Higher-order kinematical effects in deeply virtual Compton scattering

Abstract

We study the deeply virtual Compton scattering cross-section in twist-two generalized parton distribution (GPD) approximation, and show that different choices of light-cone vectors and gauges for the final photon polarization will lead to different higher-order kinematical corrections to the cross-section formula. The choice of light-cone vectors affects kinematic corrections at the twist-three level, accounting for the differences between the cross-section formulas in the literature. On the other hand, kinematical corrections from higher-twist GPDs should eliminate the light-cone dependence at twist three. Those light-cone dependencies are studied systematically at JLab 12 GeV and future EIC kinematics. They serve as the intrinsic systematic uncertainties in extracting the Compton form factors through the cross-section formula. More importantly, they are also necessary for understanding cross-section measurements with higher-twist precision and to reconstruct higher-order Compton form factors.

Twist-three cross-sections in deeply virtual Compton scattering

“…[39,[43][44][45][46][47], we find the so-called covariant Compton tensor coefficients most suitable for our analysis, as they take parts of the kinematical corrections into account and satisfy the current conservation relation manifestly, see more details in ref. [40] for how we get those covariant Compton tensor coefficients and ref. [47] where the same choice of twist-two Compton tensor coefficients is made.…”

“…whereas hadronic matrix element of the pure DVCS cross-section can be written with the polarization vectors introduced in ref. [40],…”

“…As the twist-two pieces are already presented in the previous work in ref. [40], here we will focus on the twist-three and twist-four hadronic tensor of each polarization, see eqs. (B.2) -(B.8) in appendix B.…”

“…With the twist expansion, two types of corrections shall be considered for a systematical analysis of the higher-twist effectsthe kinematically higher-order corrections associated with the leading-twist GPDs and the effects of the higher-twist GPDs. The kinematical twist-three effects [35][36][37][38][39][40] and twist-four effects such as finite t and target mass corrections [41][42][43][44][45][46][47] in the DVCS process have been studied extensively in the literature. In this work, we focus on the effects of higher-twist GPDs, specifically the twist-three ones.…”

“…The set-up follows our previous works in ref. [40], and we review part of them in this paper for consistency. Consider the electroproduction of a photon off a proton as, e(k, h) + N (P, S) → e(k , h ) + N (P , S ) + γ(q , Λ ) ,…”