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

Hadrons inelastic scatteringp

p

p

π

π

p

Processes of type: 2→many

Dependence of total inelastic scattering cross-section on energy (a,b- theory, c -experiment)

(a)

(c)

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

The starting point of new approach in calculation of hadrons inelastic scattering cross-section

221

20 1

1

1

1

1

1

nqqqA

AA

A

lnexp

0

P2

p1

P1 P3

P4

p2

pn

q0

q1

qn

A -scattering amplitude

Scattering amplitude in the vicinity of a point of maximum:

----exact value; ----expansion to the Taylor’s series (2-nd order)

000 ˆˆˆˆˆexp XXDXXAA

T

4

Problem of “interference contributions”

Cross-section of inelastic 2→2+n process is a sum of n! “interference” contributions

P2

P1 P3

P4

1

2

n

P3

P4 P2

P1

1

2

n

-“cut” diagram, which puts the biggest contribution to the cross-section

-representation of inelastic scattering cross-section by-means of “cut” diagrams

5

Lagrangian of interacting fields

P1 and P2 –four-momentums of initial protons, P3 and P4 –final protons, pi –final π-mesons

Scattering process:

GeVM 938.0 -proton mass GeVm 139.0 -π –meson mass

322222

2

1

2

1

gmxx

gMxx

gLba

abba

ab

Lagrangian of two interacting scalar fields φ and Φ:

λ, g –interaction parameters

"" 3 - model

6

Scattering cross-section:

n

ikn

n

n PPpPPApdpdPdPdMssn

g

12143

42143

2

24

...4!

~

Scattering cross-section and scattering amplitude

s -energy of initial particles in center of mass system A - scattering amplitude

2

31

iipPP -virtuality

-n! summands

7

Problems in calculating of scattering cross-section

n

n

iii

iiii

pppPPAipppPPmipPPmiPPm

,...,,,,...

11121

211

31231

231

231

Representation of cross-section as a sum of “cut” diagrams:

n

ikiiinn PPpPPpppPPApppPPApdpdPdPd

n1

21434

312131143 ,...,,,,,...,,,,...~21

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

Peak-point of scattering amplitudeApplying integration on 4 variables we get the new equation for interference contribution (without δ-function):

niiinnnn pppppPPApppppPPApdpdPd ,...,,,,...,,,...,,,,...,,...~211312113114

ipppPPm

ippPPmpppppPPA

virtualityngativenk

invirtualityngative

n

iiin

k

n

|_______________________|

2

..1131

|___________|

2131

131

,...,

1

,...,

1,...,,,,...,,

21

0 Virtualities are negative

0,...,,,,...,,Im21131

niiin pppppPPA 0,...,,,,...,,21131

niiin pppppPPA

- before integration

9

Representation of scattering cross-section

!

1

23

1

2,024!

1

23

1

2''2,024

!

1

23

1

02,024

1~exp~

ˆˆˆˆˆˆˆˆˆˆˆ2

1exp~

n

i

n

i i

nnn

i

n

iiii

nnn

n

i

n

ii

Ti

Ti

Ti

nnn

aAgXadXAg

XPDDXXPDPDXdXAg

nA ,0

D̂

iP̂

-value of scattering amplitude in a peak-point

-matrix of second derivatives of amplitude logarithm (in a peak-point)

-permutation matrix

1n

ninelastic

Ethr≈2,7 Gev

10

The growth of scattering amplitude with energy

Standart approach in amplitude calculations [2-4]:

2

..1

2

21

2

1 1

1

1

1

1

1

nk

kpppp

A1

,...,2,10

ni

pi

A

[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

12

1

2

1

122

1

2,0

1

1

1

11

n

n

n

n

n

mS

mS

mS

A

n=8 n=10 n=14

nA ,0 nA ,0 nA ,0

New approach in scattering amplitude calculation

2,0~ nn A

-scattering amplitude in a point of maximum

11

Calculations of cross-sections at energies >>ETHRESHOLD

Values of final particles momentums in a point of maximum:

!

12

2,024

~n

ii

nn

n s

Ag !..1, nii -interference contributions

nyy 1

0

ip

yyy ii 1

yy 21

yy 2

03 y

yy 4

yy 25

m

parshy

i

i

nyyyY ,...,,ˆ21

niiii yyyY ,...,,ˆ

21

;0,ˆˆ

ˆˆcos

YY

YY i

Inte

rfer

ence

co

ntr

ibu

tion

D

YDY T

idet

ˆˆˆ2

1cosexp

D̂ -matrix of second derivatives of amplitude logarithm in a peak-point

12

Calculations of cross-sections at energies >>ETHRESHOLD

(part 2)

d

dN -contributions density (amount of Φi , which lies in an interval [θ, θ+d θ])

1,...,1,1,...,,ˆ21

niiii yyyY

!..1,,ˆˆ nkiYY ki

Sphere in (n-1)-dimensional subspace. (n=4)

0

3

3

sin

sin!

d

nd

dN

n

n

Dis

trib

uti

on f

un

ctio

n

0

300

0

3

2,0

2

24

sinˆˆˆ2

1cosexp

sin

!dXDX

d

A

s

gn nT

n

nn

n