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M2-PSA : Lectures and exams

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2nd year lecture contents

3ème Semestre M2

 

4ème Semestre M2

Compulsory courses

UE3SA Subatomic Physics (9 ECTS)

UE3SB Instrumentation and Data Analysis (6 ECTS)

4 courses to be chosen from : (3 ECTS each)

1 free course (3 ECTS)

Any optional lectures from the list above or from a different Master specialization (e.g. Radiation-Imaging, Condensed Matter, or Astrophysics)

 

Student project (3 ECTS)

  • During 1st semester, students follow lectures on the following aspect of computing for physics :
    • C++, ROOT (C. Finck)
    • Python (E. Chabert)
    • GEANT4 (M. Vanstalle)

Master thesis (30 ECTS)

The master thesis is an initiation to research in a laboratory and is a first step toward the PhD thesis. Student will integrate a team of researchers and share their problematic and ambitions. The internship is an opportunity to gain key skills for the professional world like international team work, autonomy and communication. See the dedicated page.


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1st year lectures contents

1er Semestre M1

 

2ème Semestre M1

4 UE obligatoires

  • Mécanique quantique et Physique statistique (12 ECTS)
  • Méthodes numériques (3 ECTS)
  • Physique expérimentale I (6 ECTS)
  • Recherches actuelles en physique (3 ECTS)

1 UE optionnelles au choix (3 ECTS)

  • Physique des rayonnements, détecteurs, instrumentation et imagerie
  • Théorie des groupes appliquée à la physique
  • Les objets de l’univers et leur observation
  • Théorie classique des champs
  • Programmation et calcul intensif
  • Anglais

1 UE : libre (3 ECTS)

Contenu des cours S1

 

2 UE obligatoires

  • Matière nucléaire et particules élémentaires et Physique de la matière (9 ECTS)
  • Physique expérimentale II (12 ECTS)
  • Travaux d’Études et de Recherche (3 ECTS)

1 UE optionnelle au choix (3 ECTS)

  • Particules et astroparticules
  • Physique des astres et relativité
  • Transitions de phase et groupe de renormalisation
  • Nanostructures et Nanophysique
  • Mécanique des milieux continus
  • Physique atomique et moléculaire
  • Travaux d’Études et de Recherche

1 UE : Anglais disciplinaire (3 ECTS)
1 UE : libre (3 ECTS)

Contenu des cours S2

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Quantum Field Theory / Théorie quantique des champs

This lecture review the formal concepts in Quantum Field Theory useful for students mostly targeting phenomenological and experimental studies in subatomic physics. The main sections are :

  • Lagragian formulation of a theory
  • Second quantification methods
  • Green functions
  • Perturbation theory
  • Wick theorem
  • Feynman rules

Written exam : 2 hours

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Nuclei and interactions between nuclei

  • Nucleon-nucleon interaction in vaccum, fondamental symmetries and invariance properties of associated Hamiltonians.
  • Principe de Pauli généralisé. Caractéristiques spatiales et temporelles des interactions nucléaires, courte portée, coeur dur du nucléon, tailles et temps caractéristiques. Interactions
  • Spin-orbite et tenseur. Mécanisme d’échange des mésons, origine relativiste de l’interaction spin-orbite.
  • Éléments de la théorie du champ moyen nucléaire, sa formulation non-relativiste et relativiste. Symétries SU(2), spin et symétrie pseudo-spin [pseudo-SU(2)] dans les noyaux. Éléments de base de la théorie Hartree-Fock nucléaire. Structure générale des Hamiltoniens effectifs en physique nucléaire : interactions résiduelles, autres concepts dans la modélisation des interactions complexes.
  • Appariement nucléonique dans des noyaux, éléments de la théorie de Bardeen Cooper et Schrieffer (BCS, version nucléaire). Mécanismes dites de ‘gap’ et de la superfluidité nucléaire. Notion de quasiparticules et excitations avec des nombres de particules pairs et impairs. Excitations rotationnelles en présence de l’appariement. Comparaison avec l’expérience.
  • Caractéristiques globales des excitations nucléaires et de schémas de désexcitation. Excitations collectives : rotationnelles, vibrationnelles, les résonances géantes. Hamiltonien collectif. Rotateurs quantiques et ses symétries, applications en physique nucléaire.
  • Tendances contemporaines dans la recherche de noyaux, présentation des plus grands centres de recherche associés en France et dans le monde. Exemples de stratégies de recherche : Noyaux exotiques ; Noyaux super-lourds ; Nucléosynthèse et exemples de processus nucléaires dans des étoiles.

Written exam : 3 hours

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Experimental Particle Physics

  • Prerequisites to follow the course :
    • Particle content of the Standard Model : fermions, bosons and fundamental interactions ;
    • Quarks, leptons and hadrons, anti-particles and the basic quantum numbers of particles
    • Some relativistic kinematics, fixed target and collider collisions
    • Concept of a cross-section ; Fermi’s golden rule, decays and interactions ; basic notation of a Feynman diagram ;
    • Schrödinger and Klein-Gordon equation, some knowledge of the Dirac equation
    • Some basics of particle matter interactions, detectors and accelerators.
  • Contents of the lectures
    1. Calculation of decay width and collision cross section
    2. Electromagnetic interactions (QED) and applications
    3. Quark and lepton scattering, partons and structure of the proton
    4. Symmetries and the quark model, SU(3) flavour symmetry
    5. Strong interactions (QCD), electron-positron and hadronic collisions
    6. Weak interactions, charged and neutral currents, parity violation
    7. Some aspects of Neutrino physics and CP violation
    8. Gauge invariances and Electroweak unification
    9. The Standard Model (SM) including the Higgs
    10. Experimental tests of the SM
    11. Outlook at the Physics of the LHC (selected topics)

Written exam : 3 hours

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Radiation interaction with matter

  • Origine et classification des rayonnements ionisants Généralités : Atténuation et ralentissement. Équation de transport. Méthode de Monte Carlo. Diffusion à 2corps. Sections efficaces.
  • Interaction des photons avec la matière : Probabilité de transition dans un champ électromagnétique. Absorption. Effetphotoélectrique. Diffusion Thomson. Effet Compton. Production de paires. Comparaisons des effets et distributions des électrons détectés. Coefficients caractéristiques. Interaction avec les milieux organisés.
  • Interaction des particules lourdes chargées avec la matière : Ralentissement nucléaire. Ralentissement électronique : théorie quantique, théorie diélectrique. Ralentissement à basse énergie. Charge effective. Corrections de Barkas-Bloch. Règle de Bragg.
  • Interaction des électrons avec la matière : Diffusion élastique. Ralentissement par ionisation. Ralentissement de freinage. Effet Cerenkov. Longueur de radiation. Parcours. Cas particulier des positrons.
  • Interaction des neutrons avec la matière : Classification des neutrons. Diffusion élastique : sections efficaces, ralentissement, parcours. Diffusion des neutrons thermiques, équation de transport. Interactions inélastiques.
  • Applications : Méthodes d’analyses multi-élémentaires par faisceaux d’ions et par fluorescence X. Dosimétrie des rayonnements ionisants et radioprotection. Effets biologiques.

Written exam : 2 hours

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Detector physics and systems

Physics of detectors

  • General concepts : Ramo theorem and signal creation, signal-over-noise, efficiencies, resolutions
  • Gazeous detectors : various regimes, ion chambers, micropatterned detectors, resistive plate chambers
  • Semiconductors : p-n diodes, silicon strip and pixel sensors, monolithic sensors, germanium sensors
  • Scintillators : light generation, organic and inorganic materials
  • Visible photon detectors : photocathode, photomultipliers, siliconPM
  • Cerenkov & transition-radiation detectors

Detector systems

  • Position measurements, tracking : multiple scattering, finding and fitting algorthms
  • Energy measurements : calorimetry in high-energy physics (hadronic and electromagnetic showers) and spectroscopy in nuclear physics (Compton scattering)
  • Particle identification : dE/dx, Cerenkov, transition radiation
  • Complete systems : experiments on colliders, in astroparticles, in nuclear physics

Written exam : 2 hours

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Data analysis and modelisation

  • Basic concepts :
    • Definition of statistical and systematical uncertainties on measurements.
    • Random variables, probabilities, momenta and probabilistic laws.
    • Three basic laws of random variables, the normal law and the central limit theorem.
    • Application : counting rates, selection efficiency, estimation for means.
  • Combining uncertainties from measurements :
    • Joint probabilistic laws, covariance, correlation, the two-gaussians cases.
    • Uncertainty propagation.
    • Application : combining measurements of the same quantity and some practical examples.
  • Parameter estimation :
    • Introduction to statistics.
    • Basic methods : maximum likelihood (the gaussian case, uncertainties, binned likelihood, extended likelihood), least squares (linear case, uncertainties, chi2 law).
    • Minimizing methods.
  • Hypothesis testing :
    • Histogram fits.
    • Tests : two and single hypothesis, power and error, p-value, the Neyman test, chi2-test , Kolmogorov-test.
    • Application : histogram comparison, Higgs search at LEP.
  • Advanced estimation :
    • Interval estimation (confidence levels and intervals), low statistics, nuisance parameters.
    • Dynamic estimation, Kalman filter.
    • Application : discovery limits.
  • Modelization :
    • Random number generation, Monte-Carlo techniques.
    • Application to simulation, use cases with ROOT.
  • Advanced techniques :
    • principle analysis components (PCA) for complex ensemble.
    • Multivariate Analysis (MVA), Fisher discriminants, artificial neural networks, decision trees.

Written exam : 3 hours

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Theoretical aspects of nuclear physics

  • Overview of modern many-body methods in nuclear structure (no-core shell model, large-scale shell-model, coupled-cluster, density matrix functional).
  • Fock space for fermions (Hamiltonian of many-fermion system, basis of many-body states, 2nd quantization representation).
  • Wick’s theorem (for mean values, for Slater determinants and in Fock space for fermions).
  • Bogoliubov transformation.
  • Product states (Thouless theorem, particle-hole states).
  • Hartree-Fock approximation (HF equations, self-consistent method, self-consistent symmetries, density matrix functional).
  • Many-body wave functions in m-scheme and J-scheme (conserved quantum numbers, example of 2-particle configurations, general form of 1 and 2-body matrix elements).
  • Effective Hamiltonians for shell-model calculations (OBE potentials, N3LO, renormalization methods, MBPT, phenomenology of effective Hamiltonians, monopole and multipole Hamiltonian, 3N forces).

Written exam : 3 hours

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From nuclei to stars

  • Exploration of the nuclear chart, from the valley of sability to the most exotic nuclei ; isospin effect on the nuclear structure.
  • The nucleus, its symmetries and deformation, including super-deformation. Nuclear molecules (molecular resonnances), clusters (alpha, nuclear dimers and polymers), ocopoles and tetrahedra.
  • Physiscs of heavy and super-heavy nuclei : structure of nucleai with Z>100, super-heavy and transfermian nuclei. Spectroscopy and study of reaction mechanisms.
  • Stellar nucleosynthesis, life and death of a star, importance of exotic nuclei for nuclear astrophysics. From star energy-fuel to ITER.
  • large research programs on accelerators for radioactive beams, stable beams at strong instensity (SPIRAL II, RIA, EURISOL, ...) and specific instruments of new generation (AGATA, GRETA, S3...).

Oral exam : 30 minutes per student

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Theoretical aspects of particle physics

  • Brief re-run on special relativity if needed
  • Free scalar fields : Klein-Gordon equation, field and lagrangian, propagation of scalar fields.
  • Free fermionic fields : Dirac equation, bi-spinors and lagrangian, fermion propagation.
  • Free vector fields : electrodynamics and Maxwell equation, propagation of vector fields.
  • Cross section and S matrix : transition probabilities, cross sections, decay widths and interactions.
  • Quantum electrodynamics (QED) and Gauge theory (U1) : Noether procedure, QED lagrangian, derivation of the e+e- -> mu+ mu- cross section.
  • Weak interactions : Gauge theory SU(2)L, electroweak theory.
  • Spontaneous symmetry breaking : case of U(1), electroweak case and the Higgs boson, Yukawa interactions.
  • Standard Model of particle physics : electroweak sector and flavour violation.

Written exam : 3 hours

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Physics beyond the Standard Model of particle physics

  • reminder of the electroweak theory
  • experiments at particle colliders
  • precision tests of the Standard Model
  • limits of the Standard Model
  • extensions of the Standard Model
  • introduction to Supersymmetry
  • search for beyond Standard Model at the LHC
  • flavour physics
  • the Cabibbo-Kobayashi-Maskawa matrix
  • B Factories
  • neutrino properties
  • neutrino experiments
  • neutrino oscillations

Oral exam : 30 minutes per student

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Strong interaction at hadron colliders

Experimental approach of Quantum Chromodynamics (QCD), especially as seen at hadronic colliders of high energy, like LHC

  • Part A – Typical aspects of QCD
  1. General reminder : quarks, QCD Lagrangian, chiral symmetry and quark condensate, αs running, CKM matrix
  2. Sea of quarks and gluons : Parton Distribution Function PDF ; Deep Inelastic Scattering ; Evolution equations : DGLAP, BFKL ; Nuclear PDF ; Colour Glass Condensate
  3. Hadronisation and jets : factorisation theorem ; hadronisation : fragmentation functions, coalescence ; underlying event, multi-parton interactions ; jet reconstruction
  • Part B – Physics of Quark-Gluon Plasma (QGP)
  1. Concepts of a QGP : phase diagram, Bjorken scenario, measured thermodynamic parameters
  2. QGP in experiments : experimental facilities, colliding systems (pp, pA, AA), basic observables
  3. QGP signatures : hadrochemistry of light-quark flavour (u,d,s), hydrodynamics, heavy-quark flavours (c,b), in-medium energy losses
  4. Modern experiments in heavy-ion physics (detector considerations and details)
  5. Data analysis : one concrete case

Exam : oral

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General relativity and application to cosmology

  • Reminders and complements on Special Relativity : -** Special Relativity with tensor formalism -** New concepts : the energy-momentum tensor and the perfect fluid
  • General relativity formalism
  • The standard cosmological model
  • Inflation

Examen écrit : 3 hours Written exam : 3 hours

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Astroparticles et observationnal cosmology

Observationnal cosmology :

  • Historical approach of modern cosmology and introduction to General Relativity
  • The Big-Bang model : a thermic history of the Universe
  • Observationnal tests : cosmological background, polarization, Hubble constant and type Ia supernovae for universe expansion and acceleration, dark-matter/energy and the formation of structures
  • Results of experimental programs : COBE, WMAP, Planck, BICEP2

Physics of astroparticles :

  • Compact objects and radiation processes in astrophysics, the Fermi model of cosmic ray acceleration
  • Interaction and detection of particle for astrophysical studies
  • Direct and indirect detection in space and on earth of cosmic rays from Gev to EeV and of gamma photons from GeV to TeV : Auger, EUSO, Fermi, HESS/CTA
  • Emission and detection of high energy neutrinos : Antares, IceCube, Km3Net
  • Emission and detection of gravitational waves : Virgo/LIGO

Oral exam : 30 minutes per student

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Physics of nuclear reactor and other applications of nuclear physics

  • Part A : Physics of nuclear reactors
    • Reactor operation principle from fondamental nuclear processes
    • Microscopic reactions and their impact on the reactor behaviour.
    • Reactor safety, life-cycle and limits of today’s reactors.
    • New generation reactors. Key-words : neutron, fission, criticity, numerical simulation, energy, reactor, radioactive fuel.
  • Part B : Autres applications
  1. Characterization techniques with radiations :
    • Proton Induced X-ray Emission (PIXE)
    • Rutherford Back-Scattering (RBE)
    • Nuclear Rreaction Analysis
    • neutron diffraction
  2. Applications to health :
    • Medical imaging (scanner, Pet, γ-camera)
    • Radio/hadron-therapy
    • Dosimetry
  3. Applications to environnmental measurements :
    • Ambiant radioactivty
    • Gamma spectroscopy (in-lab and in-situ)
    • Specific issue of low activities

Oral exam : 30 minutes per student

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Elements of analytical mechanics, quantum mechanics and special relativity

  • Analytical mechanics :
    • Euler-Lagrange equation, generalized coordinates, constant of the motion, Lagrange constraints and multipliers.
    • From Lagrandian to Hamiltonian, Hamilton equations, Poisson brackets, canonical transformations.
    • Varationional principle, conservation laws, Noether’s theorem.
    • Lagrangian description of continuous media.
  • Quantum mechanics :
    • Postulates, Schrödinger equation, observables and corresponding operators.
    • Coupling of orbital moment, perturbation theory, varationional method.
    • Density matrix, second quantification.
  • Special relativity for subatomic physics :
    • Postulates, Lorentz transformations, Minkowski space, lengths contraction and time dilation.
    • Energy-monentum quadrivectors and relativistic kinematics.
    • Dirac equations, derivation, formulation with gamma-matrices and solutions.

Written exam : 3 hours

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Student’s seminars

Each week, a pair of students prepares a short seminar for the other students. The presentation reviews some topics explained during past lectures (both common and optional lectures are concerned).

Example of subjects :

  • Special relativity : Definition and notation of 4-­vectors, application to deep inelastic scattering and pp collisions at the LHC. Definition and relation of some commonly used kinematic variables, Q2, ν, y, xBJ, rapidity, s, u, t.
  • Theory of signal formation in electronic detectors ; the proportional chamber ; application of Ramo’s theorem on a simple detector geometry.
  • The Dirac equation : Motivation, basic concepts and interpretation of solutions in the relativistic and non-relativistic limits.
  • Interactions of heavy charged particles with matter ; Detailed derivation of the Bethe-­Bloch formula.
  • Helicity and chirality and their conservation in the high-­energy limit ; Angular distribution in e-­e+ -> μ-­μ+ scattering. Notation of “left” and “right” handed particles, mass terms in the Lagrangian.
  • Nuclear pairing and super-­fluidity, quasi particles and BCS (Bardeen, Cooper and Schrieffer) equations.
  • Data analysis : concepts of significance and exclusion limits. Application in the context of discovery of the Higgs particle.
  • Stationary perturbation theory, exemple of the Rayleigh-­Schrödinger method.
  • Concepts of group theory applied to subatomic physics : rotations, unitary and special unitary groups. The parton and quark model.
  • Physics of fast rotating nuclei, quantum numbers, the quantum-­Coriolis effect ; Rotation-­induced phase transition.
  • The Noether theorem and current conservation ; Global and local gauge invariance and fundamental interaction.
  • Explicit calculation of elementary cross sections : From the matrix elements and the phase space factors to the experiment-­comparable quantities.

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Student project (TI2P2)

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