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“Elementary Particles” Lecture 3

“Elementary Particles” Lecture 3. Niels Tuning Harry van der Graaf. Thanks. Ik ben schatplichtig aan: Dr. Ivo van Vulpen (UvA) Prof. dr. ir. Bob van Eijk (UT) Prof. dr. M. Merk (VU). Plan. 11 Feb. Intro: Relativity and accelerators Basis Atom model, strong and weak force

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“Elementary Particles” Lecture 3

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  1. “Elementary Particles”Lecture 3 Niels Tuning Harry van der Graaf Niels Tuning (1)

  2. Thanks • Ik ben schatplichtig aan: • Dr. Ivo van Vulpen (UvA) • Prof. dr. ir. Bob van Eijk (UT) • Prof. dr. M. Merk (VU) 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. Exercises Lecture 2: QM and Scattering Niels Tuning (4)

  5. Exercises Lecture 2: QM and Scattering Niels Tuning (5)

  6. Exercises Lecture 2: QM and Scattering Niels Tuning (6)

  7. Exercises Lecture 2: QM and Scattering Niels Tuning (7)

  8. Exercises Lecture 2: QM and Scattering Niels Tuning (8)

  9. Exercises Lecture 2: QM and Scattering Niels Tuning (9)

  10. Exercises Lecture 2: QM and Scattering Niels Tuning (10)

  11. Lecture 1: Accelerators & Relativity • Theory of relativity • Lorentz transformations (“boost”) • Calculate energy in collissions • 4-vector calculus • High energies needed to make (new) particles Niels Tuning (11)

  12. Lecture 2: Quantum Mechanics & Scattering • 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 • Prediction of anti-matter Niels Tuning (12)

  13. Heisenberg How to describe a particle that is “localized” somewhere, but which is also “wave-like” ? • k can be any value: • Fourier decomposition of many frequencies • The more frequencies you add, the more it gets localized • The worse you know p, the better you know x ! Niels Tuning (13)

  14. Lecture 2: Quantum Mechanics & Scattering • Scattering Theory • (Relative) probability for certain process to happen • Cross section • Fermi’s Golden Rule • Decay: “decay width” Γ • Scattering: “cross section” σ Scattering amplitude in Quantum Field Theory Classic a → b + c a + b → c + d Niels Tuning (14)

  15. Outline for today • Resonances • Quarkmodel • Strangeness • Color • Symmetries • Isospin • Adding spin • Clebsch Gordan coefficients Niels Tuning (15)

  16. Resonances

  17. Quantum mechanical description of decay State with energy E0 ( ) and lifetime τ To allow for decay, we need to change the time-dependence: • What is the wavefunction in terms of energy (instead of time) ? • Infinite sum of flat waves, each with own energy • Fourier transformation:

  18. Resonance Pmax Pmax/2 Probability to find particle with energy E: Breit-Wigner E0-Γ/2 E0 E0-Γ/2 • Resonance-structure contains information on: • Mass • Lifetime • Decay possibilities

  19. Rutherford • 3d: incoming particle “sees” surface dσ, and scatters off solid angle dΩ • Calculate: Niels Tuning (19)

  20. Scattering Theory • Describe a stationary state, that satisfies the incoming and outgoing wave V≠0 k2=2mE Niels Tuning (20)

  21. Scattering Theory • Describe a stationary state, that satisfies the incoming and outgoing wave = φin + scattering amplitude x φout • f: “scattering amplitude”: • which we will use for: • 1st approximation: Φ depends on Φ … • How do we solve it?? Not analytic…  Perturbation series! • Scattered wave is described by Fourier transform of the potential Niels Tuning (21)

  22. Scattering Theory Let’s try some potentials • Yukawa: • Coulomb: • Centrifugal Barier: (Pion exchange) (Elastic scattering) (Resonances) Niels Tuning (22)

  23. Well-known resonances e+e- cross-section e+e-→R→ e+e- Z-boson J/ψ

  24. More resonances π+p→R→ π+p • This is how we discover(ed) many particles

  25. The number of ‘elementary’ particles 1947: electron proton neutron muon pion 1936: electron proton neutron muon 1932: electron proton neutron

  26. 1947 • 1932: the positron had been observed to confirm Dirac’s theory, • 1947: and the pion had been identified as Yukawa’s strong force carrier, • So, things seemed under control!? • Ok, the muon was a bit of a mystery… • Rabi: “Who ordered that?”

  27. Quark model

  28. Discovery strange particles Discovery strange particles

  29. Discovery strange particles • Why were these particles called strange? • Large production cross section (10-27 cm2) • Long lifetime (corresponding to process with cross section 10-40 cm2) ? Niels Tuning (29)

  30. Discovery strange particles • Why were these particles called strange? • Large production cross section (10-27 cm2) • Long lifetime (corresponding to process with cross section 10-40 cm2) • Associated production! Niels Tuning (30)

  31. Discovery strange particles • Why were these particles called strange? • Large production cross section (10-27 cm2) • Long lifetime (corresponding to process with cross section 10-40 cm2) • Associated production! Niels Tuning (31)

  32. Discovery strange particles • Why were these particles called strange? • Large production cross section (10-27 cm2) • Long lifetime (corresponding to process with cross section 10-40 cm2) • Associated production! New quantum number: • Strangeness, S • Conserved in the strong interaction, ΔS=0 • Particles with S=+1 and S=-1 simultaneously produced • Not conserved in individual decay, ΔS=1 π π K π p Λ π Niels Tuning (32)

  33. Discovery strange particles • Why were these particles called strange? • Large production cross section (10-27 cm2) • Long lifetime (corresponding to process with cross section 10-40 cm2) Production: π-p→K0Λ0 Decay: K0 → π-π+ Λ0 → π-p • Associated production! New quantum number: • Strangeness, S • Conserved in the strong interaction, ΔS=0 • Particles with S=+1 and S=-1 simultaneously produced • Not conserved in individual decay, ΔS=1 π π K π p Λ π Niels Tuning (33)

  34. Intermezzo: conserved quantities • What is conserved in interactions? • Decays & Scattering • Energy, momentum • Electric charge • Total angular momentum (not just spin) • Strangeness? • Baryon number • Lepton flavour • Colour? • Parity? • CP ? • … Niels Tuning (34)

  35. Kinematics  - + K0S m1 m2 Specific (m1=m2=m): M before after What is the energy of final-state particles?

  36. Kinematics p 0  - m1 m2 M Specific: (m1=m2=m) What if masses of final-state particles differ, m1m2 ? General:

  37. Strange particles Strangeness Strangeness Mesons Baryons What is different…? Corresponding anti-baryons have positive Strangeness

  38. 50’s – 60’s • Will Lamb: • “The finder of a new particle used to be awarded the Nobel Prize, but such a discovery now ought to be punished with a $10,000 fine.” • Enrico Fermi: • “If I could remember the names of all these particles, I'd be a botanist.” • Wolfgang Pauli: • “Had I foreseen that, I would have gone into botany." Niels Tuning (38) Many particles discovered ‘particle zoo’

  39. The number of ‘elementary’ particles “Particle Zoo”

  40. Strange particles The 8 lightest strange baryons: baryon octet Breakthrough in 1961 (Murray Gell-Mann): “The eight-fold way” (Nobel prize 1969) Also works for: Eight lightest mesons - meson octetOther baryons - baryon decuplet

  41. Strange particles The Noble Eightfold Path is one of the principal teachings of the Buddha, who described it as the way leading to the cessation of suffering and the achievement of self-awakening. The 8 lightest strange baryons: baryon octet Breakthrough in 1961 (Murray Gell-Mann): “The eight-fold way” (Nobel prize 1969) Also works for: Eight lightest mesons - meson octetOther baryons - baryon decuplet

  42. Strange particles The 8 lightest strange baryons: baryon octet strangeness: Breakthrough in 1961 (Murray Gell-Mann): “The eight-fold way” (Nobel prize 1969) Also works for: Eight lightest mesons - meson octetOther baryons - baryon decuplet

  43. Discovery of  Not all multiplets complete… 1232 MeV 1385 MeV 1533 MeV Gell-Mann and Zweig predicted the Ω- … and its properties

  44. Discovery of  Not all multiplets complete… 1232 MeV 1385 MeV 1533 MeV 1680 MeV Gell-Mann and Zweig predicted the Ω- … and its properties

  45. Discovery of  Not all multiplets complete… 1232 MeV 1385 MeV 1533 MeV 1680 MeV Gell-Mann and Zweig predicted the Ω- … and its properties

  46. Quark model • Gell-Mann en Zweig (1964): • “All multiplet patterns can be explained if you assume hadrons arecomposite particles built from more elementary constituents: quarks” • First quark model: • 3 types: up, down en strange (and anti-quarks) • Baryons: 3 quarks • Mesons: 2 quarks 26  3+3 mesonen up down strange baryonen p = uud n = udd Λ0 = uds Σ+ = uus Ξ0 = uss

  47. Quark model • Mesons: • Octet • Baryons: • Octet • Decuplet Niels Tuning (47)

  48. The number of ‘elementary’ particles

  49. “Problems” • Are quarks ‘real’ or a mathematical tric? • How can a baryon exist, like Δ++ with (u↑u↑u↑), given the Pauli exclusion principle? Niels Tuning (49)

  50. “Problem” of quark model s s s u u u Intrinsic spin: = symmetric  quarks: = symmetric Intrinsic spin: = symmetric ++ quarks: = symmetric J=3/2, ie. fermion, ie. obey Fermi-Dirac statistics: anti-symmetric wavefunction New quantum number: color! • 3 values: red, green, blue • Only quarks, not the leptons  s s s s

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