Generalized parton distributions from meson leptoproduction
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eneralized Parton Distributions from Meson Leptoproduction1, 2 P. Kroll Fachbereich Physik, Universität Wuppertal, D42097 Wuppertal, Germany Abstract—Generalized parton distributions (GPDs) extracted from exclusive meson leptoproduction within the handbag approach are briefly reviewed. Only the GPD E is discussed in some detail. Applications of these GPDs to virtual Compton scattering (DVCS) and to Ji’s sum rule are also presented. DOI: 10.1134/S1063779613060129 21
1. INTRODUCTION
2. THE DOUBLE DISTRIBUTION REPRESENTATION
The handbag approach to hard exclusive leptopro duction of photons and mesons (DVMP) off protons has extensively been studied during the last fifteen years. The handbag approach is based on factorization of the process amplitudes in a hard subprocess, e.g. γ*q → γ(M)q, and soft hadronic matrix elements parametrized in terms of GPDs. This factorization property has been shown to hold rigorously in the gen eralized Bjorken regime of large photon virtuality, Q, and large energy W but fixed xB. Since most data, in particular the data from Jlab, are not measured in this kinematical regime one has to be aware of power cor rections from various sources. Which kind of power corrections are the most important ones and have to be taken into account is still under debate. Nevertheless progress has been made in the understanding of the DVCS and DVMP data. In this talk I am going to report on an extraction of the GPDs from DVMP [1]. In this analysis the GPDs are constructed from double distributions (DDs) [2, 3] and the subprocess ampli tudes are calculated taking into account quark trans verse degrees of freedom as well as Sudakov suppres sion [4]. The emission and reabsorption of the partons by the protons are treated collinearly. This approach also allows to calculate the amplitudes for transversely polarized photons which are infrared singular in col linear factorization. The transverse photon amplitudes are rather strong for Q2 ⱗ 10 GeV2 as is known from the ratio of longitudinal and transverse cross sections [5]. I am also going to discuss several applications of the extracted set of GPDs like the calculation of DVCS observables from them [6] or the evaluation of the par ton angular momenta.
There is an integral representation of the GPD Fi = ˜ i , … (i = u, d, s, g) in terms of DDs [2, 3] H i, Ei, H 1 i
F ( x, ξ, t ) =
1– ρ
∫ dρ ∫
–1
dη δ ( ρ + ξη – x )f i ( ρ, η, t )
–1+ ρ 2
(1)
2
+ D i ( x, t )Θ ( ξ – x ), where D is the socalled Dterm [7] which appears for the gluon and flavorsinglet quark combination of the GPDs H and E. The advantage of the DD representa tion is that polynomiality of the GPDs is automatically satisfied. A popular ansatz for the DD is i
f i ( ρ, η, t ) = F ( ρ, ξ = 0, t )w i ( ρ, η ).
(2)
where the weight function wi that generates the skew ness dependence of the GPD, is assumed to be n
Γ ( 2n i + 2 ) [ ( 1 – ρ ) 2 – η 2 ] i w i ( ρ, η ) = 2n + 1 2 2n + 1 2 i Γ ( ni + 1 ) ( 1 – ρ ) i
(
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