“The standard theory may survive as a part of the ultimate theory, or it may turn out to be fundamentally wrong. In either case, it will have been an important way-station, and the next theory will have to be better.”

― Sheldon Lee Glashow

About this course:

  • Lecturer: Prof. Dr. M. Drees
  • Year: 2018
  • Difficulty:
  • Course page: PI
  • Tutor: R. Mehra
  • Literature:

Alike the first theoretical particle physics course, I did not like this course too much. Apart from my subjective opinion, it was also increasingly difficult compared to the first one because of topics like the supersymmetric extension of the standard model and grand unified theories. Exercise 6 and 9 exist twice, the second of each is supposed to be exercise 7 and 10 respectively.

Exercise 1:

Keywords: Quark Mass Terms, Unitary Transformations, Diagonalized Mass Terms, Generation Space, Physical Quarks, Mass Eigenstates, W Bosons, Z Bosons, Charged Lepton Mass Term, Lepton Yukawa Couplings, Neutrinos, Dirac Spinor, Chiral Representation, Two-component Spinors, Dirac Mass Term, Majorana Spinor, Charge Conjugation Matrix, Right-handed Field, Chiral Projectors, Projection Operators, Majorana Condition, Majorana Mass Term, Physical Mass, Gauge Invariance, Power-counting Renormalizable, Higgs Boson, Vacuum Expectation Value, Non-renormalizable Terms

  1. Fermion Masses in the SM
  2. Dirac and Majorana Masses
Homework 1

Exercise 2:

Keywords: Neutrino Oscillation, Quantum Mechanical Time Evolution, Interaction Eigenstates, Flavor Eigenstates, Unitary Matrix, Neutrino Mass Matrix, Diagonalization, Two Flavors, Free Hamiltonian, Eigenvalues, Reduced Hamiltonian, Mass Eigenstates, Effective Hamiltonian, Neutrino Propagation, Coherent Interactions, Neutral Currents, Electron Neutrinos, Electron Number Density, Feynman Diagram, Critical Density, Effective Mixing Angle, Eigenvector, Real Scalars, Mass Terms, Heavy Mode, Integrate Out, Equation of Motion, Energy Scales, Resumming the Propagator

  1. Neutrino Oscillation in the Sun (MSW Effect)
  2. Integrating out a Heavy Mode
Homework 2

Exercise 3:

Keywords: β Decay, Decaying Nucleus, Quark Level, Feynman Diagrams, Standard Model, Neutrino Masses, Majorana Neutrino, Neutrino Propagator, Clashing Dirac Arrows, Flow of Fermion Number, Flow of Lepton Number, Charge Conjugation Matrix, Spin Sum, Dirac Spinors, Free Dirac Equation, Physical Neutrino Masses, Neutrino Flavor, Mass Eigenstates, Electron Flavor, Lower Bound, Gauge Theory, Anomalous, Chiral Fermion, Loop, Triangle Diagrams, Eigenvalues, Group Generators, Helicity, Left-handed Fermions, SU(2) Doublets, Singlet, Anomaly Cancellation, Weak Isospin, Group Representation, Quantum Chromodynamics, QCD, Vector-like Theory, SU(3)c, B Bosons, W Bosons, Mixed Gauge Anomalies, Gravitational Anomalies, Gravitons, Hypercharges, U(1)X, U(1)Y

  1. Neutrinoless Double β Decay (0νββ)
  2. Gauge Anomalies in (Extensions of) the SM
Homework 3

Exercise 4:

Keywords: Beta Function, β Function, Gauge Couplings, Energy Scale, Momentum Scale, One-loop Order, SU(N), Fundamental Representation, Hypercharge, Unification Scale, SU(2)L, SU(3)c, SU(5), Representations, 5-dimensional Representation of SU(5), 10-dimensional Representation of SU(5), Kinetic Energy Term, Gauge Interactions, Ten-dimensional Fermionic Representation, Charge Conjugation

  1. Running Gauge Couplings
  2. The 10 of SU(5)
Homework 4

Exercise 5:

Keywords: Symmetry Breaking, SU(5), SU(5) → SU(3)c x SU(2)L x U(1)Y, Real Higgs Field, 24-dimensional Representation of SU(5), Vacuum Expectation Value, Higgs Potential, Bounded from Below, Minimum of the Potential, Renormalization Group Equation, RGE, Yukawa Couplings, Beta Function, β Function, Runnings Gauge Couplings, Top Quark, Feynman Diagrams, CKM Mixing, Upper Bound on the Mass of the Top Quark

  1. Alternative SU(5) Breaking
  2. Yukawa RGE
Homework 5

Exercise 6:

Keywords: Left-right Symmetric Extension of the Standard Model, Gauge Group, Right-handed Neutrino, Right-handed SU(2)R Doublets, Isospin, SU(2)R Multiplet, SU(2)L Doublet Fermions, U(1)X, Baryon Number, Lepton Number, Yukawa Couplings, Higgs Field, Bi-doublet, Vacuum Expectation Value, Symmetry Breaking, SU(2)L Triplet, Pauli Matrix, Gauge Bosons, W Bosons, Z Boson, Doublet Higgs Field, Froggatt-Nielsen Mechanism, Flavor Symmetry, Flavon Field, Non-renormalizable Operators, Grand Unified Theory Scale, GUT Scale, Planck Scale, Cabbibo Angle, Electroweak Scale, Renormalizable Terms, Mass Matrix, See-Saw Mass Matrix

  1. Left-right Symmetric Model
  2. Froggatt-Nielsen Mechanism
Homework 6

Exercise 7:

Keywords: Top Quark Loops, Higgs Boson, Bosonic Sector, Quadratically Divergent Corrections, Feynman Gauge, Massive Gauge Bosons, W Boson, Z Boson, Feynman Diagrams, Propagators, Higgs two-point Function

  1. Quadratic Divergences from the Bosonic Sector
Homework 7

Exercise 8:

Keywords: Four-component Spinors, Supersymmetric Extension of the Poincaré Algebra, SUSY, Majorana Spinor, Fermionic Supercharges, Anti-commutation Relations, Commutators, Generators, Translations, Charge Conjugation Matrix, Majorana Condition, Jacobi Identity, Rotations, Lorentz Boosts, Supermultiplets, Irreducible Representations, SUSY Algebra, Witten Index

  1. SUSY Algebra
  2. Properties of Supermultiplets
Homework 8

Exercise 9:

Keywords: Rest Frame, Supermultiplet, Anti-Commutators, Supercharges, Angular Momentum, Irreducible Representation, Poincaré Algebra, Eigenvalues, Quartet Representation, Wess-Zumino Multiplet, Superfield, Grassmann Coordinates, Component Fields, Supersymmetry Transformation, Superspace

  1. Massive Supermultiplet
  2. Supersymmetry Transformations
Homework 9

Exercise 10:

Keywords: Chiral Superfield, Component Fields, Superspace, Vector Superfield, Wess-Zumino Gauge, Chiral Coordinates, SUSY covariant Derivative, Left-chiral Superspace, Right-chiral Superspace, Supersymmetric Action

  1. Kinetic Energy of Chiral Superfields
  2. Vector Superfields
Homework 10

Exercise 11:

Keywords: Interacting Chiral Superfields, Scalar Potential, Superpotential, Left-chiral Superfields, Renormalizable Theories, Fermionic Mass Matrix, Scalar Mass Term, Spontaneously Broken, Eigenvalues, Supersymmetric Field Theory, Lagrangian, Component Fields, Equation of Constraint, Four-component Spinors, Majorana Spinor, Weyl Spinor, Yukawa Interaction, Chiral Projector

  1. Mass Terms in a Theory with Interacting Chiral Superfields
  2. Wess-Zumino Model
Homework 11

Exercise 12:

Keywords: Supersymmetric Invariant Lagrangian, Abelian Vector Superfield, Left-chiral Superfield, Supergauge Transformation, Fayet-Iliopoulos Term, Equations of Constraint, Dirac Fermion, Majorana Gaugino, Feynman Rules, Loop Diagrams, Sfermion, Quadratic Divergences

  1. SQED
Homework 12
0 0 votes
Article Rating
Subscribe
Notify of
guest
0 Comments
Inline Feedbacks
View all comments