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UNIT 2: OUTLINE SYLLABUS:

1st Lecture. Introduction Hadrons and Leptons Spin & Anti-Particles The conservation laws: Lepton Number Baryon number Strangeness. 2nd Lecture. 3rd Lecture. Follow-up Fundamental forces and field particles The standard model. UNIT 2: OUTLINE SYLLABUS:.

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UNIT 2: OUTLINE SYLLABUS:

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  1. 1st Lecture Introduction Hadrons and LeptonsSpin & Anti-Particles The conservation laws: Lepton Number Baryon number Strangeness 2nd Lecture 3rd Lecture Follow-upFundamental forces and field particles The standard model UNIT 2: OUTLINE SYLLABUS: Problem solving Check a decay for violation of conservation laws Quarks Properties of a particle given quark combination

  2. Checking Baryon Numbers a) p+ + n p+ + n p+ + p+ + n + p p+ + p + p+ _ Method: B=+1 for baryons, -1 for anti-baryons, 0 for everything else Answer: a) B = 1+1 on left hand side B = 2 on right hand side too! Allowed reaction! b) B = 2 on left hand side B = 1 on right hand side Forbidden reaction

  3. Checking Lepton Numbers a) µ- b) π+ e- + ne + n µ+ + n + ne Method: L=+1 for Leptons, -1 for anti-Leptons, 0 for non-Leptons BUT separate Lepton number for e-, m, t and their neutrinos _ Answer: a) Before decay Le = 0 and Lm = +1 After decay Le = 0 and Lm = +1 Allowed reaction! b) Before decay Lm = 0 and Le = 0 After decay Lm = 0 and Le = 1 Forbidden reaction!

  4. Method: Strangeness is a property of some hadrons – see Tipler Fig 41-2 P.1322 Is Strangeness Conserved? a) π+ + n b) π- + p K+ +  -+  Answer: a) Initial state has S = 0 Final state has S = +1 - 1 = 0 Allowed reaction! b) Initial state has S = 0 Final state has S = -1 Forbidden reaction!

  5. Conservation Laws(Tipler Chap 41 Q14) • Test the following decays for violation of the conservation of energy, electric charge, baryon number and lepton number. Assume that linear and angular momentum are conserved. • (a) n -> p+ + p- + m+ + m- • (b) p0 -> e+ + e- + g

  6. Conservation Laws(Tipler Chap 41 Q14)Solution • Method: Use Table 41-1 and the conservation laws for Baryon number and Lepton number • (a) n -> p+ + p- + m+ + m- • mn > 2mp + 2mm • Total charge on both sides = 0 : conserved • Baryon number changes from +1 to 0: violated • Lm = 0 on both sides : conserved • Process not allowed • (b) p0 -> e+ + e- + g • mp > 2me • Total charge on both sides = 0 : conserved • Baryon number on both sides = 0 : conserved • Le = 0 on both sides: conserved • Process is allowed

  7. Quarks - The Smallest Building Blocks of Matter Gell–Mann & Zweig 1963: see Tipler section 41-4

  8. π+ Meson u Name Spin Charge (e) Baryon Strangeness Up u 1/2 +2/3 1/3 0 Down d 1/2 -1/3 1/3 0 Strange s 1/2 -1/3 1/3 -1 Anti-quarks maintain spin, but change sign of S and B! d p u u Baryon d Three Different Types of QUARKS There are three elementary quarks (flavors) That make up the fundamental particles: Up u Down d Strange s

  9. Different types of quarks contd. • Mesons – quark + anti-quark ( q q ) • Baryons – three quarks ( q q q ) • Anti-baryons – three anti-quarks ( q q q) By 1967 it was realised that new kinds of quarks were required to explain discrepancies between the model and experiment Charm (c) Bottom (b) – discovered 1977 Top (t) – discovered 1995

  10. Quark combinations (Tipler Chap 41 problem 17) • Find the baryon number, charge & strangeness of the following quark combinations and identify the hadron: • (a) uud • (b) udd • (c) uus • (d) dds

  11. Quark combinations (Tipler Chap 41 problem 17)Solution Method: for each quark combination determine the baryon number B, the charge q and the strangeness S; then use Tipler Table 41-1 and Fig. 41-2 to find a match. • (a) uud • B = 1/3 + 1/3 + 1/3 = 1 • q = 2/3 + 2/3 – 1/3 = 1 • S = 0 • It is a proton • (b) udd • B = 1/3 + 1/3 + 1/3 = 1 • q = 2/3 – 1 /3 – 1/ 3 = 0 • S = 0 • It is a neutron • (c) uus • Ditto, B=1, q=1, S= -1 and it is a S+ • (d) dds • Ditto, B=1, q=-1, S= -1 and it is a S-

  12. Quark spin(orange booklet) • The angular momentum vector of a spin ½ quark can have one of two settings up or down • So a meson can have its two quark spins parallel with each other or anti-parallel: Spin 1 Spin 0

  13. Quark spin contd. Spin 3/2 Spin 1/2 • Baryons e.g. uud: The spin ½ particle is a proton, spin 3/2 particle is a D+ Note that is also spin ½ (parallel, parallel, anti-parallel)

  14. EIGHT FOLD WAY PATTERNS (see also Orange booklet) n S = 0 p S = -1     S = -2   Q = +1 Q = 0 Q = -1 (ddu) (uud) The Baryon Octet - Eight Spin 1/2 Baryons

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