Elementary Particle Physics

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Elementary Particle Physics

• David Milstead
• milstead_at_physto.se
• A41021
• tel [phone]

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Format

• 19 lecture sessions
• 2 räkneövningnar
• Homepage http//www.physto.se/milstead/fk7003/cou
  rse.html
• Course book
• Particle Physics (Martin and Shaw,3rd edition,
  Wiley)
• Earlier editions can be used handouts to be
  provided where appropriate.
• Supplementary books which may be useful but which
  are not essential
• Introduction to Elementary Particles (Griffiths,
  Wiley)
• Subatomic Physics (Henley and Garcia, World
  Scientific)
• Particles and Nuclei (Povh, Rith, Scholz and
  Zetsche, Springer)
• Quarks and Leptons (Halzen and Martin, Wiley)
• Assessment
• 2 x inlämningsuppgifter
• tenta

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Lecture outline
Lecture Topic Martin and Shaw (2nd edition) Martin and Shaw (3rd edition) Extra info
1 Antiparticles, Klein-Gordon and Dirac equations, Feynman diagrams, em and weak forces 1 1 Handout
2 Units, fundamental particles and forces, Charged leptons and neutrino oscillations 2 2 Handout
3 Quarks and hadrons, multiplets, resonances 2,5 3
4 Räkneövning 1
5 Symmetries Noethers theorem, C, P and T 4 5
6 Symmetries C, P, CP violation, CPT 10 10
7 Hadrons isospin and symmetries 5 6
8 Hadrons bound states, quarkonia 6 6
9 Quantum chromodynamics asymptotic freedom, jets, elastic lepton-nucleon scattering 7 7
10 Räkneövning 2
11 Relativistic kinematics four-vectors, cross section Appendix B Appendix B Handouts
12 Deep-inelastic lepton-nucleon scattering quark parton model, structure functions, scaling violations, parton density functions 7 7 Handouts
13 Weak interaction charged and neutral currents, Caibbo theory 8 8
14 Standard Model renormalisation, Electroweak unification, Higgs 9 9
15 Beyond the Standard Model hierarchy problems, dark matter, supersymmetry, grand unified theories 11 11
16 Accelerators synchrotron, cylcotron LHC 3 4 Handouts
17 Detectors calorimeter, tracking, LHC detectors, particle interactions in matter 3 4 Handouts
18 Revision lecture 1
19 Revision lecture 2
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?? particle physics research
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Particle physics is frontier research of
fundamental importance.
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The aim of this course

• Survey the elementary constituents in nature
• Identification and classification of the
  fundamental particles
• Theory of the forces which govern them over short
  distances
• Experimental techniques
• Accelerator
• Particle detectors

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Lecture 1 Basic concepts

• Particles and antiparticles
• Klein-Gordon and Dirac equations
• Feynman diagrams
• Electromagnetic force
• Weak force

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Going beyond the Schrödinger equation
small
Classical mechanics
Quantum mechanics (Schrödingers equation)
fast
Quantum field theory (Dirac, Klein-Gordon
equations, QED, weak, QCD)
Relativistic mechanics
8
Implications of introducing special relativity
9
Negative energy states
x
t
x
t
10
What does a particle moving backwards in time
look like ?
The equation of motion of charge q moving
backwards in time in a magnetic field is the same
as the equation of motion of a particle with
charge -q moving backwards in time.
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Antiparticles

• Special relativity permits negative energy
  solutions and quantum mechanics demands we find a
  use for them.
• (1) The wave function of a particle with
  negative energy moving forwards in time is the
  same as the wave function of a particle with
  positive energy moving backwards in time.
• Ok, the negative energy solutions must be
  used but we can convert them to positive energy
  states if we reverse the direction of time when
  considering their interactions.
• (2) A particle with charge q moving backwards in
  time looks like a particle with charge q moving
  forwards in time.
• General argument that a particle with
  negative energy and charge q behaves like a
  particle with positive energy and charge -q.
• We expect, for a given particle, to see
  the same particle but with opposite charge
  antiparticles.
• Antiparticles can be considered to be
  particles moving backwards in time - Feynman and
  Stueckelberg.
• Hole theory (not covered) provides an
  alternative, though more old fashioned way of
  thinking about antiparticles.

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Electron and the positron
1897 e- discovered by J.J. Thompson 1932
Anderson measured the track of a cosmic ray
particle in a magnetic field. Same mass as an
electron but positive charge The positron (e )
- anti-particle of the electron Nobel prize
1936 Every particle has an antiparticle. Some
particles, eg photon, are their own
antiparticles. Special rules for writing
particles and antiparticles, eg antiproton p,
given in next lecture.
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Klein-Gordon equation
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The Dirac Equation
15
Implications of the Dirac Equation
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How particles interact exchange forces
Electromagnetic force
Particles carrying charge interact via the
exchange of photons (g) mass0, spin1 (boson)

-
-
-
photon

-
-
-
-
-

-
Attraction
Repulsion
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Electromagnetic processes
18
Feynman diagrams
19
(1) Electromagnetic processes
vertex
s
t
20
(1) Basic electromagnetic diagrams
vertex
s
t
((g) and (h) become clear soon)
21
(2) Is energy conservation violated ?
virtual particle (g)
real particle
Dt
22
(3) Using Feynman diagrams
a
a
a
a
Negative energy solutions antiparticles. QM
insists we use them!
23
(3) Using Feynman diagrams
a
a
a
5 other contributions
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Question
25
(3) Using Feynman diagrams
e-
e-
e-
e-

e-
e-
e-
e-

e-
e-
e-
e-

.
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Question
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Understanding forces
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The weak force
e-
e-
e-
W-
ne
e
(b-decay)
(neutrinos next lecture)
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The fundamental forces
Different exchange particles mediate the forces
electromagnetic
weak
strong
Interaction Relative strength Range Exchange Mass (GeV) Charge Spin
Strong 1 Short (? fm) Gluon 0 0 1
Electromagnetic 1/137 Long (1/r2) Photon 0 0 1
Weak 10-9 Short (? 10-3 fm) W W-,Z 80.4,80.4, 91.2 e,-e,0 1
Gravitational 10-38 Long (1/r2) Graviton ? 0 0 2
No quantum field theory yet for gravity
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Summary

• Antiparticles and spin states are predicted when
  when relativity and quantum mechanics meet up!
• Antiparticles correspond to negative energy
  states moving backwards in time.
• Feynman diagram formalism developed and used for
  (very basic) rate estimation
• Generic approach for all forces
• Weak force is weak because of the mass of the
  exchanged particles.