Prof. Mark Lancaster

Course Pre-requisites

Students should have taken level-3 Quantum Mechanics (PHAS3226) and Nuclear and Particle Physics (PHAS3224), or equivalent and have familiarity with non-relativistic Quantum Mechanics (Schrodinger's equation), Special Relativity, Maxwell's equations and the particle content of the Standard Model.

Course Aims

This course aims to:

• introduce the student to the basic concepts of particle physics, including the fundamental interactions and particles and the role of symmetries;

• emphasise how particle physics is actually carried out - to this end, data from experiments at CERN, DESY, FNAL and SLAC will be used to illustrate the underlying physics of the strong and electroweak interactions, gauge symmetries and spontaneous symmetry breaking.

Course Objectives

On completion of this course, students should have a broad overview of the current state of knowledge of particle physics. Students should be able to:

• state the particle content and force carriers of the standard model;

• manipulate relativistic kinematics (Scalar products of four-vectors);

• state the definition of a cross section;

• be able to convert to and from natural units;

• state the Dirac and Klein-Gordon equations;

• connect these equations to conserved currents;

• connect conserved current to propagators;

• state the propagator for the photon, the W and the Z and give simple implications for cross sections and scattering kinematics;

• derive the Breit-Wigner equation from the massive propagator and the Klein-Gordon equation;

• understand and draw Feynman diagrams for leading order processes, relating these to the Feynman rules and cross sections;

• give an account of the basic principles underlying the design of modern particle physics detectors and describe how events are identified in them;

• explain the relationship between structure function data, QCD and the quark parton model;

• manipulate Dirac spinors;

• state the electromagnetic and weak currents and describe the sense in which they are unified;

• give an account of the relationship between chirality and helicity and the role of the neutrino;

• give an account of current open questions in particle physics; derive the expression for neutrino oscillations in two generations;

Course assessment will be based on a 2.5 hr written exam (90%) and 4 problem sheets (10%). A mark of at least 1.5% (from 10%) must be attained from the problem sheets, unless there are extenuating circumstances, otherwise the course will be denoted as incomplete and the examiniation cannot be taken.

No single book is recommended since in general the books on the market are aimed at the PhD level or the BSc level and much of our material is at a level in between. That said, all of the course is covered in different sections of the following books:

• "Introduction to High Energy Physics" by D. Perkins (4th edition)

• "An Introduction to the Standard Model of Particle Phyiscs" by W.N. Cottinghma and D. Greenwood (2nd edition)

• "Practical Quantum Electrodynamics" by D. Gingrich

• "Introduction to Elementary Particles" by D. Griffiths

• "Quarks and Leptons" by F. Halzen and A. Martin

• "Femtophysics" by M. Bowler

The least technical and most general book is the book by Perkins (4th edition).

**Lecture Notes** :

There are 10 weeks of material. Time in the lectures will also be used to cover solutions to problem sheets.

Week 1 : Introduction & Reaction Rates : [26 slides] : 2-slides/page

Particles and forces. Natural units. Four vectors and invariants. Cross sections & luminosity. Fermi's golden rule. Feynman diagrams and rules.

Week 2 : Reaction Rates, Renormalisation; Symmetries and conservation Laws [7 slides] : 2-slides/page

Phase space. Flux. Reaction rate calculation. CM frame. Mandelstam variables. Higher Orders. Renormalisation. Running coupling constants.
Symmetries and Conservation Laws. Parity and C symmetry. Parity and C-Parity violation, CP violation.

Week 3/4 : Relativistic perturbation theory and spin : Dirac Eqn [8 slides] : 2-slides/page

From Schrodinger to Klein Gordon to the Dirac Equation; Dirac Matrices; Spin and anti-particles; Continuity Equation; Dirac observables.

Week 5 : Relativistic Maxwell's equations [9 slides] : 2-slides/page

Maxwell's equations using 4 vectors; Gauge transformations; Dirac equation + EM, QED Lagrangians.

Week 6 : QED calculation, Angular distributions; Quark Properties [13 slides] : 2-slides/page

QED scattering Cross Sections calculation; helicity and chirality; angular distributions; forward backward asymmetries; quark properties

Week 7 : Deep Inelastic Scattering; QCD [11 slides] : 2-slides/page

QCD - running of strong coupling, confinement, asymptotic freedom. Elastic electron-proton scattering. Deep Inelastic scattering. Scaling and the quark parton model. Factorisation. Scaling violations and QCD. HERA and ZEUS. Measurement of proton structure at HERA. Neutral and Charged Currents at HERA; Running of strong coupling; Confinement; QCD Lagrangian;

Week 8 : Detectors & The Weak Interaction [11 slides] : 2-slides/page

Weak interactions; The two component neutrino. V-A Weak current. Parity Violation in weak interactions. Pion and Muon Decay.

Week 9 : Electroweak Interactions [11 slides] : 2-slides/page

The electroweak interaction; quark sector in electroweak theory; GIM mechanism,CKM matrix; detecting heavy quark decays.

Week 10 : The Higgs and Beyond The Standard Model [ *substitute slides* from introductory EPP course (QMUL) ]

Higgs mechanism; alternative mass generation mechanisms; SUSY; extra dimensions; dark matter.

Week 11 : Neutrino Phenomenology [8 slides] : 2-slides/page

Neutrino oscillations, neutrino mass issues, nature of neutrino, ultra high energy cosmogenic neutrinos.

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