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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:. - PowerPoint PPT Presentation
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UNIT 2: OUTLINE SYLLABUS:
1st Lecture IntroductionHadrons and LeptonsSpin & Anti-ParticlesThe conservation laws: Lepton Number
Baryon number Strangeness
2nd Lecture
3rd Lecture Follow-upFundamental forces and field particlesThe standard model
Problem solving Check a decay for violation of conservation laws Quarks Properties of a particle given quark combination
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+ + nb) p+ + n
p+ + p+ + n + p p+ + p + p+
_
Method: B=+1 for baryons, -1 for anti-baryons, 0 for everything else
Answer: a) Before decay Le = 0 and L = +1 After decay Le = 0 and L = +1
Allowed reaction! b) Before decay L = 0 and Le = 0 After decay L = 0 and Le = 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
Is Strangeness Conserved?
a) π+ + nb) 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
Conservation LawsConservation Laws(Tipler Chap 41 Q14)(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- +
Conservation LawsConservation Laws(Tipler Chap 41 Q14)(Tipler Chap 41 Q14)
SolutionSolution• Method: Use Table 41-1 and the conservation laws for Baryon number
and Lepton number• (a) n ->
– mn > 2mm
– 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- + – m2me – Total charge on both sides = 0 : conserved– Baryon number on both sides = 0 : conserved– Le = 0 on both sides: conserved– Process is allowed
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Quarks - The Smallest Building Blocks of Matter
Gell–Mann & Zweig 1963: see Tipler section 41-4
Three Different Types of QUARKSThree 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 StrangenessUp u 1/2 +2/3 1/3 0Down d 1/2 -1/3 1/3 0Strange s 1/2 -1/3 1/3 -1
Anti-quarks maintain spin, but change sign of S and B!
ud
π+
Meson
u u
d
p
Baryon
Different types of quarks contd.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
Quark combinations Quark combinations (Tipler Chap 41 problem 17)(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
Quark combinations Quark combinations (Tipler Chap 41 problem 17)(Tipler Chap 41 problem 17)
SolutionSolutionMethod: 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 -
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
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)
EIGHT FOLD WAY PATTERNSEIGHT FOLD WAY PATTERNS(see also Orange booklet)(see also Orange booklet)
S = 0
S = -1
S = -2
Q = +1
Q = 0Q = -1
n
p
The Baryon The Baryon Octet - Octet -
Eight Spin 1/2 Eight Spin 1/2 BaryonsBaryons
(uud)(ddu)