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Andrii Tykhonov, Ukraine, Odessa. Education data: - bachelor diploma with honors of Odessa National Polytechnic University (2006) - PowerPoint PPT Presentation
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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
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