Features of ds/dt at small t at LHC (elastic scattering)

1. Features of ds/dt at small t at LHC (elastic scattering) O.V. Selyugin(JINR Dubna)

2. With the construction of large accelarators, it is hoped that the mysteries of high-energy scattering will unfold in the near future. Hung Cheng, Tsai Tsun Wu Phys.Rev.Lett. (1970)

3. The r parameter linked to stot via dispersion relations sensitive to stot beyond the energy at which is measured predictions of stot beyond LHC energies Or, are dispersion relations still valid at LHC energies?

4. Problems Comment

6. Predictions

7. Usual assumptions or UA4/2 or TOTEM

9. Proton-proton

10. Proton-antiproton

16. Dependence of the slopeB(s,t) from the size of the examined interval t for UA4/2 experiment triangles – exponential form of F Circles - + additional term sqrt(-t) k F

17. Donnachie-Landshoff model; Schuler-Sjostrand model Soft and hard Pomeron

18. Dubna Dynamical Model

19. Impact parameter representation and unitarization schemes Eikonal R.Arnold (1964). N.Nikolaev, E.Predazzi (1993) K-matrix R.Blankenberger, M.Goldberger(1962); S.Troshin, N.Tyurin (1993) ; L.Jenkovszky et. all. U-matrix

20. Eikonal represantation Ratio - Im T(s,t)/Re(s,t) (Soft+hard Pomeron)

21. Eikonal represantation Slope of the differential cross sections

22. LHC 14 TeV Simulation of the experimental data by the model with non-exponential behavior of B(s,t) and r( s,t) N=90

23. J.-R. Cudell, O.V. Selyugin, Phys.Rev.Lett. , 102 (2009) 0320003

24. Non-exponetial t-dependence stot = 152.5 mb; r = 0.24 (t=0); B(t=0) = 21.4 GeV-2; rfix = 0.15; stot = 155.3+/-0. 5; nfix = 1; B = 23.1+/-0.15; stot = 180+/- 2.1; rfix = 0.15; B = 23.2+/-0.15; n = 0.74+/0.07; stot = 153.4+/- 0.7; r = 0.26; B = 23.5+/-0.17; nfix = 1; stot = 142.3+/- 2.8; r = 0.29; B = 23.6+/-0.19; nfix = 1.15+/0.04;

25. Features - DR

26. Experiment ISR

27. Experiment ISR Polynomial fit 6 parameters

28. Proton-proton elastic scattering at LHC COMPETE values

29. AKM theorem(G.Anderson, T. Kinoshita, A. Martin) The regime of the maximal axiomatic growth of F(s,t) [Im F(s,t) ~ Re F(s,t) ~ Ln2(s)] Allowed by asymptotic theorem The scattering amplitude must have infinity many zerous in a very nerow region of t

33. Statistical independent choices

35. 1 1 1 1 1 1 1 2 2 2 2 2 2 2

36. stot = 62.2 mb; B = 15.5 GeV-2; r = 0.135; Proron-antiproton UA4/2 - parameters

37. 1 1 1 1 1 1 1 2 2 2 2 2 2 2

38. stot = 63.54 mb; B = 15.485 GeV-2; r = 0.158; New parameters (model fit)

39. END

40. The experiments on the proton elastic scatteringoccupy the important place in the reserch program at LHC. • Non-linear equations correspound to the different form of the unitarization schemes. They have the same assymptotic regime. They lead to the non-exponential behavior of the scattering amplitude.. • The additional researches is needed. • Very likely that BDL regime will be reached at LHC energies. It will be reflected in the behavior of B(t) and r(t). Summary • The effects have to be account in the fitting procedure of all 4 values – L, s, B, r simulteniously.

41. To reserch of the non-lenear behavior of the parameters of the scattering amplitude it is neeed to develop new methods. • The new method of the determination of the real part of the elastic hadron amplitude give the possibility to find the special features in its behavior • The non-fitting (statistical) method can shows the existance some oscillations in the differential cross sections and help to check up the values ofL, s, B, r Summary