# Lecture courses

## Michaelmas Term 2014

### Accelerator Physics - Professor E. Wilson, Professor E. Tsesmelis and Dr R. Bartolini

- Overview of the history of accelerators from the invention of linear accelerators and cyclotrons, the discovery of phase stability, the invention of the synchrotron leading to the modern circular and linear colliders.
- Magnet configurations for guiding and focusing the beam of accelerated particles, magnetic rigidity, and two dimensional field expansions. The design of dipoles, quadrupoles and multipole magnets.
- Transverse optics – strong and weak focusing, Hill’s equation and its solutions in algebraic and matrix form. Computational methods for patterns of focusing magnets. Invariants of transverse motion and the parameters which describe beam size and emittance.
- Longitudinal beam dynamics – phase stability in a repetitive acceleration system. Transition and momentum compaction. The effect of momentum spread.
- Principles and design of microwave cavities for acceleration, phase and group velocity – transit time factor and shunt impedance.
- Synchrotron radiation effects in electron accelerators including the spectrum, energy loss per turn, damping of both transverse and longitudinal oscillation and equilibrium beam size.
- Basic concepts in plasmas, fluid basics, single particle motion, drift motion, adiabatic invariants, distribution functions, the Vlasov Fokker Planck equation and waves in fluid plasmas.

This is the first half of a series to be completed in Hilary Term 2014. The format is two lectures in each week of Michaelmas Term supplemented by four two hour classes on Wednesday or Thursday afternoons in weeks 3, 4, 6 and 8. The aim of these classes is to show the student how to use a standard application program which calculates one of the important design features of an accelerator. Specialists in the fields of Magnets, Machine Lattices and Cavities (respectively) will lead the classes. At the end each class students should be able to run simple data input sets for each program. They will prepare further examples for marking at the next class.

For the first time this year the course includes a basic grounding in plasma physics and lasers to prepare students for the invention of laser driven devices for particle acceleration.

In Hilary Term 2014 the classes will apply the skills learned in the first term to prepare an outline of a design study of a new accelerator. Participating students will hand in draft chapters of different parts of a design review report for marking.

Topics which will be covered in the lectures of the second term are: magnet design, non-linear dynamics, beam transport, space-charge effects, beam-beam effects and Linear Colliders, as well as further study of laser-driven plasma accelerators.

The underlying text is "An Introduction to Particle Accelerators" by Edmund Wilson (OUP) IBSN 0 19 850829 8 with "Engines of Discovery" by Andrew Sessler and Edmund Wilson (WSP) IBSN 978-981-270-071 as background reading.

### Advanced Quantum Mechanics - Dr. F. Azfar

- Review of Fourier transformations, Dirac-delta functions, bra and ket notation and Green-functions/propagators (concepts). Units. Contour integration in the complex plane.
- A review of Special Relativity, 4-vectors, co-variant and contra-variant transformation properties, and the 4-vectors with either. Lorentz-scalars, and tensors, some kinematics if time, E-M tensor and transformation properties of E and B fields.
- Time-dependent perturbation theory, and Fermi's Golden rule. Rates and cross-sections. Rutherford scattering example if time.
- Relativity and Quantum Mechanics. Operator substitution in p
^{2}c^{2}+m^{2}c^{4}, Klein-Gordan equation. Negative energy solutions probability current. Motivation for a relativistic equation linear in the time derivative. - Derivation of the Dirac Equation. Gamma matrices, simple free particle solutions of the Dirac equation, interpretation of spinor components etc. Helicity eigenstates. Introduction of the electromagnetic field into the Dirac and Klein-Gordan equations, p->(p-eA/c)
- Electron Propagator. Start with a simple example: propagation of an electron in an arbitrary electro-magnetic field. Expand perturbative series for the propagator and motivate Feynmann graphs from this series. Apply to Rutherford scattering cross-section calculation which in turn will require use of Gamma matrix manipulation, spin sums and trace theorems. Motivate as we go along.
- Feynmann rules for scattering explained in conjunction with simple scattering processes. Compton, Moeller, and electron-muon scattering, calculate as many processes as possible. At least one spinless scattering process as well (K-G equation for charged particles). Higher order corrections: a comment on divergences.

### Statistics - Professor H. Kraus

- Statistics and probability. Mean and standard deviation. Random and systematic errors. Error propagation.
- Distributions: Binomial, Poisson and Gaussian. Gaussian in 2-dimensions. Error matrix.
- Parameter fitting and hypothesis testing. Methods of χ
^{2}, moments and maximum likelihood. Maximisation techniques. - Detailed examples: straight line fit, Breit-Wigner with background. Monte Carlo techniques.
- Limits
- Case studies

### Introduction to Symmetries - Dr Emanuele Re

This course of 7 lectures (plus 1 examples class) is intended for first year graduate students in experimental Particle and Nuclear Physics. It aims to give an informal introduction to the general subject of symmetries in quantum systems, and to provide the basis for a "practical" knowledge of the most common continuous symmetry groups and their representations, as used in particle physics. The course will assume knowledge of basic non-relativistic quantum mechanics (e.g. hermitian and unitary operators, eigenvalues, constants of the motion, degeneracy, spin-½ formalism), of the mathematics of vectors and matrices, and of four-vectors in Special Relativity.

The topics to be covered are:-

- Symmetries in quantum systems: translation and rotation invariance, and conservation of linear and angular momentum.
- Symmetry and degeneracy: representations of SO(3).
- Spin-½ particles.
- The Lorentz group.
- SU(2).
- SU(3).
- Symmetries in Lagrangian field theory.

Note:

- The above sections do not necessarily correspond to single lectures.
- The course will cover a lot of ground, quite rapidly; copies of the lecture notes will be available.

The lectures will follow the notes of Prof. Aitchison (who lectured this class in the past) that can be found here http://www.slac.stanford.edu/~aitchiso/ - Some preparation for topic 7 above would be desirable, e.g. Lagrangians in classical mechanics.

Textbooks

A useful general introduction to symmetries in quantum mechanics (including ones like P and T which this course won't cover) is provided by chapter 7 of Schiff’s book on Quantum Mechanics (3rd Edition). An alternative is chapter 17 of Merzbacher’s Quantum Mechanics (3rd Edition). A book that is in some ways at about the right level for the course is "Groups, Representations and Physics" by H.F. Jones (IOP Publishing), but it includes far more than I can cover (in particular, the group theory). An earlier but still useful book is "Unitary Symmetry and Elementary Particles" by D.B. Lichtenberg (2nd Edition, Academic Press).

### Computing - Mr. P. Gronbech, Mr. C. Hunter and Dr S. Brisbane

We have a set of lectures on the web.

The Computing Facilities

- PP Unix Overview. Sean Brisbane
- Networking and Communication. Chris Hunter

Linux - Sean Brisbane

- Use of the local batch systems, connecting via X and ssh.
- Other large scale computing facilities.

Introduction to python and pyROOT - Sean Brisbane

- Overview.
- Basic introduction to python
- Using ROOT classes from within python

*Please Note: The sole function of this short computing lecture course is to help new postgraduate students in PP exploit the local computing facilities effectively. As the computing environment is dynamic, the contents of this course is kept under constant review, in consultation with its intended audience.*

### Particle Detectors and Electronics - Dr. R. Nickerson and others

1. Introduction RBN

- Explanation of course purpose, structure etc.
- Overview of Elements in PP Experiments
- Discussion to establish level of student knowledge

2. Electronics 1 RBN

- Basic architectural elements
- Typical tasks for electronics
- Racks, Crates, Protocols

3. Electronics 2 RBN

- Pulse bouncing, grounding
- basic bits and pieces
- boards, design methods
- technologies and trade-offs

4. Electronics 3 RBN

- Trigger Systems
- Hierarchy
- Level 1
- Level 2
- labVIEW

5. Opto-electronics AW

- Data transmission
- fibre optics

6. Electronics 5 HK

- Techniques for low T

7. Conventional Scintillator detectors

### Introduction to Quantum Field Theory - Dr B Volker

Quantum field theory forms the backbone of many areas of theoretical physics, from gauge theories of particle physics to advanced condensed matter problems. This 18-hour lecture course is intended as an introduction to the subject, taking the student from quantum mechanics to the formulation and solution of relativistic field theories in terms of path integrals.

The course will provide the basic knowledge necessary to study quantum electrodynamics (QED), quantum chromodynamics (QCD) and advanced quantum field theories for condensed matter physics.

A basic knowledge of classical, statistical and quantum mechanics will be assumed, together with complex variable calculus.

The subjects to be covered include

- Path integral formulation of quantum mechanics
- Path integrals in field theory: generating functionals
- Feynman diagrams, Feynman rules
- S-matrices
- Divergences and regularisation
- Renormalisation and renormalisation group
- Path integrals for fermions

## Hilary Term 2015 - to be updated

### Accelerator Physics - Professor E. Wilson, Professor E. Tsesmelis and Dr R. Bartolini

In Hilary Term this pattern will continue and classes will apply the skills learned in the first term to prepare an outline of a design study of the LHeC Design Project, the Energy Recovery Linac (ERL) for the Large Hadron electron Collider (LHeC). Specialists in the fields of Magnets, Machine Lattices and Cavities (respectively) will lead the classes. At the end of each class students should be able to run simple data input sets for each program. They will prepare further examples for marking at the next class. Participating students will hand in draft chapters of different parts of a design review report for marking and the term will end with a presentation of their work by the students.

Topics for the lectures in Hilary Term are:

- Coherent and incoherent tune shifts (Professor Ted Wilson)
- Magnet Design
- Non Linear Dynamics
- Instabilities
- Beam Transport
- Diamond Control System (Dr Riccardo Bartolini)

The underlying text is "An Introduction to Particle Accelerators" by Edmund Wilson (OUP) IBSN 0 19 850829 8 with "Engines of Discovery" by Andrew Sessler and Edmund Wilson (WSP)

IBSN 978-981-270-071 as background reading.

### Hamiltonian Dynamics - Dr. C. Warsop

This is an eight lecture course which introduces the essentials of Analytical Mechanics. The aim is to provide the background necessary for students studying advanced beam dynamics or particle physics. The basics of Lagrangian Mechanics, Hamiltonian Mechanics, Canonical Transformations, Hamilton-Jacobi theory and Perturbation theory are covered. The first four lectures are general mechanics and appropriate for particle and accelerator physics students, whilst the last four lectures concentrate on applications for accelerator physicists. A problems class will also be arranged for accelerator physics students.

### Particle Detector Course Outline - Dr. R. Nickerson and others

This course is the continuation of the Michaelmas term lectures. The course in Hilary builds on the earlier more general material with lectures with increased detail on specific detector issues.

Lecture 1

Calorimetry: Shower Theory B; Homogeneous & Sampling Methods; Radiation lengths, material examples; Interaction lengths, material examples; Compensation; low energy detectors.

Lecture 2

Calorimeters: em calorimetry, resolutions etc.; photons electron separation; statistical pi zero separation; liquid Ar/Kr, gas sampling, scintillator sampling; Crystal detectors

Lecture 3

Calorimetry: Hadronic Calorimeters, resolutions; steel scintillator; compensating; hadron & muon

Lecture 4

Wire Chambers: Wires, gasses, rates, radiation damage; Modes, proportional, streamer, Geiger; Straws; MWPCs

Lecture 5

Wire Chambers: Drift chambers; Jet chambers; TPCs; photon detectors, TEA, TAME

Lecture 6

Silicon: Silicon Signals; Lorenz angle, Shaping and speed; Radiation effects

Lecture 7

Silicon: CCDs; silicon drift detectors; x-ray detectors

Lecture 8

PID: Time of flight, dEdx, gamma/e/pizero; muon detectors; neutrino detection

Lecture 9

PID 2 Threshold Cherenkov detectors; RICH Cherenkov; Transition Radiation

Lecture 10

non-accelerator/dark matter detector design

Lecture 11

Collider Detector Design

Lecture 12

Neutrino detector design

### Electromagnetism for Accelerators and Detectors - Dr I. Konoplev

Introduction. The EM phenomena exhibited by charges moving in vacuum and in media.

- The EM field of a charge or bunch in a vacuum.Lienard-Wiechert potential. Synchrotron radiation.
- Wakefields in accelerators. Smith Purcell radiation. Beam diagnostics.
- Some useful models of moving charge in a transparent medium.. A moving charge in a real dispersive and absorptive medium.
- Interaction of charged particles with matter: energy loss. Cherenkov and Transition Radiation.

There are 4 lectures. The Powerpoint file of the lectures will be available.

### Introduction to QCD - Professor A. Cooper-Sarkar

The course introduces the basics of QCD, the properties of quarks and gluons as revealed in experiments at both high and low momentum transfers. The course will focus on the large momentum, short distance phenomena that give rise to the parton model and perturbative QCD.

Methods for calculating matrix elements in perturbation theory and models for non-perturbative processes will be described. Prior knowledge of QED will be assumed.

The foundations of the parton-model picture in QCD and the formalism of QCD, such as asymptotic freedom, the evolution equations, and first and higher order perturbation theory effects will be described and confronted with data.

The theory and phenomenology of deep-inelastic lepton-hadron scattering and hadron-hadron scattering, such as Drell-Yan annihilation and hadronic jet production, will be discussed. QCD beyond the conventional DGLAP formalism will be briefly covered. The course gives a grounding for understanding QCD at the LHC.

### Electroweak Interactions - Dr C. Hays

This course will give a general overview of gauge theories before addressing the key elements of the Electroweak theory: the parameters and measurements that allow high-precision tests of the theory.

Geometry of forces:

description of a gauge force as the curvature of a fiber bundle; principle of least action.

Particle and interactions:

path integral formulation of transition amplitudes and application to scalar and gauge fields.

Cross sections and lifetimes:

Feynman diagrams and rules and the scattering matrix.

Renormalization:

divergences, regularization, and the renormalization group.

Electroweak theory:

Higgs mechanism and the Electroweak Lagrangian.

Z boson production:

mass and cross section measurements and the forward-backward asymmetry.

Muon decay:

calculation of differential distributions; experimental measurements.

Electron magnetic moment:

QED renormalization and the one-loop anomalous magnetic moment.

W boson mass:

tree-level relations, renormalization of the Electroweak boson propagators, and one-loop results.

Higgs boson:

production via gluon-gluon fusion and vector-boson fusion; partial widths.

Bs mixing:

meson mixing amplitudes; the CKM triangle.

**Prerequisites:** Dr. Azfar's course on Advanced Quantum Mechanics

**Books:**

Quantum Field Theory, L. H. Ryder

Gauge theory of elementary particle physics, T-P Cheung and L-F Li

Electroweak Interactions, P. Renton

### Modern Particle Physics Experiments - Professor P. Burrows and others

The aim of this course is to give an overview of present and future Particle Physics experiments, with particular emphasis to the interests of this Department. For each of the broad subjects listed below there will be a brief historical overview, the discussion of the present experiments and future plans and possibilities. The lectures will highlight the specific experimental difficulties to be overcome in these areas as well as the physics goals and achievements.

Lepton Collider Physics: Phil Burrows

The production of Standard Model fermion-antifermion pairs in the electron-positron annihilations will be reviewed, including cross-section and asymmetry measurements with polarised and unpolarised beams. Production of pairs of W and Z0 bosons at LEP2 will be discussed. These measurements will be interpreted in terms of constraints on the Standard Model. The physics potentially accessible at future higher-energy lepton colliders will be reviewed briefly.

Neutrino physics: John Cobb

These lectures will cover, in a more or less historical order, the evidence for, and understanding of, neutrino oscillations, and why the experiments are what they are and where they are, (e.g. underground); the compromises involved in their design will be discussed.

Accelerator neutrino beams, 'superbeams' and 'off-axis' beams will be described, as will the idea of Neutrino Factories; the technical challenges to be faced if a Neutrino Factory is to be built will be discussed briefly.

Dark Matter and precision measurements: Sam Henry

The dark matter problem. Direct and indirect dark matter searches. Low-background environments. Liquid xenon time projection chambers. Cryogenic detectors. The LUX-ZEPLIN experiment.

Precision measurement particle physics. Particle electric dipole moments. Neutron EDM and the cryoEDM experiment. The anomalous magnetic dipole moment of the muon and the new g−2 experiment.

## Trinity Term 2015 (this will be updated)

### Theory of Strong Interactions - Dr G. Zanderighi

Strong Interactions - G. Zanderighi

Experimental evidence for color, SU(3) group, QCD Lagrangian, gauge invariance, Feynman rules, gauge fixing & ghosts, color algebra, isospin symmetry, R-ratio, UV divergences and renormalization, the running coupling and the beta function, asymptotic freedom & confinement, soft & collinear divergences & infrared safety, Sterman- Weinberg jets, parton model, sum rules. determination of parton densities, radiative corrections (failure of parton model), factorization of initial state divergences, DGLAP evolution, current status of pdfs, parton evolution as branching process, parton shower and Sudakov form factor, virtuality ordering and angular ordering, hadronization and underlying event, exact leading order matrix elements matched to parton shower, next-to-leading order, jets.

### Astroparticle Physics - Professor S. Sarkar

Lecture 1: The universe observed

Lecture 2: Relativistic world models

Lecture 3: Reconstructing the thermal history

Lecture 4: Big bang nucleosynthesis

Lecture 5: Dark Matter: astrophysical observations

Lecture 6: Relic particles & their detection

Lecture 7: Cosmic particle accelerators

Lecture 8: Cosmic ray propagation in the Galaxy

Lecture 9: Cosmic gamma rays

Lecture 10: Ultrahigh energy cosmic rays

Lecture 11: High energy cosmic neutrinos

Lecture 12: The early universe: constraints on new physics

Lecture 13: The early universe: relic topological defects

Lecture 14: The early universe: baryo/leptogenesis

Lecture 15: The early universe: inflation & the primordial density perturbation

Lecture 16: Cosmic microwave background & large-scale structure