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“Elementary Particles” Lecture 1

“Elementary Particles” Lecture 1. Niels Tuning Harry van der Graaf. Thanks. Ik ben schatplichtig aan: Dr. Ivo van Vulpen (UvA) Prof.dr.ing. Jo van den Brand (VU) Prof.dr.ir. Bob van Eijk (UT). Plan. 11 Feb. Intro: Relativity and accelerators Basis Atom model, strong and weak force

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“Elementary Particles” Lecture 1

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

  2. Thanks • Ik ben schatplichtig aan: • Dr. Ivo van Vulpen (UvA) • Prof.dr.ing. Jo van den Brand (VU) • Prof.dr.ir. Bob van Eijk (UT) Niels Tuning (2)

  3. Plan 11 Feb • Intro: Relativity and accelerators • Basis • Atom model, strong and weak force • Scattering theory • Hadrons • Isospin, strangeness • Quark model, GIM • Standard Model • QED • Parity, neutrinos, weak inteaction • QCD • e+e- and DIS • Higgs and CKM 1900-1940 18 Feb 1945-1965 4 Mar 1965-1975 18 Mar 1975-2000 22 Apr 2000-2013 13 May Niels Tuning (3)

  4. Books • M. Thomson “Modern Particle Physics” (2013, 49 EUR) • D. Griffiths “Introduction to Elementary Particles” (2008, 68 EUR) • C. Tully “Elementary Particle Physics in a Nutshell” (2011, 65 EUR) • F. Halzen & A.D.Martin “Quarks and Leptons” (1984, 68 EUR) Niels Tuning (4)

  5. Outline of today • Introduction • Why particle physics? • Why high energy? • How to create high energy? • How to calculate with high energ ies? • Lorentz Transformation • Invariants • Colliding particles Niels Tuning (5)

  6. Why high energy? particles

  7. Particle Physics Study nature at small distances < 10-15 m 10-15 m atom nucleau Quantum mechanics describes nature at distances 10-18 m (Compare: 10+18 m = 100 lightyear)

  8. Elementary particles • Questions that are asked since 2000 years • What are the building blocks of matter ? • What forces act on matter ? 1905 1864 1687 400 v.Chr. Demokritos atom Newton forces Maxwell electromagnetism Einstein a lot …

  9. How to make matter ? Albert Einstein: E=mc2 materie + anti matter = light (and vice versa) e+ e- e+ e-

  10. I. Open questions: “Anti-matter” Where did it go ? No anti-matter with satellites No anti-matter galaxies

  11. II. Open questions: “Dark Matter” Temperature fluctuations Rotation curves Gravitational lensing What is Dark matter?

  12. Open questions Higgs?? (what makes particles heavy) Anti-matter?? (where did it go) Dark matter?? (what clustered the galaxies)

  13. Astronomy Particle physics Fundamental (curiosity driven) research Waar is de Anti-materie heen?

  14. What energy is needed? 10-15 m atom nucleus How to make energies around 100.000.000 eV or more ? Energy of 1 e- that passes a potential difference of 1 V: 1 eV Energy of maas of 1 proton: m = E/c2: 1 GeV

  15. How do you create enough energy? Accelerators

  16. Cockcroft-Walton Bart Hommels Cockcroft Walton Cavendish lab Cambridge Operation principle 100 V 200 V 400 V 1932: 800 kV 0.8 MeV: energy threshold to split atoms Li + p  He + something 1951: Nobelprize

  17. Van de Graaff High voltage elctro static generator Robert van de Graaff 1) Gas ionizes (ΔV) Harry van der Graaf 2) Moving belt transports charge

  18. Van de Graaff Robert van de Graaff Harry van der Graaf 1929: 80,000 volt1931: 1,000,000 volt 1933: 7,000,000 volt Nowadays: Oak Ridge 25 MeV Vivitron 35 MeV

  19. Van de Graaff + + + 2) Tandem mode + + H- p 1) Single acceleration electronen strippers

  20. Cyclotron Ernest “atom smasher” Lawrence Nobelprijs 1939 First cyclotron 1930

  21. Cyclotrons in real life First Largest TRIUMF Dee Dee 1931: r = 12 cm  1 MeV protons 1974: B = 0.46 [T], r = 9 [m]  520 MeV protons

  22. Synchrotron In a synchrotron, particles move in fixed orbit M. Oliphant versnellen afbuigen Accelerate: higher E  higher p r constant: also higher B • Known synchrotrons: • Bevatron • Tevatron (Fermilab) collider • LEP (CERN) collider • LHC (CERN) collider

  23. Linac (principle) Hollow tube (no field) + + ~ - - Equal frequency, larger velocity  (space between) tubes increasingly larger Linac typically first step in acceleration chain Typical: ~50m, ~100 MeV

  24. Linac’s & traveling wave guide Big Linac’s SLAC: Stanford Linear Accelerator Center (San Francisco) 3.2 km long  50 GeV electrons

  25. From bubble chamber to LHC Discoveries made with the help of Accelerators: - 2012: Higgs discovered The Nobel Prize in Physics 2013 Niels Tuning (25)

  26. Search for elementary building blocks

  27. LHC accelerator Geneve

  28. LHC Energy limited by field of 1232 dipole magnets: B= 8.4 T

  29. Klassiek botsen Quantummechanisch botsen proton proton

  30. E = mc2 Create new particles if energy is large enough (and if they exist…)

  31. Calculate with high energies Special relativity

  32. Summary special relativity • Lorentz transformation • Length contraction & Time dilatation • Adding velocities • Relativistic energies • Relativistic kinematics • Collision • Decay Niels Tuning (33)

  33. Lorentz transformation • Speed of light constant • Every (inertial) coordinate system equivalent • Find transformation rules: Galilei: Lorentz: x=ct becomes x’=ct’ : x’ = γ(x – vt ) t’ = γ(t – vx/c2) • Find  : Niels Tuning (34)

  34. Consequences: Lorentz contraction • Stick with length L0 in system S’ : • moving relative to system S with speed v • Length is factor  smaller in rest frame S: Niels Tuning (35)

  35. Consequences: Time dilatation • Clock is moving in frame S’ with relative speed v • Suppose clock is emitting light pulses • Time interval between pulses in frame S’: Δt’ = t2’-t1’ • Light pulses are emitted from same point: x1’ = x2’ • What sees the observer at rest? • First pulse: t1 =γ(t1 ’+ vx1’/c2) • Second pulse: t2 = γ(t2 ’+ vx2’/c2) • Hence: Δt = t2 - t1 = γ(t1 ’ - t2 ’+ v/c2 (x1’-x2’)) = γ Δt’ • Clock period is seen γlonger for observer at rest Δt = γ Δt’ Niels Tuning (36)

  36. Adding velocities • Time and space transformation: • Hence: Niels Tuning (37)

  37. m mo v Relativistic energies Before: V • Momentum conservation :mv+0=MV • Total mass unchanged: m+mo=M • Hence: m=m0(V/(v-V)) • Relative speed between frames: V • Transformatie: v=2V/(1+V2/c2) • Hence:m = γmoc After: M m m V V Before: After: Mo Niels Tuning (38)

  38. Relativistic energies • Hence:m = γmoc • p=mv  Niels Tuning (39)

  39. Relativistic energies • Momentum: • In rest: p = m0v • Moving mass: p = m0v • Einstein: equivalence between energy and mass • In rest: E = m0c2 • Moving mass: E = m0c2 E = pc2/v  v/c=pc/E • E: • Btw, a Taylor expansion gives classical kinetic energy: Niels Tuning (40)

  40. 4-vectors • Write t, x as 4-vector x: • Nicely symmetric form of Lorentz transformation: “Boost” in x-direction:  Niels Tuning (41)

  41. Invariants • Write t, x as 4-vector x: • Covariant and contravariant 4-vector related through metric g: • Any pair of 4-vectors is invariant as: • Any combination of 4-vectors : Niels Tuning (42)

  42. Intermezzo: Use of 4-vectors The famous Dirac equation: Remember! • μ: Lorentz index • 4x4 γmatrix: Dirac index Less compact notation: • 4-vectors • Use for relativistic kinematics in particle collisions • Use for quantum-field description of matter fields: – – – Niels Tuning (43)

  43. Energy-momentum 4-vector • Example of invariant: rest mass (“invariant mass”) • Lorentz transformation on energy-momentum 4-vector: Niels Tuning (44)

  44. Calculate with 4-vectors: colliding particles • Elastic collission of two particles a and b: a + b  c + d • Take c=1 (“natural units”) • Invariant mass of initial state: • Invariant mass of initial state = invariant mass of final state: = “center-of-mass energy” , s: Niels Tuning (45)

  45. “Fixed target” vs “colliding beams” • Calculate center-of-mass energy for beam of 450 GeV protons: • Fixed target: • Colliding beams: Niels Tuning (46)

  46. Niels Tuning (47)

  47. Last week Future Circular Collider (FCC) ??? • 80-100 km tunnel infrastructure in Geneva area • design driven by pp-collider requirements • with possibility of e+-e- (TLEP) and p-e (VLHeC) • CERN-hosted study performed in international collaboration 16 T  100 TeV in 100 km 20 T  100 TeV in 80 km From: CLIC Workshop – Feb 2014

  48. Plan 11 Feb • Intro: Relativity and accelerators • Basis • Atom model, strong and weak force • Scattering theory • Hadrons • Isospin, strangeness • Quark model, GIM • Standard Model • QED • Parity, neutrinos, weak inteaction • QCD • e+e- and DIS • Higgs and CKM 1900-1940 18 Feb 1945-1965 4 Mar 1965-1975 18 Mar 1975-2000 22 Apr 2000-2013 13 May Niels Tuning (49)

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