1. Niels Tuning (1) “Elementary Particles” Lecture 5 Niels Tuning Harry van der Graaf

2. Thanks Ik ben schatplichtig aan: –Dr. Ivo van Vulpen (UvA) –Prof. dr. ir. Bob van Eijk (UT) –Prof. dr. Marcel Merk (VU) Niels Tuning (2)

3. Homework

4. Exercises Lecture 4: Niels Tuning (4) Adjoint spinor: +

5. Exercises Lecture 4: Niels Tuning (5) +

6. Exercises Lecture 4: Niels Tuning (6)

7. Exercises Lecture 4: Niels Tuning (7)

8. Plan 1)Intro: Standard Model & Relativity 2)Basis 1)Atom model, strong and weak force 2)Scattering theory 3)Hadrons 1)Isospin, strangeness 2)Quark model, GIM 4)Standard Model 1)QED 2)Parity, neutrinos, weak inteaction 3)QCD 5)e + e - and DIS 6)Higgs and CKM Niels Tuning (8) 1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 17 Feb 3 Mar 17 Mar 21 Apr 19 May 10 Feb

9. Summary Lects. 1-4

10. Theory of relativity –Lorentz transformations (“boost”) –Calculate energy in collissions 4-vector calculus High energies needed to make (new) particles Lecture 1: Relativity Niels Tuning (10)

11. 4-vectors: –Space-time x  –Energie-momentum p  –4-potential A  –Derivative ∂  –Covariant derivative D  –Gamma matrices   Tensors –Metric g  –Electromagnetic tensor F  Lecture 1: 4-vector examples Niels Tuning (11)

12. Schrödinger equation –Time-dependence of wave function Klein-Gordon equation –Relativistic equation of motion of scalar particles  Dirac equation –Relativistically correct, and linear –Equation of motion for spin-1/2 particles –Described by 4-component spinors –Prediction of anti-matter Lecture 2: Quantum Mechanics & Scattering Niels Tuning (12)

13. Scattering Theory –(Relative) probability for certain process to happen –Cross section Fermi’s Golden Rule –Decay: “decay width” Γ –Scattering: “cross section” σ Lecture 2: Quantum Mechanics & Scattering Niels Tuning (13) Classic Scattering amplitude Scattering amplitude in Quantum Field Theory a → b + c a + b → c + d

14. “Partice Zoo” not elegant Hadrons consist of quarks  Observed symmetries –Same mass of hadrons:isospin –Slow decay of K, Λ :strangeness –Fermi-Dirac statistics Δ ++, Ω :color Combining/decaying particles with (iso)spin –Clebsch-Gordan coefficients Lecture 3: Quarkmodel & Isospin Niels Tuning (14)

15. Arbitrary “gauge”  Physics invariant  Introduce “gauge” fields in derivative  Interactions! QED Weak interactions QCD Lecture 4: Gauge symmetry and Interactions Niels Tuning (15) 1 photon 3 weak bosons 8 gluons

16. 1)Reminder: Gauge invariance, and the Lagrangian  Electro-magnetic interactions: QEDElectric charge  Weak interactions: “QFT”Weak isospin/Flavour  Strong interactions: QCDColour 2)e + e - scattering  e + e - →μ + μ -  e + e - →cc Discovery of charm and colour (quantity “R”)  e + e - →qq g Discovery of the gluon  e + e - →Z 3 neutrino’s  e + e - → WW 3)Deep Inelastic Scattering (DIS) (lepton-proton scattering)  Quarkmodel: do quarks exist??  Sub-structure  Bjorken-x, sum rules  Scaling (violations)  ‘Parton density functions’ (pdf) and ‘structure functions’ Outline for today: Niels Tuning (16)

17. QED & QCD

18. spin-0 particles (Klein-Gordon) spin-1/2 fermions (Dirac) Photons Lagrangian  Equation of motion Niels Tuning (18) Klein-Gordon equation Dirac equation Maxwell equations

19. 1)Assume symmetry ψ → ψ’= ψe iα(x) 2)Keep Eqs valid  Covariant derivative Gauge Invariance Niels Tuning (19) 1)Arbitrary gauge 2)Keep Eqs valid  This implies: ψ → ψ’= ψe iα We started globally: Then we went local:

20. Quantum Electro Dynamics - QED Niels Tuning (20) Fermion ψ with mass m Interaction with coupling q Photon field A μ m qγμqγμ

21. Weak Interaction

22. We had: How about? More gauge transformations Niels Tuning (22)

23. We had: How about? Why? Historical origin: proton and neutron exhibit isospin symmetry More gauge transformations Niels Tuning (23)

24. We had: How about? Introduce new covariant derivative: B μ is now 2x2 matrix:  with three gauge fields: More gauge transformations Niels Tuning (24)

25. The three b, are associated to the W +,W - and Z 0 Electro-weak theory Niels Tuning (25)

26.  We measured that left and right are different! Instead of “strong” isospin, switch to “weak” isospin: Formalism the same Electroweak theory Niels Tuning (26) (What is difference between chirality and helicity…?)

27.  We measured that left and right are different! Instead of “strong” isospin, switch to “weak” isospin: Formalism the same Electroweak theory Niels Tuning (27) dLdL g W+W+ uLuL

28. QCD

29. Symmetries Niels Tuning (29) Charge Isospin Color

30. We had: U(1) (QED) Then: SU(2) (Weak) How about: SU(3) (QCD) More gauge transformations Niels Tuning (30) (Why 8…? Group theory: 3x3=8+1 … )

31. We had: U(1) (QED) Then: SU(2) (Weak) How about: SU(3) (QCD) SU(2)  SU(3) Niels Tuning (31)  Gell-Mann matrices: SU(3)-equivalent of Pauli-matrices

32. Symmetries Niels Tuning (32) ChargeU(1) (QED) IsospinSU(2) (Weak) ColorSU(3) (QCD) (Why 8…? Group theory: 3x3=8+1 … )

33. We had: U(1) (QED) Then: SU(2) (Weak) How about: SU(3) (QCD) More gauge transformations Niels Tuning (33) a=1,8: 8 gluons Another covariant derivative: with 8 A μ fields: which transform as: Gluonic field tensor:

34. QCD Lagrangian Niels Tuning (34) Fermion ψ with mass m Interaction with coupling q 8 Gluon fields A μ m Self-interaction qγμqγμ

35. Local SU(3) gauge transformation Introduce 8 A μ a gauge fields Non-“Abelian” theory, Self-interacting gluons –Gluons have (color) charge Different “running” Local U(1) gauge transformation Introduce 1 A μ gauge field “Abelian” theory, No self-interacting photon –Photons do not have (electric) charge Different “running” QED QCD QED QCD Niels Tuning (35) QED and QCD

36. Which symmetries do we impose ? QED: U(1) Y  1 degree of freedom: γ Weak Force: SU(2) L  3 degrees of freedom: W +, W - en Z 0 Strong Force: SU(3) C  8 degrees of freedom: 8 gluons All spin-1 Rotations in color space Rotations in weak isospin space Rotations in hypercharge space For example SU(2) L : 2x2 complex matrices (det=1)  3 basis-rotations  3 vector fields

37. Standard Model now (almost) complete! Niels Tuning (37)

38. Standard Model Niels Tuning (38) Fermion fields ψ Gauge fields A μ Interactions through D μ

39. Niels Tuning (39) Prof.dr. J. Ellis Standard Model

40. Niels Tuning (40) Todo-list: e + e - scattering –QED at work (LEP): R, neutrinos e + p scattering –QCD at work (HERA): DIS, structure functions, scaling No masses for W, Z –(LHC/ATLAS) Higgs mechanism, Yukawa couplings Consequences of three families –(LHC/LHCb) CKM-mechanism, CP violation

41. Break? Niels Tuning (41)

42. Consider e + e - →e + e - scattering: More possibilities! –“Higher order” diagrams –Each coupling has strength 1/137  Perturbation series “Running” Coupling Constant (QED) Niels Tuning (42) α~q 2 q q

43. Consider e + e - →e + e - scattering: More possibilities! –“Higher order” diagrams –Each coupling has strength 1/137  Perturbation series Effectively: “Running” Coupling Constant (QED) Niels Tuning (43) α~q 2 q q

44. Coupling depends on the scale! –α(0)=1/137 –α(M 2 Z )=1/128 Effectively: “Running” Coupling Constant (QED) Niels Tuning (44)

45. Do you need all fermions in the loop??  Yes: “Running” Coupling Constant Niels Tuning (45)

46. Running in QCD Also gluon loops  It turns out, the gluon has opposite effect! “Running” Coupling Constant Niels Tuning (46)

47. Running in QCD NB: if α s >1 perturbation theory breaks down… “Running” Coupling Constant Niels Tuning (47)

48. Running in QCD High energy: coupling small Asymptotic Freedom Niels Tuning (48) Asymptotic freedom

49. Running in QCD Low energy: coupling big “Confinement” Niels Tuning (49) Confinement barrier

50. Unification? Niels Tuning (50) A reason to believe that there are more particles?

51. Feynman diagrams

52. Fermi’s Golden Rule Niels Tuning (52) Fermi's “golden rule” gives: The transition probability to go from initial state i to final state f 1)Density of final states Integral of final states that can be reached “Phase space” Φ 2)Matrix element Scattering amplitude M 3)Flux factor “Number of incident particles per unit area”

53. Process: A+B → C+D (Explicit Example: ) Niels Tuning (53) 3)Flux factor “Number of incident particles per unit area” Decay: A → C+D 2)Density of final states “How many quantum states can be put in volume V?” “Phase space” Φ

54. How to calculate M ? Example QM: Example spin-1/2 scattering: Feynman Rules Niels Tuning (54)

55. How to calculate M ? Example QM: Example spin-1/2 scattering:  Remember: M is “just” a complex number Feynman Rules Niels Tuning (55)

56. Feynman Rules Niels Tuning (56) From (p.149) Halzen & Martin

57. Feynman rules: Example Niels Tuning (57) Process: e - μ - →μ - e -

58. Feynman rules: Example Niels Tuning (58) Process: e - μ - →μ - e - Remember the 4-component spinors in Dirac-space:

59. e + e - Scattering

60. e + e - →μ + μ - e + e - →cc –Confirmation of “color” –Discovery of charm e + e - →qq g –Discovery of the gluon e + e - →tt –Hunt for the top e + e - →Z –3 neutrino’s e + e - →WW Shopping list Niels Tuning (60)

61. e + e - colliders Niels Tuning (61) AcceleratorLab s (GeV) Year SPEARSLAC2 – 81972 - 1990 DORIS I, IIDESY101974 - 1993 CESR(-c)Cornell3.5 - 121979 - 2008 PEPSLAC 20 - 291980 - 1990 PETRADESY12 – 471978 - 1988 TRISTANKEK50 – 601987 - 1995 SLCSLAC901988 - 1998 LEP I, IICERN90 – 2081989 - 2000

62. Examples of e + e - processes time

63. Examples of e + e - processes

64. Rutherford scattering (scattering off static point charge) Mott scattering (now with high energy, taking into account recoil of target and magnetic moment: spin ½) spin-½ spin-½ scattering (average over incoming spin, sum over outgoing spin) Scattering Niels Tuning (64)

65. Point cross section At √ s=10 GeV: σ(e + e - →μ + μ - ) ~ 0.9 nb e+e-→μ+μ-e+e-→μ+μ- Niels Tuning (65)

66. e + e - →hadrons Point cross section At √ s=10 GeV: σ(e + e - →q + q - ) ~ 3.6 nb

67. e+e+ e-e- γ f f - e + e - →hadrons Compare cross section of σ(e + e - →q + q - ) to σ(e + e - →μ + μ - )  Photon couples to fermion charge!  Color of quarks?  Inspect Ratio R:

68. muons quarks Prediction R: m e+e- < 2m c Without color: R = 2/3 With 3 colors: R = 2

69. muons quarks Without color: R = 10/9 With 3 colors: R = 30/9 Prediction R: m e+e- > 2m c

70. m e+e- (GeV) 1 (3) colors 1.1(3.3) 0.7 (2) prediction 1 0 No color (udsc) No color (uds) with color(udsc) data With color (uds)

71. e+e+ e-e- γ f f - e + e - →hadrons  So, quarks have color!  How about spin?

72. Sam ‘J’ Ting. Burt ‘  ’ Richter Discovery of charm (J/  November 1976: ‘November revolution’ New meson discovered (J/ ψ ) with mass 3.16 GeV Quark model: J/ ψ consists of pair of c-quarks e + e - →cc

73. Sam ‘J’ Ting. Burt ‘  ’ Richter Discovery of charm (J/  November 1976: ‘November revolution’ New meson discovered (J/ ψ ) with mass 3.16 GeV Quark model: J/ ψ consists of pair of c-quarks e + e - →cc Because of the nearly simultaneous discovery, the J/ψ is the only elementary particle to have a two-letter name.  Richter named it "SP", after the SPEAR accelerator used at SLAC; however, none of his coworkers liked that name. After consulting with Greek-born Leo Resvanis to see which Greek letters were still available, and rejecting "iota" because its name implies insignificance, Richter chose "psi" – a name which, as Gerson Goldhaber pointed out, contains the original name "SP", but in reverse order. [2] Coincidentally, later spark chamber pictures often resembled the psi shape.  Ting assigned the name "J" to it, which is one letter removed from "K", the name of the already-known strange meson; possibly by coincidence, "J" strongly resembles the Chinese character for Ting's name ( 丁 ). J is also the first letter of Ting's oldest daughter's name, Jeanne.

74. 1970:  Prediction of charm quark  Observation K 0 →μμ Lesson: Loop diagrams are sensitive to heavy particles Intermezzo: “indirect discoveries” … … … GIM, Phys.Rev.D2,1285,1970 s d μ μ “Loop” diagram:

75. e + e - →qq g Niels Tuning (75) From: arXiv:1008.1869 1979

76. J/ψ c e-e- e+e+ γ e + e - →cc cc

77. b e-e- e+e+ bb γ e + e - →bb ? In modern times: yes! Babar experiment at SLAC (USA) Belle experiment at KEK (Japan) e + e - →Υ(4S) → B 0  B 0 M(Υ(4S)) =10579.4 MeV 2 x M(B 0 ) = 10559.2 MeV (coincidence??)  “B-factories” Y

78. Intermezzo: bottom discovery Niels Tuning (78) Fermilab (Chicago), 400 GeV proton – fixed target –p + (Cu,Pt)  μ + + μ - + anything m(b)~5 GeV –m(bb)~9.5 GeV, so m(b)~5 GeV “background subtracted”:

79. e + e - →tt t e-e- e+e+ γ e + e - cross-section tt 1977: bottom discovered topHow heavy could the top be?? –20 GeV ? –25 GeV ?? –30 GeV ??? –Built Tristan accelerator, with Topaz detector (Japan) –Reached 25.5 GeV in 1986  At minimum of cross section…

80. e + e - →tt t e-e- e+e+ γ e + e - cross-section tt 1977: bottom discovered topHow heavy could the top be?? –20 GeV ? –25 GeV ?? –30 GeV ??? –Built Tristan accelerator, with Topaz detector (Japan) –Reached 25.5 GeV in 1986  At minimum of cross section…

81. ARGUS almost discovered the top quark:  m top > 50 GeV Lesson: Loop diagrams are sensitive to heavy particles Intermezzo: “indirect discoveries” ARGUS Coll, Phys.Lett.B192:245,1987 ? b s s b

82. Z-boson f e-e- e+e+ anti-f Z e + e - →Z (From: PDG)

83. Remember: A  B+C : Total decay rate τ = ħ /Γ A+B  R  C+D: Resonance: e + e - →Z Breit-Wigner E 0 - Γ/2 E 0 E 0 - Γ/2 P max P max /2

84. 3 families ! e + e - →Z Measure total width, with energy scan: “Z-lineshape”  Total width is sum of “partial widths” Measure branching ratios of Z  qq and Z  l + l -  “Invisible width” due to neutrinos

85. e + e - →WW Upgrade of LEP: 90  208 GeV! Enough energy to create WW-pairs  and ZH-pairs?!

86. e + e - →WW (a) (b) (c) (a+c) (a+b+c) Triumph for Standard Model:

87. Time?

88. Plan 1)Intro: Standard Model & Relativity 2)Basis 1)Atom model, strong and weak force 2)Scattering theory 3)Hadrons 1)Isospin, strangeness 2)Quark model, GIM 4)Standard Model 1)QED 2)Parity, neutrinos, weak inteaction 3)QCD 5)e + e - and DIS 6)Higgs and CKM Niels Tuning (88) 1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 17 Feb 3 Mar 17 Mar 21 Apr 19 May 10 Feb

89. Intermezzo: Discovery Z and W

90. Gargamelle experiment Neutrinos on target (12,000 liter freon (CF 3 Br) Discovery neutral current υμυμ υμυμ Z quark (nucleon) quark (hadrons) 1973

91.  Spokesman UA1 experiment  In 1989 Director General CERN  Initiator of Energy Amplifier SPS proton-anti-proton collider √s = 540 GeV Carlo RubbiaSimon van der Meer Correcting signal stochastic cooling Direct observation weak-force carrier

92. Discovery Z-boson “Experimental observation of lepton pairs of invariant mass around 95 GeV/c 2 at the CERN SPS collider” Nederlands tintje M l+l- [GeV/c 2 ] Lepton pair mass (4 events) 3 June 1983

93. 24 februari 1983 Discovery W-boson Prediction: Observation: 2012: “Experimental observation of isolated large transverse energy electrons with associated missing energy at √s=540 GeV”

94. Deep Inelastic Scattering Lepton – proton scattering or: Hitting something big, using something small

95. Quarkmodel: do quarks exist?? Substructure Bjorken-x, sum rules Scaling ‘Parton density functions’ (pdf) and ‘structure functions’ Scaling violations Shopping list Niels Tuning (95)

96. Scattering Niels Tuning (96) Rutherford scattering (scattering off static point charge) e + e - →μ + μ - scattering (s-channel) e - μ + →e - μ + scattering (t-channel)

97. Point cross section e + q→e + q Niels Tuning (97) e+e+ e+e+ qq

98. Easiest: fixed target –ep scattering –μp scattering –νp scattering 1990’s: ep collider DIS experiments Niels Tuning (98)  protons  electrons ExperimentAccelLableptonE lep E had Year SLAC-MITSLACe20fixed1967-1973 GargamelleCERN fixed E80 -SLCSLACfixed CHORUSSPSCERN 10-200fixed1998 CCFRTevatronFermilab 30-360fixed NMCSPSCERN  90-280fixed1986-1989 EMC/SMCSPSCERN  100-190fixed1984-1994 BCDMSSPSCERN  100-280fixed ZEUS, H1HERADESYe27.59201992-2007 NB: Table not complete

99. electron proton beam target detector Robert Hofstadter spin ½, r=10 -15 m spin 0 spin ½, point

100. Sub-structure Niels Tuning (100) Remember Rutherford –Back-scatter of α from nucleus Now: –Back-scatter of e from quarks

101. data voorspelling electron proton beam target detector

102. J.D. Bjorken “scaling hypothesis” (1967): If scattering is caused by pointlike constituents structure functions must be independent of Q 2  Would you expect a Q 2 dependence? R. Feynmans “parton model” (1969): Proton consists of ‘constituents’ “Physicists were reluctant to identify these objects with quarks at the time, instead calling them "partons" – a term coined by Richard Feynman.” Scaling Niels Tuning (102)

103. Proton valence quarks sea quarks QCD: deep in the proton

104. Proton valence quarks sea quarks QCD: deep in the proton Two important variables: Q 2 : 4-mom. transfer, scale x: fractional momentum of quark

105. eq scattering: ep scattering: Deep Inelastic Scattering Niels Tuning (105) (From: PhD thesis N.Tuning) Form factor

106. ep scattering: F 2 (x): proton structure function q(x): parton density function Deep Inelastic Scattering Niels Tuning (106)

107. ep scattering: F 2 (x): proton structure function q(x): parton density function  But… the proton had 3 quarks?!  Sum rules: Parton Densities Niels Tuning (107)

108. Proton: x What is ‘momentum fraction’ distribution of quarks?? Quarks:  “Valence”  “Sea” (From: Halzen & Martin)

109. Proton: x What is ‘momentum fraction’ distribution of quarks?? Quarks:  “Valence”  “Sea”  Dynamic, QCD ! (From: Halzen & Martin)

110. Proton: x (From: Halzen & Martin) (From: PhD thesis N.Tuning) What is ‘momentum fraction’ distribution of quarks?? Quarks:  “Valence”  “Sea”  Dynamic, QCD ! x=1/3

111. Proton: Q 2 The “deeper” one looks into the proton, the more quarks and gluons

112. Proton: x, Q 2 (From: PhD thesis N.Tuning)

113. Proton: x, Q 2 (From: PhD thesis N.Tuning) The “deeper” one looks into the proton, the more quarks and gluons “QCD evolution” Describes quark-gluon splitting  DGLAP evolution eqs:

114. J.D. Bjorken “scaling hypothesis” (1967): If scattering is caused by pointlike constituents structure functions must be independent of Q 2 Would you expect a Q 2 dependence?  Yes, due to QCD, ie. quark/gluon splitting !  Matured in mid ‘70s  The proton is “dynamic” !  Measurement of F 2 (x,Q 2 ) very accurate test of QCD Scaling violations Niels Tuning (114)

115. Scaling violations Niels Tuning (115)  Measurement of F 2 (x,Q 2 ) very accurate test of QCD

116. Proton Structure 45  The deeper you look, the more low-x quarks

117. Proton Structure 45  The deeper you look, the more low-x quarks

118. Proton Structure

119. Proton Structure: knowledge needed for predictions

120. Plan 1)Intro: Standard Model & Relativity 2)Basis 1)Atom model, strong and weak force 2)Scattering theory 3)Hadrons 1)Isospin, strangeness 2)Quark model, GIM 4)Standard Model 1)QED 2)Parity, neutrinos, weak inteaction 3)QCD 5)e + e - and DIS 6)Higgs and CKM Niels Tuning (120) 1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 17 Feb 3 Mar 17 Mar 21 Apr 19 May 10 Feb