Download presentation

Presentation is loading. Please wait.

Published byAmerica Hollin Modified over 2 years ago

1
1

5
Internal symmetries isospin symmetry => nuclear physics SU(3) – symmetry =>hadrons chiral summetry => pions color symmetry =>quarks electroweak symmetry => SU(2)xU(1) model >

6
Internal symmetries: broken by interaction ( electromagnetism breaks isospin ) broken by explicit symmetry breaking ( SU(3) – symmetry of hadrons ) unbroken ( color symmetry of quarks ) broken by spontaneous symmetry breaking ( chiral symmetry and electroweak symmetry)

7
Rutherford: He suggested in 1919 that there must exist a neutral partner of the proton. helium nucleus: charge: 2 x proton mass: 4 x proton

8
1932: discovery of the neutron (J. Chadwick) atomic nuclei are composed of protons and neutrons

9
9

10
nucleons: doublet of SU(2)

11
Lawrence Berkeley Nat. Lab

12
1953 pion nucleus

14
delta: quadruplet ( 1230 MeV )

15
pions: triplet eta: singlet

16
16

17
17

19
U(n): group of complex unitary n x n matrices SU(n): n x n matrices with det U = 1

20
U = exp (iH) H: Hermitean n x n matrix

21
det U = exp i (trH) SU(n): det U = 1 tr H = 0

22
SU(n): (n x n - 1) generators SU(2): 3 SU(3): 8 SU(4): 15 SU(5): 24

31
quarks triplet fundamental representation

33
hypercharge

35
quark triplet

37
irreducible representations choose state with maximal value of t(3) – proceed into the U, T and V directions to the left, until it stops

38
steps p and q External line of representation

39
each state is described by 3 numbers:

46
46

47
47

48
0 1 2 3 0 1 3 6 10 1 3* 8 15 24 2 6* 15* 27 42 3 10* 24* 42* 64

49
direct product of representations

50
invariant operator e.g. for angular momentum

52
1 0 3,3* 4/3 6,6* 10/3 8 3 10,10* 6 27 8

59
Bevatron in Berkeley

60
K-mesons: 1947 => Eta-meson: 1961

64
64

65
65

66
66

68
68

69
breaking of SU(3): much larger than the breaking of isospin symmetry

70
70 940 MeV 1190 MeV 1318 MeV 1116 MeV

71
71 ??? 1232 MeV 1530 MeV 1385 MeV

73
Physics given by a(t) - the various matrix elements => Clebsch-Gordan coefficients

76
f - coupling d - coupling Wigner-Eckart theorem -- SU(3)

77
Susumu Okubo (Rochester)

82
82 1236 MeV 1672 MeV ? 1232 MeV 1530 MeV 1385 MeV

83
83

84
84

85
85 496 MeV 138 MeV 958 MeV548 MeV 496 MeV

87
mixing changes the masses lower state lower higher state higher Experiment: mixing angle about 16 degrees

90
Why pi mesons have a small mass? Gell-Mann, Oakes, Renner (1968) Chiral Symmetry SU(3) => SU(3,L) x SU(3,R)

92
Chiral symmetry breaking: all eight mesons acquire masses

93
SU(3,L) x SU(3,R) SU(2,L) x SU(2,R) SU(2) K-mesons and eta meson massive pions massless pions massive

94
Why chiral symmetry? QCD

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google