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Volodymyr Magas

Diffractive and electromagnetic processes at the LHC Trento, January 4-8, 2010. Volodymyr Magas. University of Barcelona, Spain. Dual model for J/Psi photo- and electroproduction. Collaboration:. V.K. Magas – University of Barcelona, Spain

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Volodymyr Magas

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  1. Diffractive and electromagnetic processes at the LHC Trento, January 4-8, 2010 Volodymyr Magas University of Barcelona, Spain Dual model for J/Psi photo- and electroproduction

  2. Collaboration: V.K. Magas– University of Barcelona, Spain L.L. Jenkovszky– BITP, Kiev, Ukraine A. Prokudin– Jefferson Laboratory, USA R. Fiore – Calabria University, Italy References: “Exclusive J/Psi electroproduction in a Dual Model” – Fiore, Jenkovszky, Magas, Melis, Prokudin, Phys. Rev. D80 (2009) 116001 “J/Psi Photoproduction in a Dual Model” – Fiore, Jenkovszky, Magas, Paccanoni, Prokudin, Phys. Rev. D75 (2007) 116005 "Off mass shell dual amplitude with Mandelstam analyticity” –V. Magas, Physics of Atomic Nuclei 68 (2005) 104-113

  3. Plan of the talk • Duality, Dual Model with Mandelstam analyticity (DAMA) • Dual model for J/Psi photoproduction; data fitting • Extending DAMA off mass shell • Generalization of the model for J/Psi electroproduction; data fitting

  4. Duality Simplest interpretation: Duality is a property of the scattering amplitude, which reflects the connection between low-energy (resonance) and high-energy (Regge) domains a c b d Duality means that the scattering can be described either based on the resonances or based on the reggeon exchanges equally well

  5. Veneziano Model The simplest mathematical realization of dual amplitude Only linear real Regge trajectories

  6. Two-body hadronic reactions – 1st class Go with the formation of the resonances in s-channels, and with exchange of particles/Regge trajectories in t-channel. Low-energy resonances are dual to high-energy Regge asymptotics Simplest approach – Veneziano amplitude Two-body hadronic reactions – 2nd class Do not exhibit resonances at low energies, and high-energy behavior is governed by the exchange of vacuum Regge trajectory, the Pomeron, Harari, PRL 22 (69) 562; Rosner, PRL 22 (69) 689hypothesized that low-energy non-resonant backgroundis dual to High-energy Pomeron exchange, or diffraction Can not be described in Veneziano model with infinitely narrow resonances

  7. Dual Model with Mandelstam analyticity (DAMA) Complex, non-linear trajectories

  8. Dual Model with Mandelstam analyticity (DAMA)

  9. How to model non-resonant background

  10. J/Psi Photoproduction Photoproduction of vector mesons is well described in the vector meson dominance model: J/Psi-p scattering is an ideal tool to study diffraction: in the direct channel only exotic trajectories areallowed and they are dual to the exchange of the Pomerontrajectory Diffraction can be studied uncontaminated by secondarytrajectories

  11. J/Psi Photoproduction for D(s,t), D(u,t) only imaginary part is convergent D(s,t,u) converges for any values of sandt

  12. J/Psi Photoproduction

  13. Differential Elastic Cross-Section Fiore, Jenkovszky, Magas, Paccanoni, Prokudin PRD75 (07) 116005

  14. Differential Elastic Cross-Section

  15. Integrated Elastic Cross-Section Prediction ! The calculated curve is fully consistentwith the date in the wholekinematical region.

  16. Regge assymptotic behaviour “Low-energydiffraction” region: between threshold and Reggeasymptotics Below 50 GeV non-asymptotic, non-Regge effects become important The contribution of the background is not anymore negligible

  17. Generalization of our model to describe J/Psi electroproduction requires off mass shell continuation of DAMA Modified DAMA (M-DAMA): V.K. Magas, Yadernaya Fizika (Phys. Atom. Nucl.) 68 (2005) 106

  18. -t Large-x SF Small-x SF 0 s

  19. Modified DAMA

  20. Comparison with nucleon SF

  21. Comparison with nucleon SF

  22. J/Psi Electroproduction: generalization of the Dual Model

  23. Generalization of the Dual Model

  24. J/Psi Electroproduction Generalization of the Dual Model Martynov, Predazzi, ProkudinPRD 67 (2003) 074023; EPJ C26 (2003) 271

  25. J/Psi Electroproduction Fiore, Jenkovszky, Magas, Melis, Prokudin, PRD80 (09) 116001

  26. Differential Elastic Cross-Section Experimental points are from ZEUS, NP B695 (04) 3 Experimental points are from H1, EPJ C46 (06) 585

  27. Integrated Elastic Cross-Section Data are from H1 and ZEUS The agreement with data is also fairly good, however, one can notice that the fits deteriorate progressively as Q2 increases

  28. J/Psi Electroproduction Why our fits deteriorate progressively as Q2 increases ? The main reason is the violation of the crossing symmetry in the model ! However , in the off-shell case, the (s-u) symmetry is progressively violated as Q2 increases More advanced form of the total amplitude should be used

  29. Conclusions Dual models allow us to calculate scattering amplitude in whole kinematic region Our dual model, based on DAMA and super-broad-resonance approximation, reproduces very well J/Psi photoproduction data Generalized model, based on off shell M-DAMA, is in a good agreement with the J/Psi electroproduction data These models offer a complementary approach to soft dynamics of strong interaction, namely to its component dominated by the diffraction, which is beyond the scope of pQCD Such a technique can be used for a background parameterization in other reactions Further development is necessary

  30. Differential Elastic Cross-Section We predict that the shape of the cone (exponentialdecrease in t), an important characteristics of diffraction, survives at low energies

  31. Pomeron trajectory

  32. Pomeron trajectory

  33. Asymptotic properties of M-DAMA

  34. Comparison with nucleon SF (low x limit) Now everything is fixed !

  35. Comparison with nucleon SF (large x limit)

  36. Off mass shell continuation of DAMA

  37. Two-dimensionally dual picture of strong interaction

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