Lecturer: Paul Harrison

Weighting: 15 CATS

The Standard Model (SM) of Particle Physics is a quantum field theory with local gauge symmetries. We will describe these symmetries and show how to calculate cross sections (experimental observables). We will discuss the Higgs mechanism and spontaneous symmetry breaking, which explain the origin of mass in the SM. Finally, we will look beyond the group structure of the current Standard Model to discuss possible mechanisms for unification of the strong process with the electroweak interaction.

Aims:
To develop ideas used in gauge theories and apply these to the field of particle physics. To describe the theory underpinning the Standard Model of Particle Physics and to highlight the symmetry properties of the theory. To discuss the formulation of the Standard Model, including the concept of spontaneous symmetry breaking, and consider further model extensions.

Objectives:
By the end of the module, students should be able to:

• Explain the gauge principle, the mathematical description of symmetry, and the symmetry properties associated with gauge invariance
• Describe how the quarks and leptons, and the bosons that mediate their interactions, can be described by local gauge theories
• Derive Feynman rules from the Lagrangian description of quantum fields
• Use the gauge structure of each of the three interactions, to calculate basic processes in QED
• Explain how the electromagnetic and weak forces were unified and how the concept of spontaneous symmetry breaking (and the Higgs Mechanism) can account for massive gauge fields
• Describe some of the current ideas for extensions of the Standard Model

Syllabus:

Introduction and revision of relativistic quantum mechanics

The mathematical description of symmetries

The gauge principle and implications of gauge invariance

Quantum Field Theory and the generation of Feynman Rules

The gauge structure of QED, QCD and the Electroweak forces

Electroweak unification, predictions and experimental validation

Spontaneous Symmetry Breaking and the Higgs Mechanism

Extensions of the gauge structure of the Standard Model

Commitment: 30 Lectures

Assessment: 2 hour examination

Recommended Texts:
I. J. R Aitchison and A.J.G. Hey, Gauge Theories in Particle Physics, CRC Press (2013)
M. Thomson, Modern Particle Physics, Cambridge University Press (2013)
D. Griffiths, Introduction to Elementary Particles, Wiley (2008)