Next-to-leading logarithmic QED radiative corrections will be evaluated for several processes of elementary particle interactions at high energies. The formalism of electron (photon) structure and fragmentation functions will be applied. A few general lectures on the Standard Model phenomenology will be given in addition.
Tasks
1. Learn the standard QCD factorization formalism in the collinear leading logarithmic approximation.
2. Consider the modification of this formalism for the case of quantum electrodynamics.
3. Get experience in analytic convolution of typical functions including polylogarithms.
4. Reproduce several analytic calculations of next-to-leading corrections to cross-sections of particle interactions.
5. Get new results for an analogous interaction process.
Preliminary schedule by topics/tasks
1st week: studying the standard leading logarithmic approximation and collinear factorization theorem.
2nd week: exercises in construction of QED radiative corrections to several processes within the leading logarithmic approximation.
3rd week: exercises in solving evolution equations within perturbative QED.
4th week: evaluation of analogous calculations in the next-to-leading level following the known examples.
5th week: getting new results for some relevant high-energy processes (for advanced students).
Required skills
1. A basic knowledge in particle physics.
2. Knowing quantum field theory (medium level).
3. Computer skills: Mathematica, LaTeX.
Acquired skills and experience
Students will become familiar with the actual problems of the phenomenology of high energy physics. Experience in construction of high-precision theoretical predictions will be acquired. The method of collinear structure functions will be mastered in the next leading approximation, which is common for QED and QCD. A journal publication is possible upon sufficient results achieved.
Recommended literature
1. G. Altarelli, "Partons in Quantum Chromodynamics", Phys.Rept. 81 (1982) 1 DOI: 10.1016/0370-1573(82)90127-2
2. M. Skrzypek, "Leading logarithmic calculations of QED corrections at LEP,'' Acta Phys. Polon. B 23 (1992), 135-172
3. A.B. Arbuzov, "Leading and Next-to-Leading Logarithmic Approximations in Quantum Electrodynamics,'' Phys. Part. Nucl. 50 (2019) no.6, 721-825
