Renormalons and power corrections in pseudo- and quasi-GPDs

High-order behavior of the perturbative expansion for short-distance observables in QCD is intimately related to the contributions of small momenta in the corresponding Feynman diagrams and this correspondence provides one with a useful tool to investigate power-suppressed nonperturbative corrections. We use this technique to study the structure of power corrections to parton quasi- and pseudo-GPDs which are used in lattice calculations of generalized parton distributions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-GPDs on $x$ variable for nonzero skewedness parameter $\xi$. The kinematic point $x=\pm \xi$ turns out to be special. We find that the nonperturbative corrections to quasi-GPDs at this point are suppressed by the first power of the hard scale only. These contributions come from soft momenta and have nothing to do with the known UV renormalon in the Wilson line. We also show that power corrections can be strongly suppressed by the normalization procedure.

Figure 1

Typical singularity structure of the Borel transform.

Figure 2

Bubble-chain contribution to the gluon propagator.

Figure 3

Bubble-chain contribution to $\mathrm{pGPDs}/\mathrm{qGPDs}$. The Wilson line connecting the quark fields is shown by double dots.

Figure 4

GPD model (43) for $\xi =0.3$ used in our calculations: $H(x,\xi )$ and the derivative $H^{\prime }(x,\xi )$ as functions of $x$ (left and middle panels, respectively), and the real part of the corresponding position space GPD $I(\tau ,\xi )$ a function of $\tau$ (right panel).

Figure 5

Renormalon ambiguity for the position space (Ioffe-time) valence quark distribution for the model (43) and the choice (45) for the overall normalization, corresponding to the quark-antiquark separation of the order of 1 fm.

Figure 6

Renormalon ambiguity for the valence quark pseudo-GPD for the model (43) and the choice (45) for the overall normalization, corresponding to the quark-antiquark separation of the order of 1 fm.

Figure 7

Renormalon ambiguity for the valence quark quasi-GPD in the DGLAP region $x>\xi$ for the model (43) and the choice (46) for the overall normalization, corresponding to the target momentum approximately 1.5 GeV.

Figure 8

Renormalon ambiguity for the valence quark quasi-GPD in the ERBL region $-\xi <x<\xi$ for the model (43) and the choice (46) for the overall normalization, corresponding to the target momentum approximately 1.5 GeV.