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Oleg V. Selyugin

ASI-2008 « SYMMETRY and SPIN ». PRAHA -2008. Oleg V. Selyugin. Spin-flip amplitude in the impact parameter represantation. BLTPh,JINR. Introduction Structure of hadron elastic scattering amplitude Non-linear equations and saturation

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Oleg V. Selyugin

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  1. ASI-2008 « SYMMETRY and SPIN » PRAHA -2008 Oleg V. Selyugin Spin-flip amplitude in the impact parameter represantation BLTPh,JINR

  2. Introduction • Structure of hadron elastic scattering amplitude • Non-linear equations and saturation • Basic properties of the unitarization schemes • b-dependence of the phases • Analysing power in different unitarization schemes • Summary

  3. Total cross-section • Understand the asymptotic behavior of stot • new (precise) data to constraint the fit: stotvs (ln s)g • 1% error  ~1mb

  4. Predictions

  5. Pomerons stot(s)~ Regge theory Landshoff 1984 – soft P a = 0.08 Simple pole – (s/s0)a Double pole – Ln(s/s0) Triple pole – Ln2(s/s0) +C 1976 BFKL (LO) - P -a2 = 0.4 a2 = 0.45 1988 HERA data (Landshoff ) – hard P 2005 – Kovner – 7 P -ai = 0. ..0.4. .0.8

  6. Regge limit for fixed t The crossing matrix factorized in the limit the Regge-pole contributions to the helicity amplitudes in the s-chanel when exchanged Regge poles have natural parity

  7. Impact parameter representation

  8. Unitarity in impact parameter representation S S+ = 1

  9. Saturation bound

  10. Non-linear equation (K-matrix)

  11. Non-linear equation (eikonal)

  12. Eikonal and K-matrix

  13. Eikonal and K-matrix

  14. Interpolating form of unitarization

  15. Normalization and forms of unitarization Low energies

  16. Inelastic cross sections eikonal U-matrix

  17. Asymptotic features of unitarization schemes Low energies High energies

  18. Effect of antishadowing S. Troshin (hep-ph/0701241 v4 June 4 « Black Disk Limit is a direct consequence of the exponential unitarization with an extra assumption on the pure imaginary nature of the phase shift » Renormalized eikonal

  19. 2 TeV

  20. 14 TeV

  21. Corresponding phases

  22. Renormalization of the U-matrix - K-matrix

  23. RHIC beams +internal targets º fixed target mode Ö s ~ 14 GeV

  24. Analysing power

  25. Eikonal case

  26. K-matrix U-matrix

  27. A N - eikonal

  28. A N - eikonal

  29. A N – Born term

  30. A N – K-matrix

  31. A N – K-matrix

  32. A N – UT-matrix

  33. A N – UT-matrix

  34. A N – UT-matrix (New fit of from

  35. Summary • Unitarization effects is very important for the description spin correlation parameters at RHIC • Non-linear equations correspond to the different forms of the unitarization schemes. They can have the same asymptotic regime. • An interpolating form of unitarization can reproduce both the eikonal • and the K-matrix (extended U-matrix} unitarization

  36. Summary • The true form of the unitarization, which is still to be determined, • can help to determine the form of the non-linear equation, • which describes the non-perturbative processes at high energies.

  37. END

  38. The experiments on proton elastic scattering occupy • an important place in the research program at the LHC. It is very likely that BDL regime will be reached at LHC energies. It will be reflected in the behavior of B(t) and r(t).

  39. Double Spin Correlation parameter

  40. The Elastic Process: Kinematics scattered proton (polarized) proton beam RHIC beams + internal targets º fixed target mode Ö s ~ 14 GeV polarized proton target or Carbon target recoil proton or Carbon essentially 1 free parameter: momentum transfer t = (p3 – p1)2 = (p4 – p2)2 <0 + center of mass energy s = (p1 + p2)2 = (p3 – p4)2 + azimuthal angle j if polarized ! Þ elastic pp kinematics fully constrained by recoil proton only ! Alessandro Bravar

  41. Complex eikonal and unitarity bound

  42. Some AN measurements in the CNI region pC Analyzing Power E950@BNL p = 21.7 GeV/c PRL89(02)052302 pp Analyzing Power E704@FNAL p = 200 GeV/c PRD48(93)3026 no hadronic spin-flip with hadonic spin-flip AN(%) no hadronic spin-flip r5pCµ Fshad / Im F0had Re r5 = 0.088 ± 0.058 Im r5 = -0.161 ± 0.226 highly anti-correlated -t Alessandro Bravar

  43. Spin correlation parameter - AN ANbeam (t ) = ANtarget (t ) for elastic scattering only! Pbeam = Ptarget . eB / eT

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

  45. Such form of U-matrix does not have the BDL regime Predictions at LHC (14 TEV)

  46. Corresponding phases

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