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Dual model for J/Psi photo - Workshop

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Diffractive and electromagnetic processes at the LHC
Trento, January 4-8, 2010
Dual model for J/Psi photoand electroproduction
V.K. Magas – University of Barcelona, Spain
L.L. Jenkovszky – BITP, Kiev, Ukraine
A. Prokudin – Jefferson Laboratory, USA
R. Fiore – Calabria University, Italy
“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
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
Simplest interpretation:
Duality is a property of the scattering amplitude, which reflects the
connection between low-energy (resonance) and high-energy (Regge)
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 – 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) 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)
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
“Low-energy diffraction” region: between threshold and Regge asymptotics
Below 50 GeV
non-Regge effects
become important
The contribution
of the background
is not anymore negligible
Generalization of our model to describe
J/Psi electroproduction
off mass shell continuation of DAMA
Modified DAMA (M-DAMA):
V.K. Magas, Yadernaya Fizika (Phys. Atom. Nucl.) 68 (2005) 106
Large-x SF
Small-x SF
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
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
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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