Diffractive and electromagnetic processes at the LHC Trento, January 4-8, 2010 Dual model for J/Psi photoand electroproduction Collaboration: V.K. Magas вЂ“ University of Barcelona, Spain L.L. Jenkovszky вЂ“ BITP, Kiev, Ukraine A. Prokudin вЂ“ Jefferson Laboratory, USA R. Fiore вЂ“ Calabria University, Italy References: вЂњExclusive J/Psi electroproduction in a Dual ModelвЂќ вЂ“ Fiore, Jenkovszky, Magas, Melis, Prokudin, Phys. Rev. D80 (2009) 116001 вЂњJ/Psi Photoproduction in a Dual ModelвЂќ вЂ“ Fiore, Jenkovszky, Magas, Paccanoni, Prokudin, Phys. Rev. D75 (2007) 116005 "Off mass shell dual amplitude with Mandelstam analyticityвЂќ вЂ“ V. Magas, Physics of Atomic Nuclei 68 (2005) 104-113 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 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 b c d Duality means that the scattering can be described either based on the resonances or based on the reggeon exchanges equally well Veneziano Model The simplest mathematical realization of dual amplitude Only linear real Regge trajectories Two-body hadronic reactions вЂ“ 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 вЂ“ Veneziano amplitude Two-body hadronic reactions вЂ“ 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) 689 hypothesized that low-energy non-resonant background is dual to High-energy Pomeron exchange, or diffraction Can not be described in Veneziano model with infinitely narrow resonances Dual Model with Mandelstam analyticity (DAMA) Complex, non-linear trajectories Dual Model with Mandelstam analyticity (DAMA) How to model non-resonant background 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 are allowed and they are dual to the exchange of the Pomeron trajectory Diffraction can be studied uncontaminated by secondary trajectories J/Psi Photoproduction for D(s,t), D(u,t) only imaginary part is convergent D(s,t,u) converges for any values of s and t J/Psi Photoproduction Differential Elastic Cross-Section Differential Elastic Cross-Section Integrated Elastic Cross-Section The calculated curve is fully consistent with the date in the whole kinematical region. Regge assymptotic behaviour вЂњLow-energy diffractionвЂќ region: between threshold and Regge asymptotics Below 50 GeV non-asymptotic, non-Regge effects become important The contribution of the background is not anymore negligible 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 -t Large-x SF 0 Small-x SF s Modified DAMA Comparison with nucleon SF Comparison with nucleon SF J/Psi Electroproduction: generalization of the Dual Model Generalization of the Dual Model J/Psi Electroproduction Generalization of the Dual Model J/Psi Electroproduction R (Q ) пЂЅ пЃі L / пЃі T 2 Differential Elastic Cross-Section Experimental points are from ZEUS, NP B695 (04) 3 Experimental points are from H1, EPJ C46 (06) 585 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 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 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 Differential Elastic Cross-Section We predict that the shape of the cone (exponential decrease in t), an important characteristics of diffraction, survives at low energies Pomeron trajectory Pomeron trajectory Asymptotic properties of M-DAMA Comparison with nucleon SF (low x limit) Comparison with nucleon SF (large x limit) Off mass shell continuation of DAMA Two-dimensionally dual picture of strong interaction

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