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

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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)