Dispersion relations and subtractions in hard exclusive processes

Abstract

We study analytical properties of the hard exclusive processes amplitudes. We found that QCD factorization for deeply virtual Compton scattering and hard exclusive vector meson production results in the subtracted dispersion relation with the subtraction constant determined by the Polyakov-Weiss $D$-term. The relation of this constant to the fixed pole contribution found by Brodsky, Close and Gunion and defined by parton distributions is proved, while its manifestation is spoiled by the small $x$ divergence. The continuation to the real photons limit is considered and the numerical correspondence between lattice simulations of $D$-term and low energy Thomson amplitude is found.Comment: 4 pages, journal versio

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

“…(22) of Ref. [180]. Our formula (47), approximated to LO, expressed in momentum fraction space, and written down for CFF H, yields the aforementioned result and contains a prescription for treating the appearing divergencies.…”

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

“…Following Refs. [6,8], the subtraction function F q (0, t) can be related to the D-term form factor D q (t) [13] as follows…”

“…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].…”

“…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].…”

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

“…By plugging the imaginary part of (8) into the subtracted DR (5) and equating it with the LO convolution formula (8) for the CFF, one can work out the GPD sum rule [13,14]:…”