On the Wandzura-Wilczek approximation for the twist-3 DVCS amplitude

We present a derivation of Wandzura-Wilczek (WW) like relations for skewed parton distributions. It is demonstrated for photon-pion scattering that for transverse photon polarization the skewed twist-3 parton distributions contributing to the DVCS amplitude have discontinuities at the points x = ±ξ in the WW approximation. Unless these discontinuities are cancelled by the neglected genuine higher twist pieces they lead to a violation of factorisation for the twist-3 DVCS amplitude with transverse polarization of the virtual photon. For the scattering of longitudinally polarized photon the twist-3 amplitude is free of such divergencies. Introduction Deeply Virtual Compton Scattering (DVCS) [1, 2] is the cleanest hard process which is sensitive to the Skewed Parton Distributions (SPD) and has been the subject of extensive theoretical investigations for a few years. First experimental data became recently available (see e.g. [3, 4]) and much more data are expected from JLAB, DESY, and CERN in the near future. It was demonstrated [5, 6, 7] that in leading order (1/Q) the DVCS amplitude factorizes. However, as the typical Q are by no means large, studies of the power corrections to the DVCS amplitude are very important. Recently the DVCS amplitude was computed [8, 9, 10] including the terms of order O(1/Q). The inclusion of such terms is mandatory to conserve the electromagnetic gauge invariance of the DVCS amplitude. Moreover, they provide the leading contribution to some spin asymmetries. To this order the amplitude depends on a set of new skewed parton distributions. Recently it was shown in ref. [10] that in the so-called Wandzura-Wilczek (WW) approximation these new functions can be expressed in terms of twist-2 SPD’s. In this note we give a derivation of these WW-like relations which is technically slightly different from the approach used in [10], see the Appendix for details. Then we demonstrate 1 for the case of DVCS on the pion the new SPD’s in WW approximation generically posses discontinuities at the points x = ±ξ. This leads to a formally divergent expression for the DVCS amplitude. As a result, the factorisation is spoiled at the 1/Q level. We also observed that in the twist-3 DVCS amplitude with longitudinally polarized virtual photons the divergencies mentioned above are cancelled. We discuss the theoretical implications of this phenomenon and its possible experimental verification. DVCS on the pion The expression for the DVCS amplitude on the pion as obtained in [8] and reproduced in refs. [9, 10] has the form: T μν = − 1 2P ·Q ∫