Andrii Tykhonov, Ukraine, Odessa

1. Andrii Tykhonov, Ukraine, Odessa Education data: -bachelor diploma with honors of Odessa National Polytechnic University (2006) -master diploma with honors of Odessa National Polytechnic University (2008),“Department of Theoretical and Experimental Nuclear Physics”, speciality – nuclear and high-energy physics • Additional information: • -participant of Ukrainian physics and math Olympiads (took prize place in 2005) • -took part in work of department in field of Stochastic Resonance (created the device for generating the stochastic resonance events, 2005-2006) • -2007-… work in the field of high-energy physics in department: • Head of department – prof. Vitaliy Rusov. • Mentor – doc. Igor Sharf. • One published paper* (as co-author), and the other one is publishing now. • In 2008 was awarded by National Academy of Science in Ukraine for the article (one of the chapters of my diploma thesis) in this field of research and on January 2008 defenced my diploma thesis. *I.V. Sharf, A.J. Haj Farajallah Dabbagh, A.V. Tikhonov, V.D. Rusov “Mechanisms of hadron inelastic scattering cross-section growth in multiperipheral model within the framework of perturbation theory. Part 2” arXiv:0711.3690

2. p p π π p p Hadrons inelastic scattering Processes of type: 2→many (c) (a) Dependence of total inelastic scattering cross-section on energy (a,b- theory, c -experiment) 1. Sharf I.V., Rusov V.D. Mechanisms of hadron inelastic scattering cross – section growth in the multiperipheral model within the framework of perturbation theory. arXiv:hep-ph/0605110

3. P1 P3 q0 p1 q1 p2 pn qn P2 P4 The starting point of new approach in calculation of hadrons inelastic scattering cross-section Scattering amplitude in the vicinity of a point of maximum: ----exact value; ----expansion to the Taylor’s series (2-nd order) A -scattering amplitude

4. P1 P3 P3 P1 1 1 2 2 n n P2 P4 P2 P4 Problem of “interference contributions” -representation of inelastic scattering cross-section by-means of “cut” diagrams Cross-section of inelastic 2→2+n process is a sum of n! “interference” contributions -“cut” diagram, which puts the biggest contribution to the cross-section

5. -proton mass Lagrangian of interacting fields Scattering process: P1 and P2 –four-momentums of initial protons, P3 and P4 –final protons, pi –final π-mesons Lagrangian of two interacting scalar fieldsφandΦ: - model -π –meson mass λ, g –interaction parameters

6. -energy of initial particles in center of mass system Scattering cross-section and scattering amplitude Scattering cross-section: A - scattering amplitude -virtuality -n! summands

7. Problems in calculating of scattering cross-section Representation of cross-section as a sum of “cut” diagrams: Where every summand (here and further - interference contribution [1]) is –(3n+6) dimensional integral: • Multidimensional integral doesn’t split into a product of less-dimensional integrals • There are n! such integrals (interference contributions) to calculate

8. Virtualities are negative Peak-point of scattering amplitude Applying integration on 4 variables we get the new equation for interference contribution (without δ-function): - before integration

9. -value of scattering amplitude in a peak-point -matrix of second derivatives of amplitude logarithm (in a peak-point) -permutation matrix Representation of scattering cross-section Ethr≈2,7 Gev

10. n=8 n=10 n=14 Standart approach in amplitude calculations [2-4]: The growth of scattering amplitude with energy New approach in scattering amplitude calculation -scattering amplitude in a point of maximum [2] Amati D., Stanghellini A., Fubini S. Theory of High – Energy Scattering and Multiple Production // Il Nuovo Cimento. – 1962. - Vol. 26, № 5. - P. 896-937.P. [3] Collins Introduction to Rigge-theory and high-energy physics , “Atomizdat”,1980 [4] Nikitin U.P. Rozental I.L.High-energy physics . – , “Atomizdat”,1980

11. -interference contributions -matrix of second derivatives of amplitude logarithm in a peak-point Calculations of cross-sections at energies >>ETHRESHOLD Values of final particles momentums in a point of maximum:

12. Calculations of cross-sections at energies >>ETHRESHOLD(part 2) -contributions density (amount of Φi , which lies in an interval [θ, θ+d θ]) Sphere in (n-1)-dimensional subspace. (n=4)