High Energy Physics 390-FS2-1FWE
High Energy Physics is one semestral course of the subject. It includes 45 hours of the lecture and 45 hours of the discussion session (3 hours of the lecture and 3 hours of the discussion session per a week).
Educational profile: general academic.
Type of the studies: full-time.
Block (unit): theoretical physics, mandatory subject.
Field of knowledge and discipline of science: physical science, high energy physics.
Year of the studies, semester: 1st year, 8th semester, graduate studies.
Introductory conditions: course of analysis, course of algebra, course of classical mechanics, course of quantum mechanics, course of classical electrodynamics.
Didactic methods: lecture, solving the problems, homework, discussions, consultations, unassisted studying.
ECTS points: 9.
Balance sheet of the student's work: lecture (45 hours), discussion session (45 hours), homework (90 hours), discussions (5 hours), consultations (15 hours), unassisted studying (90 hours).
Quantitative indicators: lecture (2 ECTS points), discussion session (2 ECTS points), homework (2 ECTS points), discussions (0,5 ECTS points), consultations (0,5 ECTS points), unassisted studying (2 ECTS points).
The content is following:
1) Historical introduction. Works of Thomson and discovery of electron. Rutherford scattering - discovery of atomic nucleus. Works of Planck and Einstein, radiation of ideal black-body, ultraviolet catastrophe, beginning of quantum era, properties of photon, Compton scattering. Yukawa's theory of atomic nuclei binding forces, „mesons” named π. Appearance of relativistic quantum mechanics, works of Dirac, introduction of antiparticle idea, hole theory. Anderson's discovery of positron. Discussions on the nature of antielectron. Beta decay spectrum, necessity of new particle – neutrino. Discovery of next generations of leptons. Discovery of strange particles.
2) Estimate calculations of physical quantities. Scales of physical quantities. Dimension analysis: Gauss units, SI units, natural units in high energy physics and nuclear physics: ћ=1=c. Application of the uncertainty principle and relations: E=mc2 E=h*ni for estimate calculations of physical quantities and parameters. Comparison of Coulomb and Yukawa potentials. Coulomb potential in two and three dimensions. Stefan-Boltzmann and Wien's laws of ideal black-body radiation.
3) Eightfold way. Bootstrap. Strangeness. Multiplets: octet and decuplet of baryons, octets of mesons. Quark model: light quarks u and d. S quarks. Discovery of heavy quark flavours: c, b, t. Flavour quantum numbers. Supermultiplets of hadrons (weight diagrams with third, charm axis). Discovery of particles with non-zero heavy flavour quantum numbers. Intermediate bosons: photon, gluons, graviton, W± and Z° bosons. Standard Model: families (generations) of leptons and quarks.
4) Setting down of hadronic and leptonic quantum numbers. Symmetries of flavour and spin wavefunctions in multiplets of elementary particles. Flavour and spin wavefunction of pion. Flavour and spin wavefunction of proton. Magnetic moments of elementary particles: pion and proton. Isospin of elementary particles, third component of isospin. Isospin symmetry. Isospin multiplets. Application of isospin symmetry for deriving the relations between cross sections of processes with elementary particles.
5) Types of fundamental interactions and their general properties. Time scales of interactions. What do not we know about gravitation. Quantum electrodynamics (QED): gauge symmetry U(1), Feynman's diagrams, coupling constant, type(s) of vertice(s), higher order corrections. Quantum chromodynamics (QCD): gauge symmetry SU(3), types of vertices, nonlinaearity of QCD, colour confinement, asymptotic freedom. QED versus QCD: comparison of coupling constants and vertices. Vacua of QED and QCD. Comparison of running coupling constants.
6) Elements of Feynman's diagrams: wavefunctions, propagators, vertices. Drawing of Feynman's diagrams in QED and QCD. Feynman diagrams in Born's approximation. Higher order diagrams: wavefunction corrections, mass corrections, charge and magnetic moment corrections, other diagrams. Comparison of QED and QCD diagrams.
7) Properties of electroweak sector of interactions (EW): see above and also Higgs mechanism, quark diagrams, mixing of quark generations: Cabbibo-Kobayashi-Maskawa matrix (CKM), absence of flavour changing neutral currents (FCNC), Glashow-Illiopoulos-Maiani mechanism (GIM). Problems with elementary forces unification, due to energy dependence of coupling constants.
8) Drawing of Feynman's diagrams in EW theory. Forbidden vertices in EW interactions. Presence of flavour channging charged currents (FCCC). Absence of FCNC currents. Informations of Higgs potential. Illustrations of spontaneous symmetry breakdown scenario.
9) Absolute and approximate conservation laws in elementary particle physics. Conservation laws of: charge, baryon number, lepton numbers, four-momentum. Gauge symmetries and laws of charge conservation relevant to definite group of symmetry. Approximate law of flavour conservation. Okubo-Zweig-Iizuka rule (OZI).
10) Analysis of elementary particle processes with respect to absolute and approximate conservation laws. Approximate conservation laws in different fundamental interactions. Masses of stable particles in light of conservation laws of baryon and lepton numbers.
11) Operators of translations, hamiltonian, commutative condition of invariance. Rotational invariance: opearator of rotation, properties of hamiltonians due to rotation, angular momentum operator, algebra of angular momentum operator, spin of particles and its classification: bosons, fermions and anyons. Problem of angular momentum of hadrons in quark model, spectroscopic notation. Parity of fermion and boson wavefunctions, parity operator and its eigenvalues. Parity of fermion-antifermion systems, parity of pion, symmetric and antysymmetric wavefunctions, parity of photon.
12) Parity coservation and violation in the processes with elementary particles. Characteristic of elementary forces in context of parity. Examples of wavefunctions with definite and indefinite parity.
13) Charge conjugation, C-parity of pairs of charged bosons and fermions. Decay channels of pion π° and meson η°, decay widths and branching ratios for this particles. Combined parity CP. Time reversal, properties of time reversal operator (T), transformations of physical quantities and wavefunctions under the time reversal operation. The CPT symmetry. Positronium spectroscopy.
14) C-parity conservation and violation in the processes with elementary particles. Characteristic of fundamental interactions in context of C-parity. Combined parity (CP) conservation and violation in the processes with elementary particles. Characteristic of fundamental interactions in the light of combined parity. Analysis of allowed decay channels for neutral and charged pions and neutral meson eta. Decay widths and branching ratios for this processes. Discussion of quantum numbers of ground and excited states of positronium.
15) Phenomenology of strong interactions: jets, running coupling constant, three-jet events. R coefficient. Deep inelastic scattering, formfactor of proton, radius of proton. Parton model: structure functions, fragmentation functions, Callan-Gross relations, Björken's scaling, scaling violation. Role of gluons in parton model. Phenomenology of electroweak interactions: intermediate bosons decays, low-energy properties of the electroweak sector, Fermi's constant, leptoquark symmetry, K°-K° mixing, phenomenon of regeneration, strangeness oscillations.
16) Infinite momentum frame. Kinematic variables in process of electron – proton deep inelactic scattering or photon – proton deep inelastic scattering. Valence partons (quarks). Sea partons (quarks and gluons). Wee partons. Momentum and spin of hadron due to its parton structure. Altarelli-Parisi equations. Analysis of some processes in beam of neutral kaons.
17) Physics of hadrons. Quantum numbers and valence components of hadrons. Relation between charge and strangeness of hadrons. Probable exotic states of hadrons in light of colour confinement. Valence quark structure of probable exotic baryons and mesons. Strong and weak hypercharge. Isospin. Gell-Mann-Klein-Nishijima rule for isospin, charge and hypercharge. Processes of particles and resonances production. Breit-Wigner shape, decay width, lifetime. Discussion of quark diagrams in the case of processes with resonance states. Multiplets of excited mesons and baryons. Spin and radial excitations. Flavour, spin and colour wavefunctions of hadrons.
18) Deriving of hypercharge for hadrons ald leptons by different methods. Flavour quantum numbers and hypercharge of quarks. Analysis of some processes in the context of hypercharge conservation and violation. Quark diagrams for processes with hadrons: single particle decay, 2 in 2 colissions, cascade processes. Quantum number of exotic hadrons. Examples of spin and radial excitations.
19) Scattering in classical and quantum mechanics. Cross section. Elements of model independent theory of reactions. Scattering amplitude (scattering matrix). Fermi's golden rule. Width of decay. Phase space. Decay processes of the type 1→2+3+... . Processes of the type 1+2→3+4; general and massless case. Crossing symmetry.
20) Classical scattering for some potentials. Scattering in quantum mechanics. Special case – Rutherford scattering, giving the same results for both, classical and quantum mechanics. Formulae for scattering amplitudes of 1→2+3+... and 1+2→3+4 processes.
21) Perturbation calculus. Feynman's diagrams. Born approximations. Examples: λΦ3 model, λΦ4 model.
22) Calculation of lifetime of scalar particle in the λΦ3 and λΦ4 models.
23) Perturbative calculations for quantum electrodynamics. Feynman graphs. Compton scattering. Electron – electron scattering. Electron – muon scattering.
24) Perturbative deriving of differential cross section for scattering of electron on heavy nucleus.
25) Electron – positron pair annihilation. Rutherford scattering. Higher order processes: light – light scattering.
26) Some informations for higher order processes.
27) Elementary QCD processes in the perturbation calculus: quark – quark scattering, quark – gluon and gluon – gluon scattering (in Born's approximation).
28) Comparison of Born's approximation for QED and QCD processes.
29) Beyond the Standard Model: supersymmetry, string theory, cosmology. Some important and open questions.
30) Qualitative discussion onto chosen unification theories.
Discussion session embraces the same scope of the program as the lecture does and comprises its illustration.
Type of course
Mode
Requirements
Analysis I
Analysis II
Elements of Classical Electrodynamics
Elements of Quantum Mechanics
Elements of Theoretical Mechanics
Prerequisites
Analysis I
Analysis II
Elements of Classical Electrodynamics
Elements of Quantum Mechanics
Elements of Theoretical Mechanics
Prerequisites (description)
Course coordinators
Learning outcomes
A student:
1. Has enlarged knowledge of chosen parts of theoretical physics, he knows and comprehends fundamental ideas of theoretical physics, he understands mathematical models of chosen physical systems and phenomena.
2. Has deepen knowledge of mathematics in the subject of mathematical methods of physics.
3. Is capable to present understandingly basic theoretical concepts in chosen parts of physics and to bound them up with an experiment.
4. Can interpret results of experiments, basing on theoretical knowledge.
5. Is able to use understandingly mathematical methods of theoretical physics to quantitative and qualitative analysis of chosen physical systems and phenomena.
7. can understandingly and judgmentally examine professional literature and Internet sources, including in English, with regard to studied problems of physics.
7. Is capable to use known mathematical tools for defining and solving chosen problems of physics.
8. Can apply learned computer tools, among other things, programmes to symbolic computations for analysis of theoretical problems.
9. Is able understandingly and judgmentally examine professional literature and Internet sources, including in English, with regard to chosen problems of mathematics and computer science.
10. Realizes necessity of continuing enlargement of his knowledge and transmitting reliable and based on proofs knowledge from physics and its applications.
Labels:
K_W10, K_W11, K_U09, K_U10.
Assessment criteria
Students should be present on lectures and lessons of calculations. They are stimulated for asking the questions and initiating the discussion.
Written and oral examinations undergo after the end of the course of High Energy Physics. They verify acquirement of knowledge.
Students get the series of questions, exercises and problems for individual and unassisted solving. Content of the series of questions is correlated with the lecture. During the courses, students present solutions of given problems. Lecturer is advised to pay close attention to understanding used concepts and clarity of presentations. He stimulates students group for asking the questions and discussions. Lecturer tries to create sense of responsibility for team inside the students group and he encourages the group to joint work.
Assessment of student learning is based on the grade, which includes:
1. Ability to solve the problems from definite parts of high energy physics.
2. Ability to present the solutions.
3. Ability to discuss subjects and problems of the course.
4. Ability to use the literature and Internet sources.
5. Ability to collaborate inside the team.
6. Creative approach to solved problems.
Permanent grading by lecturer.
Final grade is expressed by the number established in the study regulation, which includes evaluation of the knowledge, abilities and competencies of the student.
Bibliography
1) D. J. Griffiths: "Introduction to Elementary Particles"
2) C. Leader, E. Predazzi: "An Introduction to Gauge Theories and Modern Particle Physics"
3) D. H. Perkins: "Introduction to High Energy Physics"
4) S. Weinberg: "The Quantum Theory of Fields", vol. 1, vol. 2, vol. 3
5) I. Białynicki-Birula, Z. Białynicka-Birula: "Quantum Electrodynamics"
6) A. Bechler: "Kwantowa teoria oddziaływań eklektromagnetycznych (in Polish)
Additional information
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