Deeply virtual Compton scattering at small xB and the access to the GPD H

Abstract

We give a partonic interpretation for the deeply virtual Compton scattering (DVCS) measurements of the H1 and ZEUS Collaborations in the small-x B region in terms of generalized parton distributions. Thereby we have a closer look at the skewness effect, parameterization of the t-dependence, revealing the chromomagnetic pomeron, and at a model-dependent access to the anomalous gravitomagnetic moment of nucleon. We also quantify the reparameterization of generalized parton distributions resulting from the inclusion of radiative corrections up to next-to-next-to-leading order. Beyond the leading order approximation, our findings are compatible with a 'holographic' principle that would arise from a (broken) SO(2,1) symmetry. Utilizing our leading-order findings, we also perform a first model-dependent "dispersion relation" fit of HERMES and JLAB DVCS measurements. From that we extract the generalized parton distribution H on its cross-over line and predict the beam charge-spin asymmetry, measurable at COMPASS. This is nothing but the RDDA model in the limit b → ∞; practically, a large value b ≫ 1 is sufficient. This ansatz implies that the skewness function is set r(η/x) = 1 for all x. With such an initial condition, evolution, starting at a rather low input scale, will rapidly lead to an increase of the r-ratio. Thus, this GPD model fails to describe data, too. We will not go into details here, 7 Usage of term "dual" was motivated by the fact that in dual models [98] the s-channel amplitude is described by the t-channel exchanges. We add that this feature is more general and arises from crossing and the Sommerfeld-Watson transform of the t-channel SO(3) partial wave expansion. In Regge theory/phenomenology the resummation of t-channel exchanges is encoded in the Regge trajectory.

Extraction of Compton Form Factors in Scalar QED

“…where 2 and we use in what follows q 2 = −Q 2 . Thus, in this approximation to the dynamics, only two out of three CFFs contribute.…”

“…In scalar QED (sQED) the number of Coulomb form factors (CFFs) is known to be five [1][2][3][4]. In the case where the incoming photon is virtual, namely produced by electron scattering, while the final photon is real, the physical amplitudes depend on only three of them [5].…”

“…In a convenient kinematics, the CFFs can be found as integrals over GPDs, see for instance Refs. [1,2,6].…”

Brief review on generalized parton distributions

“…These past few years, three groups (D. Müeller and K. Kumericki [16,17], H. Moutarde [18] and M. Guidal [19][20][21][22]) have developped fitting codes and algorithms aimed at extracting the GPD information from the DVCS data. We recall that GPDs depend on three variables: x, and t but that x is not measurable in DVCS.…”

Deeply virtual Compton scattering from gauge/gravity duality

“…Although a review of this approach is outside the scope of this paper (see for example [35] and references therein, or [36] for a quick introduction), let us briefly comment on some recent results that relate to pomeron exchange. The authors of [37] use the dipole model to fit the HERA data for exclusive diffractive processes.…”