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 arXiv0711.3690
2
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. arXivhep-ph/0605110
3
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 Taylors series (2-nd order)
A -scattering amplitude
4
Problem of interference contributions
-representation of inelastic scattering
cross-section by-means of cut diagrams
Cross-section of inelastic 2?2n process is a sum
of n! interference contributions
-cut diagram, which puts the biggest
contribution to the cross-section
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Lagrangian of interacting fields
Scattering process
P1 and P2 four-momentums of initial protons, P3
and P4 final protons, pi final
p-mesons

Lagrangian of two interacting scalar fields f
and F
- model
-p meson mass
?, g interaction parameters
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Scattering cross-section and scattering amplitude
Scattering cross-section
A - scattering amplitude
-virtuality
-n! summands
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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 (3n6)
dimensional integral

• Multidimensional integral doesnt split into a
  product of less-dimensional integrals
• There are n! such integrals (interference
  contributions) to calculate

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Peak-point of scattering amplitude
Applying integration on 4 variables we get the
new equation for interference contribution
(without d-function)
- before integration
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Representation of scattering cross-section
Ethr2,7 Gev
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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
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Calculations of cross-sections at energies
gtgtETHRESHOLD
Values of final particles momentums in a point of
maximum
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Calculations of cross-sections at energies
gtgtETHRESHOLD(part 2)
-contributions density (amount of Fi , which lies
in an interval ?, ?d ?)
Sphere in (n-1)-dimensional subspace. (n4)