Dispersion relations of deeply virtual Compton scattering: investigating twist-4 kinematic power corrections

Abstract

In this paper we include kinematic power corrections up to twist-four to the deeply virtual Compton scattering dispersion relation. We demonstrate that, both for (pseudo-)scalar and spin-$1/2$ targets, the formal expression of the $n$-subtracted leading-twist dispersion relations is preserved. However, the expression of the subtracted constants is modified by the kinematic powers. Importantly, the minimal-subtracted dispersion relation for the helicity-conserving amplitude, previously thought to depend only on the Polyakov-Weiss $D$-term, now also depends on the double distributions $F$ and $K$. These results are consistent with the ones obtained previously in the literature. Such a mixing may be critical for the Jefferson Lab kinematic range, as it is not suppressed for typical values of $t$ and $Q^{2}$ in the valence region. We therefore expect a strong impact on attempts to extract pressure forces from DVCS data.

Figures (4)

• Figure 1: Complex plane for variable $\nu$ where the region where analyticity is not granted, i.e. the physical domain $\nu\in(-\infty,-1]\cup[1,\infty)$, has been highlighted in red for the positive-$s$ region and in orange for the positive-$u$ segment. Note that they are exchanged with respect to Ref. Dutrieux:2024bgc. The contour $\gamma$ runs over and its interior is within the analytic domain of $\nu$ so that $\oint_\gamma d\nu'\ \frac{\mathcal{F}(\nu')}{\nu'-\nu} = 0$ for $\nu$ in the physical region, accordingly to Cauchy's integral theorem.
• Figure 2: Complex plane for variable $\xi$ where the region where analyticity is not granted, i.e. $\xi\in[-1-\Lambda,1+\Lambda]$, has been highlighted in red. Note that this interval is larger than the physical domain which corresponds to $|\xi| < 1$.
• Figure 3: Comparison between the present result $T_1^{++(1)}$ and the first result $2G^{(-)}$ obtained in Ref. Braun:2014sta.
• Figure 4: Ratio $\mathcal{S}_{LT} / \mathcal{S}$ as a function of $t$ for $Q^2 = 2\hbox{GeV}^2$. In red, $\mathcal{S}$ is expanded as power of $1/\mathbb{Q}^2$, while in blue it is in terms of power of $1/Q^2$. The difference is expected to be twist-6 but it is already visible for $|t|$ as small as $0.3\hbox{GeV}^2$. The dots and squares are the actual computed points, the line is only an interpolation used as a guide.