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BND Summer School in Particle Physics 2016

BND Summer School in Particle Physics 2016. Early Experimental Tests of QCD. Rick Field University of Florida. Lecture 1. The early first tests of QCD. Deep inelastic scattering. Electron-positron annihilations. University of Antwerp August 26 – September 9, 2016.

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BND Summer School in Particle Physics 2016

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  1. BND Summer School in Particle Physics 2016 Early Experimental Tests of QCD Rick Field University of Florida Lecture 1 • The early first tests of QCD. Deep inelastic scattering. Electron-positron annihilations. University of Antwerp August 26 – September 9, 2016 Lecture 2 (tonight at dinner) • Toward an understanding and simulation of hadron-hadron collisions. The early days of Feynman-Field Phenomenology. Lecture 3 (tomorrow morning) • The early first tests of QCD. Drell-Yan lepton-pair prodcution. Large pT meson and “jet” production in hadron-hadron collisions. CDF Run 2 CMS at the LHC 300 GeV, 900 GeV, 1.96 TeV 900 GeV, 7, 8, & 13 TeV Rick Field – Florida

  2. My Story of QCD The Quark Model The Eightfold Way QCD Theory! Parton Model + Perturbative QCD! Interacting quarks, anti-quarks, and gluons! The QCD Improved Parton Model Before we knew the partons were quarks and gluons! Non-interacting partons! Partons = quarks, anti-quarks, and glue! Still non-interacting partons! The Parton Model The Naïve Parton Model Rick Field – Florida

  3. BND Summer School in Particle Physics 2016 Early Experimental Tests of QCD Rick Field University of Florida Lecture 1 • My talk at ICHEP 1978 in Tokyo and my lectures in Boulder in 1979. • The “Eightfold Way”. University of Antwerp August 26 – September 9, 2016 • Classifying the forces. • Inelastic electron-proton scattering: Form Factors. • The Parton Model and the Naïve Parton Model. • Deep Inelastic Lepton-Proton Scattering: Quark & Gluon Distribution Functions. • The QCD Improved Parton Model. • The QCD Effective Coupling: Asymptotic Freedom. • Electron-Positron Annihilations. Rick Field – Florida

  4. The Feynman-Field Days 1973-1983 • FF1: “Quark Elastic Scattering as a Source of High Transverse Momentum Mesons”, R. D. Field and R. P. Feynman, Phys. Rev. D15, 2590-2616 (1977). • FFF1: “Correlations Among Particles and Jets Produced with Large Transverse Momenta”, R. P. Feynman, R. D. Field and G. C. Fox, Nucl. Phys. B128, 1-65 (1977). • FF2: “A Parameterization of the properties of Quark Jets”, R. D. Field and R. P. Feynman, Nucl. Phys. B136, 1-76 (1978). • F1: “Can Existing High Transverse Momentum Hadron Experiments be Interpreted by Contemporary Quantum Chromodynamics Ideas?”, R. D. Field, Phys. Rev. Letters 40, 997-1000 (1978). • FFF2: “A Quantum Chromodynamic Approach for the Large Transverse Momentum Production of Particles and Jets”, R. P. Feynman, R. D. Field and G. C. Fox, Phys. Rev. D18, 3320-3343 (1978). The Naïve Parton Model “Feynman-Field Jet Model” The Naïve Parton Model The Naïve Parton Model QCD Improved Parton Model QCD Improved Parton Model QCD Improved Parton Model • FW1: “A QCD Model for e+e- Annihilation”, R. D. Field and S. Wolfram, Nucl. Phys. B213, 65-84 (1983). My 1st graduate student! Rick Field – Florida

  5. ICHEP 1978 Tokyo Dynamics of High Energy Reactions • The Effective Strong Interaction Coupling Constant, as(Q2), and the Mass Scale L. Rick Field California Institute of Technology (Plenary talk presented at the XIX International Conference on High Energy Physics, Tokyo, Japan) The QCD Parton Model Approach - Outline of Talk R. D. Field ICHEP78 • Quark and Gluon Distributions within Hadrons: Scale Breaking. • Analysis of ep and mp Data. • Analysis of F2 and xF3 in Neutrino Processes. • Large pT Production of Mesons and Jets in pp Collisions. • Scale Breaking Effects: Eds/d3p. • Correlations – Evidence for Gluons. • The Jet Cross Section.. • Muon-Pair Production in pp Collisions. • QCD Factorization – “Constant” Pieces. • Large pT Muon-Pair Production. • “Scaling” in pp →m+m- +X. • A Look to the Future. • pp → p0 +X at W = 500 GeV. • Large pT Charm Production. • gg→ Jet + Jet and e+e-→ e+e-+Jet+Jet. • Three Jets: e+e-→ q+qbar+Jet and pp→Jet+Jet+Jet+X.. • Quark and Gluon Fragmentation Functions: Scale Breaking. • Gluon Jets. Rick Field – Florida

  6. Boulder 1979 • The NATO Advanced Institute on Quantum Flavordynamics, Quantum Chromodynamics, and Unified Theories, held at the University of Colorado, Boulder, Colorado, July 9 – 27, 1979. (NATO Advanced Institute Series B: Physics, Volume 24, Plenum Press, 1980) Lecturers G. Altarelli A. J. Buras C. De Tar S. Ellis R. D. Field D. Gross C. H. Llewellyn Smith J. Wess Rick Field Boulder 1979 Jimmie Field Boulder 1979 Rick Field – Florida

  7. My QCD Book • Applications of Perturbative QCD, Addison-Wesley Publishing Company, The Advanced Book Program, Frontiers in Physics (Volume No. 77), 1989. http://www.phys.ufl.edu/~rfield/cdf/RDF_QCD_Book.pdf Thanks to the DESY Theory Group, there is a scanned version on-line! Out of Print I am sorry for the many typing mistakes in the book! And in these lectures? Rick Field – Florida

  8. TheSimple Structure of Our Universe • Elementary Particle:Indivisible piece of matter without internal structure and without detectable size or shape. Mass and charge located inside sphere of radius zero! • Four Known 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: Quarks have fractional electric charge.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 Rick Field – Florida

  9. Labeling the ParticlesQuantum Numbers • Elementary particles and hadrons are labeled by their quantum numbers. These labels characterize the properties of the particles. • 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 referred to a scalars, 0- are pseudo-scalars, 1- are vectors, 1+ are pseudo-vectors, 2+ are tensors, etc. Rick Field – Florida

  10. Leptons • Leptons are spin ½+ fermions with baryon number B = 0 and with Qem = Qweak + QU1. Generation SU(2) Weak Lepton Doublets Rick Field – Florida

  11. Anti-Leptons • Leptons are spin ½+ fermions with baryon number B = 0 and with Qem = Qweak + QU1. Generation • For every particle there is a corresponding antiparticle with equal mass and opposite electric charge. SU(2) Weak Anti-Lepton Doublets Rick Field – Florida

  12. SU(3)-Flavor JP = ½+ quarks, B = 1/3, Y = B + S, Qem = Y/2 + Iz JP = ½- anti-quarks, B = -1/3, Y = B + S, Qem = Y/2 + Iz Rick Field – Florida

  13. SU(3)-Flavor 3 × 3 = 8 + 1 Rick Field – Florida

  14. Pseudo-Scalar Meson Nonet JP = 0- bosons, B = 0, Ch = 0, Bo = 0, To = 0, Y = B + S +Ch +Bo + To, Qem = Y/2 + Iz 3 × 3 = 8 + 1 Rick Field – Florida

  15. Hadrons: ½+ Baryon Octet JP = ½+ fermions, B = 1, Ch = 0, Bo = 0, To = 0, Y = B + S +Ch +Bo + To, Qem = Y/2 + Iz 3 × 3 × 3 = 10 + 8 + 8 + 1 Rick Field – Florida

  16. 3/2+ Baryon Decuplet JP = 3/2+ fermions, B = 1, Ch = 0, Bo = 0, To = 0, Y = B + S +Ch +Bo + To, Qem = Y/2 + Iz 3 × 3 × 3 = 10 + 8 + 8 + 1 Yikes! Three identical u-quark fermions in the same state! Three identical u-quark fermions in the same state. Violates Fermi-Dirac statistics. Not possible! Rick Field – Florida

  17. SU(2)-Color JP = ½+ quarks, B = 1/3, Y = B + S, Qem = Y/2 + Iz Baryons: 2 × 2 × 2 = 4 + 2 + 2 Mesons: 2 × 2 = 3 + 1 Yikes! Cannot make color singlet baryons. Let’s try SU(3)-color. Color Singlet Mesons! Rick Field – Florida

  18. SU(3)-Color JP = ½+ quarks, B = 1/3, Y = B + S, Qem = Y/2 + Iz Baryons: 3 × 3 × 3 = 10 + 8 + 8 + 1 Mesons: 3 × 3 = 8 + 1 Color Singlet Baryons! Color Singlet Mesons! The Weak Interactions are not diagonal in quark flavor! SU(2) Weak Quark Doublets CKM Matrix Rick Field – Florida

  19. SU(3)-Color JP = ½- anti-quarks, B = -1/3, Y = B + S, Qem = Y/2 + Iz SU(2) Weak QuarkAnti-Quark Doublets Rick Field – Florida

  20. Vector Bosons JP = 1- Vector Mesons(B = 0, Ch = 0, Bo = 0, To = 0, Le = 0, Lm = 0, Lt = 0) Qem = Qweak + QU1 Gluons: 3 × 3 = 8 + 1 Color Octet Gluons! Rick Field – Florida

  21. The Periodic Table Rick Field – Florida

  22. Classifying the Forces • Notation implies the transitions • U(1) of Electromagnitism (1 × 1 transition matrix): and • SU(2) Weak (2 × 2 transition matrix): • SU(3) Color (3 × 3 transition matrix) q = u, d, s, c, b, t Rick Field – Florida

  23. ElectroWeak Force Unification of Weak and Electromagnetic Forces • U(1) Transisitions: • SU(2) Transisitions: • SU(2) x U(1) ElectroWeak (contains both electromagnetic and weak force): Rick Field – Florida

  24. Electromagnetic Interactions Photons Couple to Electric Charge • Charged Lepton or Quark - Photon Vertex: • Photons do not carry electric charge and hence do not directly couple to each other. • However photons can interact with each other indirectly. Rick Field – Florida

  25. Weak Interactions: SU(2)xU(1) W & Z Couple to Weak Charge • 1st Generation “Charged Current” Interactions (flavor changing) • 1st Generation “Neutral Current” Interactions • Self-Coupling and Electromagnetic Interactions • 4-Point Couplings Rick Field – Florida

  26. Flavor Mixing: Generation Hopping The Weak Interactions are not diagonal in quark flavor: CKM Matrix • Transitions within the same generation are of order one. • 1st – 2nd generation transitions are “1st order” forbidden and are of order l ~ 0.23. • 2nd – 3rd generation transitions are “2nd order” forbidden and are of order l2 ~ 0.05. • 1st – 3rd generation transitions are “3rd order” forbidden and are of order l3 ~ 0.001. Rick Field – Florida

  27. Strong Intractions - QCD Gluons Couple to Color Charge • Quark (q = u, d, s, b, t) Color Changing and Non-Color Changing Interactions Gluons carry color and couple to each other! • Gluon Self-Coupling • 4-Point Coupling Rick Field – Florida

  28. The Naïve Parton Model Electron-Positron Annihilations: Virtual Photon Born Term = Quarks interacting with photons (electromagnetic interactions) Inelastic Electron Proton Scattering: Born Term = Rick Field – Florida

  29. The Naïve Parton Model Quarks interacting with W & Z (weak interactions) Inelastic Neutrino Proton Scattering: Born Term = Quarks interacting with photons (electromagnetic interactions) Drell-Yan Muon-Pair Production: Born Term = Rick Field – Florida

  30. The Naïve Parton Model Large Transverse Meson Production in Hadron-Hadron Collisions Quark-Quark Elastic Scattering Born Term = Quarks interacting with quarks (strong interactions) What do I do now?? Field-Feynman Black-Box Model (see my lecture tonight) Rick Field – Florida

  31. Electron-Proton Elastic Scattering: Form Factors Electron-Proton Elastic Scattering: Compare elastic electron-proton scattering with elastic electron-muon scattering (point interaction), 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 ½) has two form factors the magnetic form factor and the electric form factor, but I will ignore this complication.) Experimental Results: Electron 4-momentum transfer: 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). Beginning of the Parton Model! Rick Field – Florida

  32. Naïve Parton ModelElectron-Positron Annihilations Color Factor Count the Number of Quark Flavors:Measure the ratio Rand verify that there are indeed three colors of quarks. 3 Flavors Rick Field – Florida

  33. Naïve Parton ModelElectron-Positron Annihilations Count the Number of Quark Flavors:Measure the ratio Rand verify that there are indeed three colors of quarks. The data are from ORSAY, FEASCATI, NOVOSIBIRSK, SLAC-LBL, DASP, CLEO, DHHM, CELLO, JADE, MARK J, PLUTO, and TASSO. Compiled by B. Wiik (1978). 5 Flavors: u d s c b Rick Field – Florida

  34. Naïve Parton ModelElectron-Positron Annihilations Quark Fragmentation Functions:Measure the probability of finding a hadron of type h carrying the fraction z of the parent quarks momentum. Very unlikely that a parton will give all its momentum to a single hadron! Observed by the JADE detector at PETRA at ECM = 30 GeV (1978). z Rick Field – Florida

  35. Lorentz 4-Vectors Notation & Metric: A + B → C +D: Mandelstam Invariants Rick Field – Florida

  36. Inelastic Electron-Proton Scattering Inelastic Electron-Proton Scattering (lab frame): M = proton mass me = electron mass = 0 Electron energy loss: Electron 4-momentum transfer: Longitudinal & Transverse Structure Functions Ratio of the longitudinal and transverse virtual photon proton total cross section. Rick Field – Florida

  37. Parton Model: DIS In the early days of the Parton Model we did not know the partons were quarks, anti-quarks, and gluons! We learned this from DIS and e+e- experiments! Parton Model: Virtual photon with 4-momentum q interacting with a parton of type i with mass m and electric charge ei carrying fraction x of the proton’s 4-momentum P. (M = proton mass) Provided Q2is large! Deep Inelastic Scattering (DIS) A fast moving proton is a collection of partons(constituents of the proton) each carrying a certain fraction x = x of the proton momentum, P. is thenumber of partons of type i within a fast moving hadron of type A with fraction of momentum x (pi = xP) between x and x + dx. Scaling: Predict that the DIS structure functions are not a function of both n and Q2, but are simply a function of the parton scaling variable, x. Also predict: Momentum Sum Rule:The sum of the momentum of all the constituents must equal one. Rick Field – Florida

  38. Naïve Parton Model: DIS A fast moving proton is a collection of partons(quarks, anti-quarks, and gluons) each carrying a certain fraction x of the proton momentum, P. Inelastic Electron-Proton Scattering: Net Number of Quarks:The net number of u quarks in a proton is 2 and the net number of d quarks is 1. 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: The remaining momentum must be carried by electrically neutral partons (i.e.gluons). Rick Field – Florida

  39. Naïve Parton Model: DIS 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. Parton Distribution Functions (PDF’s)! Inelastic Electron-Proton Scattering: Rick Field 1976 Inelastic Neutrino-Proton Scattering: Rick Field – Florida

  40. QCD Improved Parton Model Electron-Positron Annihilations Born Amplitude = Born Term = “Born” Virtual Photon Include Leading Order QCD Corrections (Order as) “Gluon Radiation” Virtual Corrections Rick Field – Florida

  41. QCD Improved Parton Model Inelastic Electron Proton Scattering Born Amplitude = Born Term = “Born” Include Leading Order QCD Corrections (Order as) “Gluon Radiation” “Photon-Gluon Interactions” Virtual Corrections Rick Field – Florida

  42. QED Effective Coupling Renormalization Vacuum Polarization Bubble Elastic Electron-Electron Scattering 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 correction to the virtual photon propagator diverges like log(l), where l is some ultraviolet cutoff that can be arbitrarily large. • Leading Order Bubble Contribution (bare coupling) where q is the 4-momentum of the virtual (space-like) photon. • Effective Coupling: It is convenient to define an effective coupling that includes the vacuum polarization bubbles as follows: Rick Field – Florida

  43. QED Effective Coupling Renormalization • Renormalization We see that the effective QED coupling is given by where BQED(Q2) is infinite (diverges as the cutoff l becomes large) and a0 is the unmeasurable bare coupling. We must express all experimental observables in terms of other experimental observables and so we define the fine structure constantaQED = e2/4p to be the effective charge at Q2 = 0. This is called the Thompson limit and corresponds a large distance limit. Now writing the effective coupling in terms of aQED gives Finite and independent of cut-off l The QED effective coupling is equal to 1/137 at small Q2 = 0 and then increases as Q2 increases! or Rick Field – Florida

  44. QCD Effective Coupling: Asymptotic Freedom Elastic Quark-Quark Scattering: In QCD there are two types of bubbles, quark loops and gluon loops and the leading order bubble contribution is, where l is the ultraviolet cutoff and a0 = g02/4p is the bare strong coupling and The 11 comes from the gluon loop bubbles and the –2nf/3 comes from the quark loop bubbles (nf is the number of quark flavors). 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 = m2 to define the coupling and express all observables in terms of the coupling at this point (called the renormalization point). . Finite and independent of cut-off l which approaches zero as Q2 becomes large (asymptotic freedom). Rick Field – Florida

  45. QCD Effective Coupling:The l 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 m1 and define as to be the effective coupling at that point: However, it does not matter which point m one chooses (physical observables are independent of the choice of m). If instead one chooses the point m2 then the two couplings are related (to lowest order) by which means that there are not two parameters as(m2) and m but rather one scale L that is independent of the point m. In terms of L the effective QCD coupling is given by Current experiments indicate that L is around 200 MeV. Rick Field – Florida

  46. 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. This causes a breaking of scaling and the quark (and gluon) distributions become a function of the scale, Q2, of the probing virtual photon: 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 D is and hence more and more hard gluons are emitted as Q2 increases producing a logarithmic scale breaking. However, given one can compute (via QCD perturbation theory) provided Q02 and Q2are both large (Q2 > Q02). Rick Field – Florida

  47. Q2 Evolution: QCD Non-Singlet Distribution: Singlet Distribution: Rick Field – Florida

  48. QCD Splitting Functions Altarelli-Parisi “splitting functions”! Probability that after radiating a gluon the quark will have momentum fraction z of it’s initial momentum. Pq→qg(z) G. Altarelli and G. Parisi, Nucl. Phys. B126, 278 (1977). Pq→gq(z) Probability that a radiating gluon will have momentum fraction z of the initial quark’s momentum. Probability that when a gluon splits into a quark-antiquark pair that one of the quark has momentum fraction z of the initial gluon’s momentum. Pg→gg(z) Pg→gg(z) Probability that when a gluon splits into two gluons that one of the gluons has momentum fraction z of the initial gluon’s momentum. Rick Field – Florida

  49. R. Field ICHEP78 • (a) Illustrates that the change in the non-singlet quark distribution with t is due to the radiation of a gluon with probability Pq→qg(z) of finding a quark with momentum fraction z “within” a quark. (b) Illustrates that the change in the quark distribution with t is due to the Bremstrahlung radiation of a gluon with probability, Pq→qg(z), and the production of quark-antiquark pairs from a gluon, Pg→qq(z). (c) Illustrates that the change in the gluon distribution with t is due to the Bremstrahlung radiation of a gluon from a quark with probability, Pq→gq(z), and from a gluon, Pg→gg(z). Rick Field – Florida

  50. Convolution Method Convolution: Renormalization Group Improved PDF’s! 2-Component Spinor Rick Field 1978 2 × 2 Matrix Rick Field – Florida

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