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Exploring Fundamental Particles: Quarks, Hadrons, and Leptons

Learn about the basics of elementary particle physics, conservation laws, quarks, spin, and the standard model in these lectures. Dive into the properties of quark combinations, baryon numbers, and strangeness, and understand how to check decay reactions for conservation violations.

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Exploring Fundamental Particles: Quarks, Hadrons, and Leptons

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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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