Abstract
Abstract We use recent results for the $ \gamma_L^{*}\to {\rho_L} $ and $ \gamma_T^{*}\to {\rho_T} $ impact factors, computed in the impact parameter representation within the collinear factorization scheme, to get predictions for the polarized cross-sections σ T and σ L of the diffractive leptoproduction of the ρ meson at high energy. In this approach the helicity amplitude is a convolution of the scattering amplitude of a color dipole with a target, together with the virtual gamma wave function and with the first moments of the ρ meson wave function (in the transverse momentum space), given by the distribution amplitudes up to twist 3 for the $ \gamma_T^{*}\to {\rho_T} $ impact factor and up to twist 2 for the $ \gamma_L^{*}\to {\rho_L} $ impact factor. Combining these results with recent dipole models fitted to DIS data, which include saturation effects, we show that the predictions are in good agreement with HERA data for photon virtuality (Q 2) larger than typically 5 GeV2, without free parameters and with a weak dependence on the choice of the factorization scale, i.e. the shape of the DAs, for both longitudinally and transversely polarized ρ meson. For lower values of Q 2, the inclusion of saturation effects is not enough to provide a good description of HERA data. We believe that it is a signal of a need for higher twist contributions in the ρ meson DAs. We also analyze the radial distributions of dipoles between the initial γ * and the final ρ meson states.
Highlights
Polarized and total cross-sections describing the hard exclusive productions of the ρ and the φ vector mesons V in the process γ∗(λγ) p → V p
We use recent results for the γL∗ → ρL and γT∗ → ρT impact factors, computed in the impact parameter representation within the collinear factorization scheme, to get predictions for the polarized cross-sections σT and σL of the diffractive leptoproduction of the ρ meson at high energy. In this approach the helicity amplitude is a convolution of the scattering amplitude of a color dipole with a target, together with the virtual gamma wave function and with the first moments of the ρ meson wave function, given by the distribution amplitudes up to twist 3 for the γT∗ → ρT impact factor and up to twist 2 for the γL∗ → ρL impact factor. Combining these results with recent dipole models fitted to deep inelastic scattering (DIS) data, which include saturation effects, we show that the predictions are in good agreement with HERA data for photon virtuality (Q2) larger than typically 5 GeV2, without free parameters and with a weak dependence on the choice of the factorization scale, i.e. the shape of the DAs, for both longitudinally and transversely polarized ρ meson
The third approach, valid down to W ∼ Q, was initiated in [25] and [26]. It is based on the collinear QCD factorization scheme [27, 28]; the amplitude is given as a convolution of quark or gluon generalized parton distributions (GPDs) in the nucleon, the ρ-meson DA, and a perturbatively calculable hard scattering amplitude
Summary
3.1 Impact factors γL∗,T → ρL,T In the Sudakov basis, the longitudinal and transverse polarizations of the photon are. The color factor T r(ta tb) = δab/2, with a and b color indices functions ψ(γqL∗q→) ρL , ψ(γqT∗q→) ρT , ψ(γqT∗q→g)ρT are respectively the and Nc the amplitudes of production of a ρ meson from a quark-antiquark (quark-antiquark gluon) system produced far upstream the target in the fluctuation of the virtual photon. These functions are computed up to twist 3 in the collinear approximation in ref. Where the function F γT∗ describes the fluctuation of the transversely polarized photon into a quark-antiquark-gluon color singlet. × y1y2ΨγL∗ (μ1, r; Q) + y2y1ΨγL∗ (μ2, r; Q) − ygΨγL∗ (μqg, r; Q)
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