Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond

Abstract

Combining dispersion and operator product expansion techniques, we derive the conformal partial wave decomposition of the virtual Compton scattering amplitude in terms of complex conformal spin to twist-two accuracy. The perturbation theory predictions for the deeply virtual Compton scattering (DVCS) amplitude are presented in next-to-leading order for both conformal and modified minimal subtraction scheme. Within a conformal subtraction scheme, where we exploit predictive power of conformal symmetry, the radiative corrections are presented up to next-to-nextto-leading order accuracy. Here, because of the trace anomaly, the mixing of conformal moments of generalized parton distributions (GPD) at the three-loop level remains unknown. Within a new proposed parameterization for GPDs, we then study the convergence of perturbation theory and demonstrate that our formalism is suitable for a fitting procedure of DVCS observables.

On the universality of theJ= 0 fixed pole contribution in DVCS

“…It is extremely convenient to address this property within the approach [15] based on operator product expansion over the conformal basis. In this case there turns to be two kinds of analytical properties relevant for GPDs and associated CFFs:…”

Spin-polarized high-energy scattering of charged leptons on nucleons

“…Based on this approach, very recently a simultaneous fit was performed to the DVCS and DIS collider data, for the first time up to NNLO accuracy [186]. The CS scheme was used which differs from the more commonly used MS scheme only in the skewness dependence of the conformal moments in the Mellin-Barnes representation, the latter being used to evaluate the CFFs.…”

“…In figure 35 the fit results are compared with the data, showing fair agreement. It is argued in [186] that this should be considered satisfactory, as several aspects of the theoretical approach are not completely settled yet, in particular regarding the skewness dependence of quarks GPDs.…”

Dispersion representation of the D-term form factor in deeply virtual Compton scattering

“…In particular, DRs for Compton scattering processes, with both real and virtual photons, had wide applications for the prediction and extraction from experimental data of lowenergy properties of hadron systems [1][2][3][4][5]. More recently, the dispersion formalism has been extended to describe the virtual Compton scattering process in the deep inelastic region [6][7][8][9][10][11][12]. In particular, it was shown that the amplitudes for deeply virtual Compton scattering (DVCS) satisfy subtracted DRs at fixed t with the subtraction function defined by the D-term form factor [6][7][8].…”

“…The D term was originally introduced to complete the parametrization of the generalized parton distributions (GPDs) in hard exclusive reactions in terms of double distributions, and restore the polynomiality property of the singlet moments of unpolarized GPDs [13]. This term turned out to be a crucial contribution in the phenomenological description of DVCS observables, where different forms have been assumed with parameters tuned to DVCS data [9,14]. Here we review the dispersive representation of the D-term form factor in terms of DRs in the tchannel, as recently proposed in Ref.…”