Exclusive Meson Production at NLO

Generalized parton distributions (GPDs) are a versatile tool to quantify important aspects of hadron structure in QCD. They contain unique information on the spatial distribution of partons [1] and on the orbital angular momentum they carry in the proton [2]. The theoretically cleanest process where GPDs can be studied is deeply virtual Compton scattering (similar to inclusive DIS, which plays a dominant role in constraining the usual parton densities). Hard exclusive meson production is harder to describe quantitatively, but it provides opportunities to obtain important complementary constraints. In particular, vector meson production is more directly sensitive to the gluon distributions, which enter the Compton amplitude only at next-to-leading (NLO) order in αs. Together with a wealth of high-quality data [3], this warrants efforts to bring meson production under theoretical control as much as possible. In the present contribution [4] we investigate exclusive ρ production (γ∗p → ρp) using collinear factorization, which is applicable in the limit of large photon virtuality Q at fixed Bjorken variable xB and fixed invariant momentum transfer t to the proton [5]. In practical terms, this means that the description is restricted to sufficiently large Q but can be used for both small and large xB , thus providing a common framework for analyzing both collider and fixed-target data. The process amplitude can then be expressed in terms of GPDs for the proton, the qq̄ distribution amplitude for the ρ, and hard-scattering kernels. The kernels are known to NLO, i.e. to order α2s [6]. The requirement of “sufficiently large” Q is demanding for meson production. Contributions that are formally suppressed by powers of 1/Q cannot be calculated in a completely systematic way, but the estimates [7, 8, 9] agree that for Q of several GeV the effect of the transverse quark momentum inside the meson cannot be neglected in the hard-scattering subprocess, as it is done in the collinear approximation. This effect can be incorporated in the modified hard-scattering picture [7, 8], in color dipole models [9], or in the MRT approach [10]. Unfortunately, the calculation of αs corrections remains not only a technical but even a conceptual challenge in these approaches, so that the perturbative stability of their results cannot be investigated at present. One strategy in this situation is to study the NLO corrections in the collinear factorization framework, identifying kinematical regions where they are moderate or small. There one may use formulations incorporating power corrections from transverse quark momentum with greater confidence. This is the aim of the present contribution. In the following we show results for the convolution of the unpolarized quark and gluon GPDsH andH with the corresponding hard-scattering kernels and the asymptotic form of the ρ distribution amplitude. We model the GPDs using a standard ansatz based on double