1. 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 Problem solving Check a decay for violation of conservation laws Quarks Properties of a particle given quark combination

2. 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 Checking Baryon Numbers a) p + + n b)p + + n p + + p + + n + p p + + p + p + _ Method: B=+1 for baryons, -1 for anti-baryons, 0 for everything else

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

4. 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! Method: Strangeness is a property of some hadrons – see Tipler Fig 41-2 P.1322

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 ->         (b)    e + + e - + 

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 ->         –m n > 2m   m  –Total charge on both sides = 0 : conserved –Baryon number changes from +1 to 0: violated –L  = 0 on both sides : conserved –Process not allowed (b)    e + + e - +  –m   2m e –Total charge on both sides = 0 : conserved –Baryon number on both sides = 0 : conserved –L e = 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. Three Different Types of QUARKS There are three elementary quarks (flavors) That make up the fundamental particles: Up u Down d Strange s 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! u d π+π+ Meson u u d p Baryon

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  + (d) dds –Ditto, B=1, q=-1, S= -1 and it is a  -

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. Baryons e.g. uud: Spin 3/2 Spin 1/2 The spin ½ particle is a proton, spin 3/2 particle is a   Note that is also spin ½ (parallel, parallel, anti-parallel)

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