Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite-$t$ and target mass corrections

TL;DR

This work provides the first complete calculation of kinematic twist-three and twist-four power corrections to DVCS observables, including finite-$t$ and target-mass effects, and demonstrates that these corrections are substantial at $Q^2 oughly 1$–$5$ GeV$^2$. By employing BMP and BMJ decompositions, GPD modeling via RDDA, and a dissipative framework, the authors show how to restore gauge/translation invariance and quantify corrections through $-t/Q^2$ and $(t_{ m min}-t)/Q^2$ terms. The analysis reveals that conventional leading-twist analyses are convention-dependent, and the full observable-level corrections depend on the chosen CFF basis, necessitating careful treatment in data analysis and global fits. The results provide practical guidance for extracting GPDs from existing and planned DVCS measurements, and stress the need for higher-$Q^2$ data to reliably map the three-dimensional nucleon structure. Overall, the paper strengthens the theoretical foundation for DVCS phenomenology and enhances the precision of QCD predictions in the intermediate-$Q^2$ regime.

Abstract

We carry out the first complete calculation of kinematic power corrections $\sim t/Q^2$ and $\sim m^2/Q^2$ to several key observables in Deeply Virtual Compton Scattering. The issue of convention dependence of the leading twist approximation is discussed in detail. In addition we work out representations for the higher twist corrections in terms of double distributions, Mellin-Barnes integrals and also within a dissipative framework. This study removes an important source of uncertainties in the QCD predictions for intermediate photon virtualities $Q^2\sim 1$-$5\,{\rm GeV}^2$ that are accessible in the existing and planned experiments. In particular the finite-$t$ corrections are significant and must be taken into account in the data analysis.

Figures (11)

• Figure 1: Imaginary parts of typical contributions to the CFFs, multiplied with $\xi/\pi$, from the toy GPD model (\ref{['GPD-toy']}): LO contribution $F(\xi,\xi)$ (dashed), convolution integral $T_1\!\circledast \!F$ (dotted), acting on it with the differential operator $\xi \partial_\xi$ (solid) and $\partial_\xi \xi$ (short-dashed), as well as $\partial_\xi \xi T^{(-)}_1\!\circledast \!F$ (dash-dotted). Normalization of the u(d)-quark PDF is set to 2 (1).
• Figure 2: Effective coefficients $k^{\mathfrak F}_{++}$ of $-t/Q^2$ corrections (\ref{['k_++^cffFbmp']}) for the 'electric' signature-even ${\mathfrak F} = {\mathfrak G}_{++}$ (thick) and signature-odd ${\mathfrak F} = \widetilde{\mathfrak G}_{++}$ (thin) CFFs evaluated for the GPD (\ref{['GPD-toy']}). The solid and dashed curves are calculated for $-t\gg -t_{\rm min}$ and $t=t_{\rm min}$, respectively.
• Figure 3: The ratios $k_{0+}^{(+)}$ (thick dash-dotted curves) and $k^{(-)}_{0+}$ (thin dash-dotted curves), cf. Eq. (\ref{['k0+']}), characterizing the magnitude of the contributions in the first line in Eq. (\ref{['cffFbmp_0+']}) to the longitudinal-to-transverse helicity flip CFFs ${\mathfrak F}_{0+}$, evaluated for the GPD model in Eq. (\ref{['GPD-toy']}). The thick and thin long dash-dotted curves show the ratios $\Delta k_{0+}^{(+)}$ and $\Delta k_{0+}^{(-)}$, respectively, which are defined in Eq. (\ref{['Delta k_0+']}) and determine the numerical size of the addenda in the two last lines in Eq. (\ref{['cffFbmp_0+']}).
• Figure 4: The ratios $k_{-+}^{(+)}$ (thick dashed curves) and $k_{-+}^{(-)}$ (thin dashed curves), defined in Eq. (\ref{['k-+']}), characterizing the magnitude of the contributions in the first line in Eq. (\ref{['cffFbmp_-+']}) to the transverse-to-transverse helicity flip CFFs ${\mathfrak F}_{0+}$, evaluated for the GPD model (\ref{['GPD-toy']}). The dashed and dotted curves show the ratios $\Delta k_{-+}^{(+)}$ and $\Delta k_{-+}^{(-)}$, respectively, which characterize the numerical size of the addenda in the two last lines in Eq. (\ref{['cffFbmp_-+']}), as defined in Eq. (\ref{['deltak-+']}).
• Figure 5: LT$_{\rm BMP}$ predictions for the imaginary parts of the BMJ CFFs $(x_{\rm B}/\pi) \Im{\rm m}\, {\mathcal{F}}_{a+}(x_{\rm B},t,Q^2)$ vs. $x_{\rm B}$ at $-t=0.375\, {\rm GeV}^2$ and $Q^2=1.5\, {\rm GeV}^2$ for the GPD model (\ref{['F^q(xi/x,xi)']}): ${\mathcal{F}}_{++}$ (dashed), ${\mathcal{F}}_{0+}$ (dash-dotted), and ${\mathcal{F}}_{-+}$ (short-dashed), compared with the LT$_{\rm KM}$ result for ${\mathcal{F}}_{++}$ (dotted).