Lecture 3: Quarks and Symmetry in Quarks

Transcription

1 Lecture 3: Quarks and Symmetry in Quarks Quarks Cross Section, Fermions & Bosons, Wave Eqs. Symmetry: Rotation, Isospin (I), Parity (P), Charge Conjugate (C), SU(3), Gauge symmetry Conservation Laws: 1

2 1 2

3 Model of Particle Physics Model of elementary particles and fundamental forces Lepton & Quark flavors Anti-particles Relativity and Quantum Theories Gauge Theories Feynman Diagram Symmetries and Conservation Laws Electromagnetic, Strong and Weak interactions Internal symmetry intrinsic nature of the particles rather than their position or motion Local symmetry (= gauge symmetry) invariance of laws of nature under a group of such position-dependent and time-dependent internal symmetry transformation. Why High Energy? Cosmic connection 3

4 PDG 2010 Quarks & Leptons 4

5 2 5

6 Interaction Rate, Cross Section, and Amplitude Consider that beam A with density n a and velocity v i, hitting target B. Flux of the beam A is: Cross Section Interaction rate per a particle B is: flux f where M if is called as amplitude of the interaction with specific initial and final states, r f is energy density dn/de of final states. The amplitude can be calculated with Feynman s rules. A cross-section s (have dimension of m 2 ) In case of particle decay, decay width G and lifetime t are defined as: B 6

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8 Transition matrix element Probability 8

9 (E f E i )/ ev Transition rate Fermi s Golden Rule 9

10 Fermions and Bosons a) Fermions spin ½ ; Bosons spin 0, 1, 2 b) Spin-statistics theorem principal of quantum field theory c) Wave function y y 2 = probability Review of Wave eq. d) Pauli s Exclusion Principle Two or more identical fermions cannot exist in the same quantum state. (No restriction for bosons Bose-Einstein condensation) 10

11 Review of Wave Equations 11

12 Recap: LGT in Particle Physics Construction: Lagrangian is to be invariant under local gauge transformation (LGT) for a given quantum number charge. Quantum Number LGT Phase Factor q (electric) charge 1 U(1) -q l(x)/ħc g w Weak isospin charge 2 SU(2) -g w t i l i (x)/ħc g s Color charge 3 SU(3) -g s T i l i (x)/ħc Let s consider SU(2) and t matrices 12

13 Isospin 13

14 t Marices 14

15 Isospin for Pions 15

16 Isospin in Two-particle System Exercise 1 lebsch%e2%80%93gordan_coefficients j m 1 m 1 m 2 16

17 I - { p + > p > } 17

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20 Summary 1 W in 1982 Z in

21 p - p interaction creates status of 3/2, -1/2> or 1/2, -1/2>. W in 1982 Z in

22 13 W in 1982 Z in

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24 Why different? ~200 mb s total s elastic ~60 mb ~20 mb s total s elastic s inelastic 24

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26 D Resonances in pp Scattering quark diagram 26

27 Resonance Particles 27

28 Resonance of quark-antiquark states Aug. 9, TeV (First 1 pb-1) 1974 J/y m + m 1977 m + m 280 nb Z m + m 1.1 pb -1 (~80 x 10 9 pp collisions) 28

29 Vector Mesons vs. Quarks Quantum Numbers 29

30 Vector Meson Decay Width 30

31 PDG 2016 J/y(1S), y(2s), y(3s), 31

32 mass Charmonuim States 32

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35 Reality Check: Spin-3/2 Top CMS B2G (draft, drfat, draft) Jan 31,

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37 3 37

38 Parity Operation Spatial Inversion of Coordinates

39 Classification of Physical Quantities Based on their rank and parity properties 1 39

40 Classification of Physical Quantities Based on their rank and parity properties 40

41 Parity of Two-Particle System 3 Exercise 1: particles. Find the parity of a system of two spin

42 Parity of Antiparticle 5 42

43 y(3s) y(2s) 2003 (5) J/y(1S) 43

44 Parity of Three-Particle System Exercise

45 Parity-Conserving Reaction 45

46 Parity Violation in Weak Interaction 1956 Parity Operaton Parity Violation 46

47 Quiz 47

48 Charge Conjugation [1] The charge conjugation operation Ĉ is the operation which replaces all particles by their anti-particles in the same state. For particles a (= e +, p +, K +, p, n, ) which have distinctive antiparticles, wavefunctions are changed with Ĉ operation as : Or simply Ĉ operation transforms: 48

49 Charge Conjugation [2] For particles a (= p 0, g, ) which do not have distinctive antiparticles are eigenstates of the Ĉ operation as a single particle : In this case one can get a quantum number C, called C parity. Clearly the charge conjugation operation satisfies:, therefore C parity of p 0 49

50 Charge Conjugation [3] C parity is conserved with electromagnetic and strong interaction : but not with the weak interaction (will be discussed later). We will discuss only C-parity conserved cases. Conserved -> (Initial state C parity) = (Final state C parity) C-parity of two-photon system is (-1)(-1) = +1; 50

51 Charge Conjugation [4] In case of multi-particle system, the C-parity is a multiplicative number: If the multi-particle system are symmetric with the Ĉ operation, the system is an eigenstate of the Ĉ operation and has definite C-parity, for example: For a case of p + p - system with orbital momentum L, the C parity is: 51

52 [1] C-parity of multiple-particle system is a multiplicative number. [2] In case of multiple-particle system of particles that don't have intrinsic C-parity assignment, we have to go through Exercise 3, 4 and 5. Charged pions and proton/anti-proton cannot be C-parity eigenstate. Thus no C- parity assignment on individual particles. However, for a (pi+, pi-) system, we can assign. That is Exercise 3. [3] Examples: C-parity C-parity of 2 photon system is (-1)(-1) = +1; C-parity of 3 photon system is (-1)(-1)(-1) = -1; (1)... C is violated. (2)... C is conserved. Then okay for others? 52

53 Exercise 3 53

54 Exercise 4 s p p - = 0, 1, or 2 4 S = 2 Symmetric S = 1 Asymmetric S = 0 Symmetric Symmetry = (-1) S 54

55 Exercise 5 _ s pp = 0 or 1 55

56 C-parity of p 0 and g Exercise 6 56

57 Quarks & Leptons Exercise 7: Conservation Why? 57

58 Exercise 8: Phys.Rev.D76:117101,2007 Why J/y gg is C-parity violating process? 58

59 Exercise 8 (cont d) Review an experimental technique: To measure Br(J/y gg), one needs to prepare a sample of J/y events and count the number of events in the gg final state. 59

60 C-parity of n 60

61 Exercise 9 61

62 Exercise 10 62

63 CP Violation in Neutral Kaons 63

64 CP Violation in Neutral Kaons 64

65 Quiz - CP Violation Experiment CP eigenstates: 2-pion system is CP = +1 3-pion system is CP = -1 K L is CP = -1 Thus, K L -> p + p - p 0 65

66 4 66

67 SU(3) Example 1: Flavor Symmetry 67

68 Color Charges The quarks cannot appear as a single free quark, due to its color charge (= red, green, blue). In any actual particles combined by quarks, the color have to be cancelled to white. Therefore there are two types of combinations: Baryons (qqq) Mesons (qq) Blue white Yellow (=anti-blue) 68

69 Three Color Charges Recap: 2x2 69

70 Three Color Charges 70

71 SU(3) c Quantum Number LGT Phase Factor q (electric) charge 1 U(1) -q l(x)/ħc g w Weak isospin charge 2 SU(2) -g w t i l i (x)/ħc g s Color charge 3 SU(3) -g s T i l i (x)/ħc 71

72 Flavor SU(3) y flavor * y spin Spin SU(2) 72

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74 Quiz [Q] Find a, b and c to satisfy the wavefunction to be symmetric.: [A]. 74

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76 Why? 76

77 Omega (W) Baryon V. E. Barnes; et al., "Observation of a Hyperon with Strangeness Minus Three". PRL 12 (8): (1964) 204. doi: /physrevlett Bubble chamber trace of the first observed Ω baryon event at Brookhaven National Laboratory 77

78 Quiz: Top-quark Baryon? A. Quadt, "Top quark physics at hadron colliders". European Physical Journal C 48 (3): (2016) doi: /epjc/s