin J (J = 0, 1, 2, …) are called bosons. • Particles with half-integral spin J (J = ½, 3/2, …) are called fermions. • Particles with spin-parity JP = 0+ are refered to a scalars, 0- are pseudo-scalars, 1- are vectors, 1+ are pseudo-vectors, 2+ are tensors, etc. • Hadrons are labeled by IGJPC. University of Florida Page 3 of 39 R. D. Field Summer 2001 Leptons & Anti-Leptons (J = ½ fermions, B = 0, Ch = 0, Bo = 0, To = 0) Generation Mass MeV Qem Le Lµ Lµ QU1 Qweak 1st ~0 -1/2 ~0 -1/2 +1/2 2nd 106 -1/2 -1/2 3rd ~0 0 0 0 0 1 1 -1/2 2nd 0 0 1 1 0 0 +1/2 0.5 1 1 0 0 0 0 -1/2 1st 0 -1 0 -1 0 -1 -1/2 +1/2 -1/2 -1/2 Lepton νe eνµ µντ τ- Qem = Qweak + QU1 rd 3 1777 Qem measured in units of the electron charge e Generation Mass MeV Qem Le Lµ Lµ QU1 Qweak 1st 0.5 ~0 0 0 0 0 +1/2 1st -1 -1 +1/2 ve +1 0 +1/2 -1/2 µ+ 2nd 106 ~0 -1 -1 0 0 +1/2 2nd 0 0 +1/2 vµ +1 0 +1/2 -1/2 τ+ 3rd 1777 0 0 -1 -1 +1/2 ~0 0 0 +1/2 3rd +1 0 +1/2 -1/2 AntiLepton e+ vτ SU(2) Weak Lepton Doublets: ν ν ν L1 = −e L 2 = µ− L 3 = τ− e µ τ SU(2) Weak Anti-Lepton Doublets: µ+ τ + e+ L1 = L 2 = L3 = ν τ ν e ν µ University of Florida Page 4 of 39 R. D. Field Summer 2001 Quarks & Anti-Quarks µ = 0, Lττ = 0) (J = ½+ fermions, Le = 0, Lµ Generation Mass MeV B Qem Y I Iz S Ch 5 1/3 2/3 1/3 1/2 1/2 0 0 0 0 +1/6 +1/2 10 1/3 -1/3 1/3 1/2 -1/2 0 0 0 0 +1/6 -1/2 1,500 1/3 2/3 4/3 0 0 0 1 0 0 +1/6 +1/2 200 1/3 -1/3 -2/3 0 0 -1 0 0 0 +1/6 -1/2 175,000 1/3 2/3 4/3 0 0 0 0 0 1 +1/6 +1/2 4,700 1/3 -1/3 -2/3 0 0 0 0 -1 0 +1/6 -1/2 Mass MeV B Qem Y I S Ch 1st 10 -1/3 1/3 -1/3 1/2 1/2 0 0 0 0 -1/6 +1/2 Rbar, Bbar, Gbar 1st 5 -1/3 -2/3 -1/3 1/2 -1/2 0 0 0 0 -1/6 -1/2 Rbar, Bbar, Gbar 2nd 200 -1/3 1/3 2/3 0 0 1 0 0 0 -1/6 +1/2 Rbar, Bbar, Gbar 2nd 150 -1/3 -2/3 -4/3 0 0 0 -1 0 0 -1/6 -1/2 Rbar, Bbar, Gbar 3rd 4,700 -1/3 1/3 2/3 0 0 0 0 1 0 -1/6 +1/2 Rbar, Bbar, Gbar 3rd 175,000 -1/3 -2/3 -4/3 0 0 0 0 0 -1 -1/6 -1/2 Rbar, Bbar, Gbar Quarks u, u, u d, d, d c, c, c s, s, s t, t, t b, b, b AntiQuarks dbar, dbar, dbar ubar, ubar, ubar sbar, sbar, sbar cbar, cbar, cbar bbar, bbar, bbar tbar, tbar, tbar Qem = Qweak + QU1 1st 1st 2nd 2nd 3rd 3rd Iz Bo To QU1 Qweak Bo To QU1 Qw Qcolor R, B, G R, B, G R, B, G R, B, G R, B, G R, B, G Qcolor SU(2) Weak Quark and Anti-Quark Doublets: Q1 Q1 R , B ,G R , B ,G t R ,B ,G u R ,B ,G cR ,B ,G R , B ,G R , B ,G Q 2 Q 3 = = = ′ ′ d R ,B ,G s R ,B ,G bR′ ,B ,G b′ R , B ,G d R′ ,B ,G sR′ ,B ,G R , B ,G R , B ,G Q2 Q3 = = = cR ,B ,G u R ,B ,G t R ,B ,G University of Florida Page 5 of 39 R. D. Field Summer 2001 Vector Bosons (J = 1-, B = 0, Ch = 0, Bo = 0, To = 0, Le = 0, Lµ = 0, Lτ = 0) Qem = Qweak + QU1 Boson Name Mass GeV Qem QU1 Qweak Qcolor γ W+ WZ G1 G2 G3 G4 G5 G6 G7 Photon 0 0 0 none W-Boson 81 0 +1 none W-Boson 81 0 -1 none W-Boson Gluon 92 0 0 0 0 0 none Gluon 0 0 0 Gluon 0 0 0 Gluon 0 0 0 Gluon 0 0 0 Gluon 0 0 0 Gluon 0 0 +1 -1 0 0 0 0 0 0 0 0 0 0 Gluon 0 0 0 0 G8 University of Florida RBbar RGbar BRbar BGbar GRbar GBbar RRbar BBbar GGbar RRbar BBbar GGbar Page 6 of 39 R. D. Field Summer 2001 Classifying the Forces • Notation a b a A B b C D a → a + A a →b + B b → a + C b →b + D implies the transisitions • U(1) of Electromagnitism (1 x 1 transisition matrix) ν e e− e− νe 0 0 e− γ ee− 0 γ also Qem u d u γ 0 d 0 γ u u γ and d γ d e- • SU(2) Weak (2 x 2 transisition matrix) u d′ ν e e− u Z W+ νe Z W + e − W − γ d′ W Z − d’ W+ Qweak Z u • SU(3) Color (3 x 3 transisition matrix) qR qB qG q RBbar Gluon Qcolor qR qB RR RB RG BR BB BG qG GR GB GG q q = u, d, s, c, b, t University of Florida Page 7 of 39 R. D. Field Summer 2001 ElectroWeak Force (Unification of Weak and Electromagnetic Forces) e, ν • U(1) Transisitions ν e e− νe V 0 0 e− V 0 V0 e, ν e, ν W0 • SU(2) Transisitions ν e e− νe W 0 W + e− W − W 0 ν W- e- e, ν • SU(2) x U(1) ElectroWeak (contains both electromagnetic and weak force) ν e e− ν e W 0 +V 0 → Z W+ e− W− W 0 +V 0 → Z + γ ν W e Qweak e University of Florida Z, γ ν Q e Z Qweak ν Page 8 of 39 R. D. Field Summer 2001 Flavor Mixing – Generation Hopping (Kobayashi-Maskawa Matrix) The Weak Interactions are not diagonal in quark flavor and hence, u → d ′ + W + c → s′ + W + t → b′ + W + where d ′ V ud s ′ = V cd b′ V td CKM Matrix V us V cs V ts V ub V cb V tb 1 d ≈ s λ λ3 b λ 1 λ2 λ3 λ2 1 d s b • Tranisitions within the same generation are of order one d s b W W W VudQweak VcsQweak VtbQweak u c t • 1st – 2nd generation transisitions are “1st order” forbidden and are of order λ ~ 0.23. s d W W VusQweak VcdQweak st u st 1 Order Forbidden c 1 Order Forbidden • 2nd – 3rd generation transisitions are “2nd order” forbidden and are of order λ2 ~ 0.05. b s W W VcbQweak VtsQweak nd c University of Florida 2 Order Forbidden nd t 2 Order Forbidden Page 9 of 39 R. D. Field Summer 2001 Flavor Mixing – Generation Hopping (continued) • 1st – 3rd generation transisitions ar “3rd order” forbidden and are of order λ3 ~ 0.001 b d W W VubQweak VtdQweak rd u rd 3 Order Forbidden t 3 Order Forbidden • Transisition Pattern: st 1 Generation nd 2 Generation u d order 1 order λ c s order 1 2 order λ rd 3 Generation t b order 1 • Experimental Summary (magnitude of the matrix elements): [0.9745 ↔ 0.9760 ] [0.217 ↔ 0.224] [0.0018 ↔ 0.0045] [0.217 ↔ 0.224] [0.9737 ↔ 0.9753] [0.036 ↔ 0.042] [0.004 ↔ 0.013] [0.036 ↔ 0.042] [0.9991 ↔ 0.9994 ] University of Florida Page 10 of 39 R. D. Field Summer 2001 Feynman Diagrams – Quantum Field Theory (Pictures) Momentum-Space ~p 4 ~3 p Amplitude = p~1 Feynman diagrams are a way to organize and summerize the rules of perturbation theory. They represent the Quantum Mechanical amplitude for the process. Probability = |Amplitude|2 ~ p2 p~1 + p~2 ~ p~3 + p 4 • Space-Time Diagrams (constructed from vertices) e e γ Time Vertex Qem e ∆E = h/∆t Qem Efinal > Einitial γ Qem e e Einitial Space e • Momemtum-Space Diagrams At a vertex quantum additive numbers are conseerved and the 4-momentum is conserved, but particles may or may not be on their mass shell. “on shell” r r ~ p2 = E2 − p ⋅ p = m2 r r ~ p2 = E2 − p ⋅ p ≠ m2 Vertex ~p 2 γ Qem ~ =~ ~ p 1 p2 +q “real” particle “off shell” “virtual” particle q~ ~ p1 • Particle-Antiparticle Relation A particle of 4-momentum p corresponds to an antiparticle of 4-momentum –p and vice-versa. University of Florida Page 11 of 39 R. D. Field Summer 2001 Electromagnetic Intractions - QED (Photons Couple to Electric Charge) • Charged Lepton or Quark - Photon Vertex e q γ γ Qem Qem q e • Photons do not carry electric charge and hence do not directly couple to each other. γ γ = zero γ • However photons can interact with each other indirectly. γ γ Charged Lepton or Quark Loop γ University of Florida γ Page 12 of 39 R. D. Field Summer 2001 Weak Intractions – SU(2)xU(1) (W & Z Couple to Weak Charge) • 1st Generation “Charged Current” Interactions (flavor changing) ν d W W Qweak Qweak e u • 1st Generation “Neutral Current” Interactions e ν Z u d Z Qweak Z Qweak Qweak ν e Z Qweak u d • Self-Coupling and Electromagnetic Interactions W W γ Z Qweak W Qem Self-coupling W EM Coupling • 4-Point Couplings γ W Q2em W γ University of Florida Z W γ W Z W W Q2weak QweakQem W Z W Q2weak W W Page 13 of 39 R. D. Field Summer 2001 Strong Intractions - QCD (Gluons Couple to Color Charge) • Quark (q = u, d, s, b, t) Color Changing and Non-Color Changing Interactions q q RBbar BBbar Gluon Gluon Qcolor Qcolor q q • Gluon Self-Coupling BGbar Gluon RBbar Gluon Qcolor RGbar Gluon Gluons carry color and couple to each other! • 4-Point Coupling BGbar Gluon RBbar Gluon Q2color Gluon RGbar University of Florida Gluon BBbar Page 14 of 39 R. D. Field Summer 2001 Hadrons – PseudoScalar Meson Nonet (JP = 0- bosons, B = 0, Ch = 0, Bo = 0, To = 0) Y = B + S +Ch +Bo + To Symbol Name π+ π0 pion Mass MeV 140 pion 135 πK+ K0 K0bar Kη pion 140 kaon 494 kaon 478 kaon 478 kaon 494 eta 549 -1 +1 0 0 -1 0 eta-prime 958 0 η’ Qem = Y/2 + Iz Qem Net Quarks I Iz Y S Qcolor +1 0 udbar uubar, ddbar dubar usbar dsbar sdbar subar 1 +1 0 0 singlet 1 0 0 0 singlet 1 -1 0 0 singlet ½ +1/2 +1 +1 singlet ½ -1/2 +1 +1 singlet ½ +1/2 -1 -1 singlet ½ -1/2 -1 -1 singlet 0 0 0 0 singlet 0 0 0 0 singlet uubar, ddbar, ssbar uubar, ddbar, ssbar Y 3 d u 3x3=8+1 Iz SU(3)flavor Triplet s 8 Y K0 η πK- SU(3)flavor Octet University of Florida 1 K+ π+ π0 Y η’ Iz Iz K0bar SU(3)flavor Singlet Page 15 of 39 R. D. Field Summer 2001 Hadrons – ½+ Baryon Octet (JP = ½+ fermions, B = 1, Ch = 0, Bo = 0, To = 0) Symbol Name Σ+ Σ0 Σp n Ξ0 ΞΛ Sigma Mass MeV 1189 Sigma 1193 Sigma 1189 Proton Neutron Cascade 938 940 1315 Cascade 1321 Lambda 1116 Qem/e Net Quarks I Iz Y S Qcolor +1 0 -1 +1 0 0 -1 0 uus uds dds uud udd ssu ssd uds 1 +1 0 -1 singlet 1 0 0 -1 singlet 1 -1 0 -1 singlet ½ ½ ½ +1/2 -1/2 +1/2 +1 +1 -1 0 0 -2 singlet singlet singlet ½ -1/2 -1 -2 singlet 0 0 0 -1 singlet Y = B + S +Ch +Bo + To 8 Qem = Y/2 + Iz Y n p Λ ΣΞ- Σ+ Σ0 Iz 0 Ξ SU(3)flavor Octet 3 x 3 x 3 = 10 + 8 + 8 + 1 University of Florida Page 16 of 39 R. D. Field Summer 2001 Hadrons – 3/2+ Baryon Decuplet (JP = 3/2+ fermions, B = 1, Ch = 0, Bo = 0, To = 0) Symbol Name ∆++ ∆+ ∆0 ∆Σ*+ Σ*0 Σ*Ξ*0 Ξ*Ω- Delta Mass MeV 1232 Delta 1232 Delta 1232 Delta 1232 SigmaStar 1385 SigmaStar 1385 SigmaStar 1385 CascadeStar 1530 CascadeStar 1530 Lambda 1672 Qem Net Quarks I Iz Y S Qcolor +2 +1 0 -1 +1 0 -1 0 -1 -1 uuu uud ddu ddd uus uds dds ssu ssd sss 3/2 +3/2 1 0 singlet 3/2 +1/2 1 0 singlet 3/2 -1/2 1 0 singlet 3/2 +3/2 1 0 singlet 1 +1 0 -1 singlet 1 0 0 -1 singlet 1 -1 0 -1 singlet ½ +1/2 -1 -2 singlet ½ -1/2 -1 -2 singlet 0 0 -2 -3 singlet Y = B + S +Ch +Bo + To Qem = Y/2 + Iz Three u quark fermions in the same state! SU(3)flavor Decuplet Y + 0 - Σ- ∆ Σ+ Σ0 Ξ*- 10 ++ ∆ ∆ ∆ Iz *0 Ξ Ω- 3 x 3 x 3 = 10 + 8 + 8 + 1 University of Florida Page 17 of 39 R. D. Field Summer 2001 Units It is convenient to set hbar = h/2π π = 1 and to set the speed of light c = 1. (1) Units of h = [M][L2]/[T] = 1 Units of c = [L]/[T] = 1 (2) where [M] = mass [L] = length [T] = time We have but one free unit left or alternatively we can measure mass, length, and time all in the same units. (1)/(2) (2) implies implies [M][L] = 1 [L] = [T] thus [Mass] = [Energy] = [momentum] = 1/[Length] = 1/[Time] • Express everyting in energy units: 1 MeV = 106 ev 1 GeV = 1,000 MeV 1 TeV = 1,000 GeV hbarc = 1.973x10-11 MeV-cm = 0.1973 GeV-fm = 1 1 fm = 10-13cm 1 GeV-1 = 0.1973 fm Fermi hbar = 6.58x10-22 MeV-sec = 0.0658 GeV-ss = 1 1 ss = 10-23sec 1 GeV-1 = 0.0658ss Strong Second University of Florida Page 18 of 39 R. D. Field Summer 2001 Particle Decay Stable Particles: At present it seems that photons, neutrinos, protons, and electrons are stable and hence everything eventually decaus into these four particles. Baryon Number Conservation: At present it seems that baryon number is conserved so that everything with B = 1 eventually decays into a proton (plus B = 0 stuff). Muon Decay (weak process): µ − → e− +υe +υµ τ = 2.2 ×10−6 s cτ = 660m νµ µ- W- Qweak νe Qweak e- Neutron Decay (weak process): n → p + e− +υe τ = 896s cτ = 2.7 ×1011m u d d u d u neutron Qweak WQweak proton νe e- Charged Pion Decay (weak process): π + → µ + +ν µ τ = 2.6 ×10−8 s cτ = 780cm νµ π+ University of Florida u d W+ Qweak Qweak µ+ Page 19 of 39 R. D. Field Summer 2001 Particle Decay Neutral Pion Decay (electromatnetic process): π 0 →γ + γ τ = 0.8×10−16 s cτ = 2.5×10−6 cm π0 γ Qem u u Qem γ Delta Decay (strong process): ∆++ → p + π + τ ≈ 10−23 s cτ = 3×10−15cm u u u u proton u d ∆++ gluon Qcolor Qcolor d u π+ • What is meant by an particle? Single coherent object with definite identity (definite mass, electric charge, angular momentum) • Does a particle have to be absolutely stable to be a particle? Look at the uncertainty principle (∆E∆t ~ h). If system has a finite ∆m = Γ called “width”) is lifetime τ then the uncertainty in its mass (∆ given by ∆m ~ h/τ. We consider an unstable object a particle provided, ∆m/m = Γ/m << 1 (called a particle). Remember that, 1 GeV-1 = 0.0658 x 10-23 sec which implies that a 1 GeV particle should live longe than ~10-23 sec. For the ∆++ Γ ~ 100 MeV so that Γ/m ~ 1/10 which satisfies the criterion. University of Florida Page 20 of 39 R. D. Field Summer 2001 The Top Quark Top Decay: eυ e (1) ( 1 ) µυ µ t → bW → b τυ τ (1) ud ′(3) cs ′(3) 1/9 6/9 Discovery Mode (µµνν µµννjj): Rate = (1/9)2 = 1/81 = 1.2% µµνν “Top” Production µ ν b W t Proton AntiProton t W b µ ν Analysis Mode (µν µνjjjj): Rate = 2(1/9)(6/9) = 12/81 = 14.8% µν “Top” Production q q b W t Proton AntiProton t b W µ ν University of Florida Page 21 of 39 R. D. Field Summer 2001 The Standard Model Higgs Boson Holy Grail of the Standard Model! Why do particles have mass? The standard model gives a partial answer to this question. All particles are massless and their mass is genereated by spontaneous symmetry breaking. The scalar Higgs (JP=0+) is a consequence of this symmetry breaking mechanism. 3-Point Veticies: f=q,l H H H V=W,Z mf Qweak f=q,l H (MV)2Qweak Higgs-Vector Boson Coupling V=W,Z Higgs-Fermion Coupling (MH)2Qweak Self-Coupling H 4-Point Couplings: H V=W,Z (MV)2Q2weak (MH)2Q2weak Higgs and Vector Bosons V=W,Z H H Self-Coupling H H H “Higgs” Production µ ν W Proton AntiProton H b University of Florida b Page 22 of 39 R. D. Field Summer 2001 Standard Model Higgs Decay The decay modes and branching fractions of the Higgs depend on its mass. In the limit of large Higgs mass (MH >> mi) then the branching fractions are as follows: Diagram Decay Γ/ΓWW H → W +W − 1 H → ZZ ½ H → tt 6mt2 / M H2 H → bb 6mb2 / M H2 H → τ +τ − 2mτ2 / M H2 H → gg α s /(16π 2 ) H → γγ α s /(16π 2 ) H H H The Higgs Mass Precision fits to the LEP data indicate that MH < 180 GeV which means that above table is not accurate and that the Higgs cannot decay to on-shell topantitop and maybe not to on-shell ZZ or WW. However, even if the Higgs µν through a virtual mass is below 2MW it can decay into, for example, µνW, W as follows: ν H W- µW+ University of Florida Page 23 of 39 R. D. Field Summer 2001 Supersymmetry Spin ½ Fermions Symmetry which relates fermions and bosons Spin 0 Bosons For every “normal” spin ½ lepton there corresponds a spin 0 “slepton” (supersymmetric partner): υ e υ~e − → ~ − SusyPartner e e Scalar neutrino: ~ “snutrino” υµ υµ − → ~ − SusyPartner µ µ υτ υ~τ − → ~ − SusyPartner τ τ For every “normal” spin ½ quark there corresponds a spin 0 “squark” (supersymmetric partner): u u~ → ~ Scalar quark: SusyPartner “stop” quark d d ~ c c Carry color ~ → charge: RBG SusyPartner s s ~ t t → ~ SusyPartner b b For every “normal” spin 1 gauge boson there corresponds a spin ½ “gaugino” (supersymmetric partner): → g~1 , g~2 , K , g~8 Gluinos (spin ½) Gluons (spin 1) g1 , g 2 , K , g 8 SusyPartners ~ ~ ~ + − →W + ,W − , Z Wino/Zino (spin ½) W/Z Bosons (spin 1) W ,W , Z SusyPartners → γ~ Photino (spin ½) Photon (spin 1) γ SusyPartner For every “normal” spin 0 Higgs there corresponds a spin ½ “fermionic” Higgs (supersymmetric partner): ~ ~ → H 1 , H 2 Higgsino (spin ½) Higgs (spin 0) H 1 , H 2 SusyPartners 2 Higgs doublets University of Florida Page 24 of 39 R. D. Field Summer 2001 Supersymmetry Super-Summary (MSSM): Fermions (24 particles) Sfermions (24 particles) Gluinos Charginos (4 particles) Neutralinos (4 particles) Higgs Bosons (5 particles) Spin ½ fermions Scalar Fermions quarks, leptons squarks, sleptons f = (u , d , s, c, b, t ,υ e , e − ,υ µ , µ − ,υτ ,τ − ) ~ ~ ~ ~ ~ ~ ~ ~ ~− ~ ~− ~ ~− f = (u , d , s , c , b , t ,υe , e ,υ µ , µ ,υτ ,τ ) g~ = ( g~ , g~ , g~ , g~ , g~ g~ , g~ , g~ ) winos, Higgsinos photino, zino, Higgsinos ~ ~ ~ ~ →W1± ,W2± W ± , H ± Mix ~ ~ ~ ~ ~ ~ ~ γ~, Z , H10 , H 20 Mix → Z1 , Z 2 , Z 3 , Z 4 Spin ½ fermions Spin ½ fermions Spin ½ fermions 1 2 3 4 5, 6 7 8 H l0 , H h0 , H P0 , H ± Spin 0 Bosons All the three point verticies involve supersymmetric particles in pairs which implies the following. • Supersymmetric partners are produced in pairs starting from normal particles. • The decay of supersymmetric particles will contain a supersymmetric particle. • The lightest supersymmetric particle (called the LSP) is stable. Some 3-Point Veticies: ~ f ~ f' γ,Z ~ f ~ f sfermion-sfermion-γγ/Z sfermion-sfermion-W q g~ squark-quark-gluino University of Florida f' ~ Z sfermion-neutralino-fermion ~ q ~ W ~ f ~ f Qcolor ~ q f W g ~ g Qcolor ~ q squark-squark-gluon sfermion-fermion-chargino g Qcolor ~ g gluino-gluino-gluon Page 25 of 39 Lightest Neutralino R. D. Field Summer 2001 Supersymmetry The Decay of Superpartners: ~ ~ f → f + Zi ~ ~ f → f ′ + Wi g~ → q~ + q Msquark > Mgluino Mgluino >Msquark q~ → q + g~ ~ g~ → g + Z i The LSP is a new stable particle which is either the lightest neutralino, ~ Z 1 , or a sneutrino, υ~ (not favored based on LEP constraints and cosmological arguments). Stable? ~ γ ,υ , p , Z 1 ~~ Stop Production at the Collider: µυ bb qq Z 1 Z 1 “Stop” Production ~ b Z1 ~ t t Proton q W q Leptons + MultiJets + Missing Energy! AntiProton ~t t b W ν University of Florida ~ µ Z1 Page 26 of 39 R. D. Field Summer 2001 Electron-Proton Elastic Scattering: Form Factors − − Electron-Proton Elastic Scattering: e + p → e + p e- Proton γ e- F(Q2) Proton Compare elastic electron-proton scattering with elastic electron-muon scattering (point interaction), 2 dσ dσ (e + p → e + p ) = F (Q 2 ) dΩ d Ω po int The form factor F(Q2) measures the distribution of charge within the proton. If F(Q2) = 1 then the proton is a “point-like” object (with no substructure). (Actually the proton (spin e- Point = ½) has two form factors the magnetic form factor and the electric form factor, but I will ignor this complication.) µ+ γ e- µ+ Experimental Results: Experiments show that the proton form factor behaves like, F(Q2) ~ 1/Q4. Thus, the proton is not a point like object (its charge is distributed over space). Small overlap with proton wavefunction e- γ e- University of Florida Proton Page 27 of 39 R. D. Field Summer 2001 Deep Inelastic Scattering: Structure Functions − − Inelastic Electron-Proton Scattering: e + p → e + X X = Anything e- In the laboratory frame (proton initially at rest) measure the energy loss of the electron ν = E – E’ and the 4-momentun transfer Q2. The differential cross section can be written in the form, Proton e- 4α 2 E'2 d 2σ 2 2θ 2 2θ = 2 ( , ) sin + ( , ) cos W x Q W x Q 1 2 2 2 dΩ' dE' Q4 ν). where x = Q2/(2Mν Parton Model: A fast moving Proton proton is a collection of partons (constituents of the proton) each carrying a certain fraction ξ of the proton momentum. momentum P s d u u s G A → i (ξ ) is the number of partons of type i within a fast moving hadron of type A with fraction of momentum ξ (pi = ξP) between ξ and ξ + dξ. Momentum Sum Rule: The sum of the momentum of all the constituents must equal one. ∑ All Partons 1 ∫ξG A → i (ξ ) d ξ = 1 0 Net Number of Quarks: The net number of u quarks in a proton is 2 and the net number of d quarks is 1. 1 ∫ (G p →u (ξ ) − G p →u (ξ ) )dξ = 2 0 University of Florida ∫ (G 1 p→d ) (ξ ) − G p → d (ξ ) dξ = 1 0 Page 28 of 39 R. D. Field Summer 2001 DIS Electron-Proton: Parton Model γ q u Proton momentum s P d p = ξP s p’ = p+q ( p' )2 = ( p + q)2 = (ξp + q)2 = m2 implies that Q2 Q2 ξ= = =x 2P ⋅ q 2Mν when Q2 = -q2 is large. Scaling: Predict that νW2 (x, Q2 ) = F2 (x, Q2 ) → F2 (x) where ep F2 ( x ) = + ( 4 1 x (G p → u ( x ) + G p → u ( x ) ) + x G p → d ( x ) + G p → d ( x ) 9 9 ) 1 x (G p → s ( x ) + G p → s ( x ) )+ K 9 DIS Experiments (1972-1975): Observe approximate scaling and measure quark distributions. Find that only about one-half of the proton momentum is carried by the charged quarks: n f 1 ∑ ∫ i=1 ( x G p → q i ( x ) + G p → q i ) ( x ) dx ≈ 0 .5 0 The remaining momentum must be carried by electricrically neutral partons (i.e. gluons). University of Florida Page 29 of 39 R. D. Field Summer 2001 Neutrino-Proton vs Electron-Proton e- DIS ep γ e- DIS νp e- W Qem νe Proton Qweak Proton Quarks have fractional electric charge: By comparing deep inelastic electron-proton scattering with deep inelastic neutrino-proton scattering one can determine the electric charge of the quarks. ( F 2 ( x ) = 2 x (G p → u ( x ) + G p → u ( x ) ) + 2 x G p → d ( x ) + G p → d ( x ) νp + 2 x (G p → s ( x ) + G p → s ( x ) )+ K ) Quark and Gluon Distributions: Proton Structure Functions 2.0 Q = 2 GeV 1.8 1.6 gluon 1.4 xG 1.2 1.0 0.8 0.6 u-quark d-quark 0.4 0.2 s-quark 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x University of Florida Page 30 of 39 R. D. Field Summer 2001 DIS Electron-Proton: QCD Perturbative QCD – Scale Breaking: QCD tells us that quarks can radiate gluons before or after the interact with the virtual photon in DIS ep scattering. Also, gluons within the proton can produce quark-antiquark pairs that then interact with the virtual photon. DIS ep e- e- γ DIS ep γ Gluon e- e- Proton Proton This causes a breaking of scaling and the quark (and gluon) distributions become a function of the scale, Q2, of the probing virtual photon: G A→ i ( x, Q 2 ) Probability of Emitting a “Hard” Gluon: QCD tells us that the probability of emitting a gluon with transverse momentum (relative to the quark direction) greater than ∆ is P∆ ∝ α s ( Q 2 ) log 2 ( Q 2 / ∆ 2 ) ~ log( Q 2 ) and hence more and more hard gluons are emitted as Q2 increases producing a logarithmtic scale breaking. However, given can compute (via QCD perturbation theory) 2 G A→ i ( x, Q 0 ) G A→ i ( x, Q 2 ) one , provided Q02 and Q2 are both large (Q02 < Q2). Gluon ∆ q q University of Florida Page 31 of 39 R. D. Field Summer 2001 QED Effective Coupling: Renormalization Elastic Electron-Electron Scattering: e- e- eeff e- γ* q eeff = e- e- e0 e- e- γ* e- e0 + e- e- e0 γ* e0 e- ee + e0 γ* e0 +… e- In QED the strength of the coupling must be determined experimentally; for example, by measuring the rate of electron-electron elastic scattering. However, one immediately runs into trouble since the vacuum polarization λ), where λ is correction to the virtual photon propagator diverges like log(λ some ultraviolet cutoff that can be arbitrarily large. In particular, the leading order bubble contribution is, α 5 α 0 B ( Q 2 ) = − 0 log( λ 2 / Q 2 ) + Q 2 / m e2 >> 1 3π 3 and α Q2 Q 2 / m e2 << 1 α 0 B ( Q 2 ) = − 0 log( λ 2 / m e2 ) − 2 3π 5me where q2 = - Q2 is the 4-momentum of the virtual (spacelike) photon and π is the bare coupling. α0 = e02/4π Effective Coupling: It is convenient to define an effective coupling that includes the vacuum polarization bubbles as follows: α eff ( Q 2 ) = α 0 (1 + α 0 B ( Q 2 ) + α 0 B ( Q 2 )α 0 B ( Q 2 ) + L ) yielding α0 α eff ( Q 2 ) = 1 − α 0 B (Q 2 ) University of Florida Page 32 of 39 R. D. Field Summer 2001 QED Effective Coupling: Renormalization Renormalization: We see that the effective coupling is given by α eff 1 1 = − B (Q 2 ) 2 (Q ) α 0 where B(Q2) is infinite (diverges as the cutoff λ becomes large) and α0 is the unmeasurable bare coupling. We must express all experimental observables in terms of other experimental observables and so we define π to be the effective charge at Q2 = 0 the fine structure constant α = e2/4π (this is called the Thompson limit and corresponds a large distance limit), 1 e2 α = ≡ α eff ( Q 2 = 0 ) ≈ 4π 137 Now writing the effective coupling in terms of α gives 1 1 1 1 2 ( ) ( 0 ) = − − = − log( Q 2 / m e2 ) B Q B 2 α eff ( Q ) α α 3π ( ) Finite and independent of cut-off λ or α QED ( Q 2 ) = α eff ( Q 2 ) = α 1 − (α / 3π ) log( Q 2 / m e2 ) The QED effective coupling strength is equal to 1/137 at small Q2 and then increases as Q2 increases! 2 αeff(Q ) QED 1/137 Large Q2 Long Distance University of Florida Page 33 of 39 R. D. Field Summer 2001 QCD Effective Coupling: Asymptotic Freedom Elastic Quark-Quark Scattering: q q geff g q q geff = g0 q g q q g0 q g0 + g0 g0 g0 + q q g0 g0 qbar q q q q q g g0 g0 +… g q q q In QCD there are two types of bubbles quark loops and gluon loops and the leading order bubble contribution is, α 0 B QCD ( Q 2 ) = −α 0 a log( λ 2 / Q 2 ) where λ is the ultraviolet cutoff and α0 = g02/4π π is the bare strong coupling and β a = − 0 β 0 = 11 − 2 n f / 3 . 4π The 11 comes from the gluon loop 2 bubbles and the –2nf/3 comes from the αeff(Q ) QCD quark loop bubbles (nf is the number of quark flavors). confinement Renormalization (or Subtraction Point): In this case we cannot define the “experimental charge” to be at Q2 = 0 (long distance limit). Instead we choose some Q2, say Q2 = µ2 to define the coupling and Asymptotic Feedom Large Q2 Long Distance express all observables in terms of the coupling at this point (called the renormalization point) and 1 1 = − B (Q 2 ) − B ( µ 2 ) 2 2 α eff ( Q ) α ( µ ) Thus, α (µ 2 ) 2 2 α s ( Q ) = α eff ( Q ) = 1 + α ( µ 2 )( β 0 / 4π ) log( Q 2 / µ 2 ) ( ) Finite and independent of cut-off λ which approaches zero as Q2 becomes large (asymptotic freedom). University of Florida Page 34 of 39 R. D. Field Summer 2001 QCD Effective Coupling: The Λ Parameter The behavior of the QCD coupling constant as takes a bit of getting used to. In QED it is easy to define the charge of an electron e. It is related to the long distance behavior of the effective QED coupling. We cannot do this for QCD since the effective coupling cannot be calculated (by perturbation theory) at low Q2. Instead we define an arbitrary point µ and define αs to be the effective coupling at that point: α s ≡ α s (µ 2 ) . However, it does not matter which point µ one chooses (physical observables are independent of the choice of µ). If instead one chooses the point µ2 then the two couplings are related (to lowest order) by 1 1 − a log( Q 2 / µ 22 ) = − a log( Q 2 / µ 2 ) 2 2 α s (µ 2 ) α (µ ) which means that there are not two parameters αs(µ µ2) and µ2 but rather one scale Λ that is independent of the point µ2, 1 1 2 log( ) + µ = + log( µ 2 ) ≡ log( Λ 2 ) 2 2 2 aα s (µ 2 ) aα (µ ) In terms of Λ the effective QCD coupling is given by 4π α s ( Q 2 ) = α eff ( Q 2 ) = . β 0 log( Q 2 / Λ 2 ) Experiments indicate that Λ is around 200 MeV. Unification: Effecitve Coupling 2 αeff(Q ) Unification Point QCD QED ElectroWeak Weak Large Q2 Long Distance University of Florida Page 35 of 39 R. D. Field Summer 2001 Electron-Positron Annihilations Hadrons qbar e+ µ+ q µ- γ* e- e+ e- Count the Number of Quark Flavors: Measure the ratio nf σ ( e + e − → Hadrons ) R e+e− = = 3 ∑ e q2i + − + − σ (e e → µ µ ) i =1 and verify that there are indeed three colors of quarks. University of Florida Page 36 of 39 R. D. Field Summer 2001 Electron-Positron Annihilations Quark Fragmentation Functions: Measure the probability of finding a hadron of type h carrying the fraction z of the parent quarks momentum: D qh ( x , Q 2 ) . Hadronization: Center-of-Mass Frame Hadronization qqbar qqbar qqbar qqbar qqbar qqbar qqbar qbar q γ* Short time – Small distance University of Florida qbar q Long time – Long distance Page 37 of 39 R. D. Field Summer 2001 Electron-Positron Annihilations Parton Showers: Parton Shower qbar q γ* Late time Hadrons Form Early time Quark Jets: Two Jet Final State Hadronic Jet Short time – Small distance qbar q Hadronic Jet γ* QCD Perturbative Corrections: gluon qbar q γ* e+ e- R(e+e-) is slightly larger due to “final state interactions”. α s ( Q 2 ) nf 2 3 ∑ e q i R e+e− = 1 + π i =1 University of Florida Page 38 of 39 R. D. Field Summer 2001 Electron-Positron Annihilations Three-Jet Final State: Three Jet Final State Hadronic Jet Short time – Small distance qbar Hadronic Jet q γ* Gluon Hadronic Jet University of Florida Page 39 of 39
