One of the observables in the high energy experiment is multiplicity - the number of secondary particles. The most popular one is multiplicity of charged particles. Experimenters also restore multiplicity of neutral particles. The main statistical characteristics of multiplicity are its mean value and a variance. pQCD allows us to calculate hard processes but it has a hard time with description of the hadronisation stage. Two stage model offers to add to the quark-gluon stage the phenomenological hadronization stage and calculate multiplicity distribution for electron-positron annihilation. The comparison of this model with data demonstrates good agreement.
Tasks
1) Calculations of multiplicity distributions (MD) for charged particles in e+ e- annihilation at high energy in the framework of Two-Stage Model (TSM). 2) Calculations of the average multiplicity, variance and second correlation moment for quark and gluon jets based on pQCD, and the same values for MD of hadrons.
2) Acquaintance with the work of the main detectors at the HEP experiments: vertex silicon detector, gas tracker, magnet, electromagnetic calorimeter, just to name a few.
3) Calculation of the factorial moments F_q and the factorial cumulative moments K_q by using MD P_n and/or the generation function G(z).
4) Calculate MD, its average multiplicity and variance for upsilon (bottomonium) decay.
Preliminary schedule by topics/tasks
(1st week) The construction of the differential equations based on the Markov's branching for getting of multiplicity distributions in q-and g-jets.
(2nd week) Justification for choice of multiplicity distributions at the hadronisation (second stage) and the convolution of both stages. (3rd week) Calculations of the average value, variance and second correlation moment for quark and gluon jets based on pQCD, and for hadrons. (4th week) The description of experimental data on multiplicity distributions by the two stage model. Definition of parameters of both stages. (5th week) Multiplicity distribution for three-gluon decay of heavy quarkoniums (bottomonium). (6th week) Factorial and cumulative moments, their ratio for multiplicity distributions in the two stage model. Report.
Required skills
probability theory and statistical physics, Markovian branching processes, e+e- annihilation, quantum chromodynamics
Acquired skills and experience
software: work with cernroot packet, fitting tasks
Recommended literature
1. Giovannini A. Nucl.Phys. B161(1979)429.
2. Kuvshinov V.I., Kokoulina E.S. Acta Phys.Pol.B13 (1982) 533.
3. Niczyporuk, B. Charged hadron production in e+e− annihilation in the Υ and Υ′
LENA Collaboration. Z. Physics C. 1981. Vol. 9. 1-8. 4. N. Barlykov, V. Dudin, E. Kokoulina, V. Nikitin. Phenomenology of High Multiplicity in Lepton Interactions. Physics of atomic nuclei. 87 (2024) 471-475. 5. E. Kokoulina and A. Kutov. Gluon dominance model. European Physical Journal Web of Conferences. 138 , 07007. 6. Henley, E.M. Subatomic physics. Ernst M.Henley and Alejandro Garcia. Third edition. World Scientific. 2007 . 7. Dokshitzer, Yu.L. Hard semi-inclusive processes in QCD. Physics Letters B. – 1978. – Vol. 78. – P. 290-294.
