1. General parton distribution and structure of the hadrons
XXXIth International Workshop on
High Energy Physics
Protvino, July 5 –
General parton distribution and
structure of the hadrons
O.V. Selyugin

2. Contents * Introduction * Elastic hadron scattering – new data LHC
* Generalized parton distribution functions and hadron structure
* Comparing the data with High Energy Generalized structure model (HEGS)
* The structure of the scattering amplitude in t and b - representation
* Results and Summery

4. Total cross sections
TOTEM
ATLAS

5. Problems
Comment
Very likely that this difference reflects the true errors of the fitting procedure of the experimental data obtained by the luminosity independent method.

6. g The Very Low t Region P + s = |Ahadronic + ACoulomb|2
around t ~ (GeV/c) Ahadronic » ACoulomb
Þ INTERFERENCE
CNI = Coulomb – Nuclear Interference
scattering amplitudes modified to include also electromagnetic contribution
hadronic interaction described in terms of Pomeron (Reggeon) exchange
electromagnetic single photon exchange
s = |Ahadronic + ACoulomb|2
unpolarized Þ clearly visible in the cross section ds/dt
polarized Þ “left – right” asymmetry AN g P +
Alessandro Bravar
С П И Н 0 5

8. L.F. Kirilova, V.A.Nikitin,..V.A.Sviridov,……
J. of Nucl. Phys. , v.1, (1965) [JINR]

11. “One doesn’t know explicit form of the nucleon matrix element of the EM current”
A.Z. Dubnickova and S. Dubnicka
Hep-ph/

12. Standard definitions

13. The proton and neutron Dirac form factors follow from
By construction

14. Form factors Mittenen (1973) – “matter distribution”
Bourrely-Soffer-Wu (1978) -
G(t) –”stands for the proton “nuclear form factor” parameterized like the e-m form factor, as a two poles, the slowly varying function reflect the approximate proportionality between the charge density and hadronic matter distribution inside a proton.”
Broniowski – Arriola (2008)
"..The gravitation form factors, related to the matrix
elements of the energy-momentum tensor [1] in a hadronic
state and thus providing the distribution of matter within
the hadron..."

15. GPDs General Parton Distributions (GPDs) X.Ji Sum Rules (1997)
Fx=0 (x;t) = F (x;t)
Hq(x;t) = H q(x,0,t) + H q(-x,0,t)
Eq(x;t) = E q(x,0,t) + E q(-x,0,t)

16. General Parton Distributions (GPDs)
Sanielevici-Valin (1984) –Valon model – Phys.Rev.D29 (1984).
“matter form factor” (MFF) measures the interaction of a gluonic probe with the excited matter of the overlapping hadrons and should incorporate the static matter distributions of the participating hadrons…”

17. General Parton Distributions -GPDs
Transision form factors
Gravitation
form factors
(matter distribution)
Compton scattering form factors
Electromagnetic form factors
(charge distribution)

18. Martin – 2002 // H. KHANPOUR..-2012 (1205.5194)
Pumplin et al (CTEQ6M)
Martin et al (MRST02) .– Martin (LO, NLO, NNLO)
Gluck-Pisano 2008
Alekhin et al (ABM12)

19. 𝐹 1 𝑡 = 0 1 𝑑𝑥 2 3 𝑞 𝑢 𝑥 𝑒 2 𝛼 𝐻 𝑡 1−𝑥 2+ 𝜖 𝑢 𝑥 0 +𝑥 𝑚 − 1 3 𝑞 𝑑 (𝑥) 𝑒 2 𝛼 𝐻 𝑡 1−𝑥 2+ 𝜖 𝑑 𝑥 0 +𝑥 𝑚
0 1 𝑑𝑥𝑥 ℋ 𝑞 𝑥,𝑡 = 𝐴 𝑞 𝑡 ; 𝑑𝑥𝑥 ℰ 𝑞 𝑥,𝑡 = 𝐵 𝑞 𝑡 .
𝐴 𝑡 = 0 1 𝑥𝑑𝑥 𝑞 𝑢 𝑥 𝑒 2 𝛼 𝐻 𝑡 1−𝑥 2+ 𝜖 𝑢 𝑥 0 +𝑥 𝑚 + 𝑞 𝑑 𝑥 𝑒 2 𝛼 𝐻 𝑡 1−𝑥 1+ 𝜖 𝑑 𝑥 0 +𝑥 𝑚 ,

20. O.S. – PR (D 89)
(2014)

25. O.V.S., Phys. Rev., D 89, , 2014

26. Quarks contributions

27. O.V.S., (PEPAN), 45, 1, 37-39, 2014

29. M. Burkardt, Phys.Rev. D74 (2006)
O.V.S., O. Terayev, Phys.Rev.D79:033003,2009
The contribution in the density of the neutron
u-quark (hard line) and (- d) – quark (dashed line)

30. Transverse density
𝜌 𝑇 𝑁 𝑏 = 𝜌 0 𝑁 𝑏 +𝑆𝑖𝑛(𝜙) 1 2𝜋 0 ∞ 𝑑𝑞 𝑞 2 2 𝑀 𝑁 𝐽 1 (𝑞𝑏) 𝐹 2 ( 𝑞 2

31. Angular-dependent contribution to quark transverse density of the proton

32. Difference in the forms of charge density and “matter” density

33. The differential cross section for that reaction can be written as

34. O.V.S., Phys. Rev., D 89, , 2014

35. High Energy General Structure (HEGS) model O. V. S. - Eur. Phys. J
High Energy General Structure (HEGS) model O.V.S. - Eur. Phys. J. C (2012) 72:2073
Extending of model (HEGS1) – O.V. S. Phys.Rev. D 91, (2015)

36. UNITARIZATION  eikonal representation

37. BSW_1
BSW_2
AGN MN
HESG0
HESG1
369
955
980
3090
7+Regge 11 36
36+7
3+2
6+3
5-1800
9-7000
0.1 - 5
0,1-
2.6
0.1- 16 10 15
4.45
1.95
1.16
1.23 2.
1.28
N_exp.
n_par.

41. O.V. S. Nucl.Phys. A,959 (2017); arxiv: 1609.08847
13 TeV (line and points) and 7 TeV – dashed line
( The normalization of the 13 TeV data on the model calculations)

42. at energies s=9.8 GeV (dashed line), s=52.8 GeV (dash-dotted line),
The profile function Г(s,b): the real part (left) and imaginary part (middle)
at energies s=9.8 GeV (dashed line), s=52.8 GeV (dash-dotted line),
s=7 TeV (long dashed line), s=14 TeV (solid line).
he spin-flip amplitude in the b- representation (right) (solid line - eq.(12),
dashed line - eq.(13) long dashed line - with q factor and normal exponential form

43. Summary
# The elastic scattering reflects the generalized structure of the hadron.
# The our model GPDs leads to the well description of the proton and neutron electromagnetic form factors and its elastic scattering simultaneously.
# The new High Energy Generalized Structure model (HEGS) gives the quantitatively description of the elastic nucleon scattering at high energy with only 6 fitting high energy parameters.
# The slope of the differential cross sections at small t has the small
peculiarity and has the same properties in the whole examined energy
region. (It is require the further researches)
# The model leads to the good coincides the model calculations with the preliminary data at 13 TeV.
# The model open the new way to determine the true form of the GPDs and standard parton distributions.

44. THANKS
For your attention