To introduce students to the basic calculation techniques and theory concepts that are needed in order to understand modern research in experimental particle physics.

(LO1) Analyse and solve equations of relativistic quantum mechanics, including the Dirac equation, and evaluate the fundamental properties of their solutions.

(LO2) Construct and use Feynman diagrams to calculate matrix elements for cross-section and branching ratio calculations for common particle physics processes.

(LO3)  Examine the fundamental interactions of the Standard Model and outline the foundational principles of beyond Standard Model physics

(LO4) Integrate concepts from relativistic quantum mechanics, Feynman diagram techniques, and Standard Model interactions to solve problems in modern particle physics research.

(S1) Problem solving skills

(S2) International awareness

(S3) Organisational skills

(S4) Problem solving/ critical thinking/ creativity analysing facts and situations and applying creative thinking to develop appropriate solutions.

Weeks 1 and 2
Relativity and tensors, including index notation; Levi-Civita symbol; Maxwell’s equations in tensor form, photon solutions and gauge invariance; Proca equation.    

Week 3
Klein Gordon equation; Dirac equation, Dirac-gamma matrices, chirality, Pauli-Dirac representation

Week 4.   
Properties and explicit form of Dirac spinors; helicity; parity and charge conjugation.

Week 5.   
Lagrangian formalism: Lagrangians for Klein-Gordon, Dirac and Proca equations, covariant derivatives, QED Lagrangian      

Week 6.   
Decay Rates, Cross-sections, Mandelstam variables, Matrix Elements.  

Week 7 and 8.   
Feynman Rules for QED. Matrix element calculations for basic scattering processes, including electron-positron annihilation to photons, Bhabha scattering, C ompton scattering, etc.

Week 9.   
Parity violation in the weak interaction; V-A structure; Fermi theory of the weak; leptonic weak interactions and lepton universality; pion decay and muon decay.

Week 10.   
Scattering and unitarity violation in the Fermi theory; intermediate vector boson theory and W bosons; scattering in the intemediate vector boson theory; top decays; Feynman rules for Z bosons.

Week 11 and 12:
Application of Feynman rules calculation: LEP and FCC-ee processes, Higgs boson decays, axion physics, mixing; elements of flavour physics; extensions of the Standard Model.

Teaching Method 1 - Lecture
Description: 
Attendance Recorded: Yes
Notes: 3 hours per week

Teaching Method 2 - Workshop
Description: 
Attendance Recorded: Yes
Notes: 4 workshops of 2 hours each

All lecture notes made available from beginning of module via VLE.

All lectures are recorded, and can be streamed by the students via the VLE within 1 day of the lecture.