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Introduction to Elementary Particles: Hadrons, Leptons, and Fundamental Forces

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This course schedule outlines the key topics to be covered in Unit 2 of the Physics and Astronomy department, focusing on elementary particles. Students will explore the properties and interactions of hadrons and leptons, conservation laws, and the fundamental forces depicted in the Standard Model. Key lectures and problem-solving workshops are scheduled, providing a comprehensive overview of quarks, baryon numbers, lepton numbers, and strangeness. Participants will engage in practical activities to test decay processes for conservation law violations, enhancing their understanding of particle physics.

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Introduction to Elementary Particles: Hadrons, Leptons, and Fundamental Forces

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  1. Department of Physics and Astronomy Option 212: UNIT 2Elementary Particles SCHEDULE 29-Jan-14 12.00pm LRA Intro lecture 3-Feb-14 9.00am LRB Problem solving (10-Feb-14 9.00am E Problem Workshop) 12-Feb-14 12.00pm LRA Follow-up

  2. 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

  3. Checking Baryon Numbers a) p+ + n p+ + n 2p+ + p + n p+ + p + p _ _ _ 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

  4. Checking Lepton Numbers a) µ- b) π+ e- + ne + n µ+ + n + ne _ 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!

  5. 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!

  6. Some Fundamental Particles Rest energy MeV B Le L Category Particle Symbol L S Antiparticle Photon photon   0 0 0 0 0 0 Neutrino Electron Muon Tau 0 0.511 105.7 1784  e  - Leptons                +      e   Hadrons Mesons 140 135 Pion Kaon  o            +1  o         K- Ko 493.7 497.7 K+ Ko Baryons 938.3 939.6 1115.6 1189.4 1192.5 1197.3             Proton Neutron Lambda Sigma p- n L    p+ no L                See also Tipler Table 41-1 Page 1337 For strangeness, examine Figure 41-3 Page 1344 _ _ _ _ +1 +1 +1 +1 +1 +1 _ _

  7. Conservation Laws • Test the following decays for violation of the conservation of electric charge, baryon number and lepton number. • (a) n -> p+ + p- + m+ + m- • (b) p0 -> e+ + e- + g

  8. Conservation LawsSolution • Method: Use Table 41-1 and the conservation laws for Baryon number and Lepton number • (a) n -> p+ + p- + m+ + m- • 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 • Total charge on both sides = 0 : conserved • Baryon number on both sides = 0 : conserved • Le = 0 on both sides: conserved • Process is allowed

  9. Quarks - The Smallest Building Blocks of Matter Gell–Mann & Zweig 1963

  10. π+ Meson u Name Spin Charge 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

  11. 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

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

  13. Quark combinations Solution Method: for each quark combination determine the baryon number B, the charge q and the strangeness S; then use Tipler Table 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-

  14. Some Fundamental Particles Rest energy MeV B Le L Category Particle Symbol L S Antiparticle Photon photon   0 0 0 0 0 0 Neutrino Electron Muon Tau 0 0.511 105.7 1784  e  - Leptons                +      e   Hadrons Mesons 140 135 Pion Kaon  o            +1  o         K- Ko 493.7 497.7 K+ Ko Baryons 938.3 939.6 1115.6 1189.4 1192.5 1197.3             Proton Neutron Lambda Sigma p- n L    p+ no L                See also Tipler Table 41-1 Page 1337 For strangeness, examine Figure 41-3 Page 1344 _ _ _ _ +1 +1 +1 +1 +1 +1 _ _

  15. Quark spin • 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

  16. 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)

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

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