Brodsky, Llanes-Estrada, and Szczepaniak emphasized the importance of the $J=0$ fixed-pole manifestation in real and (deeply) virtual Compton scattering measurements and argued that the $J=0$ fixed pole is universal, i.e., independent on the photon virtualities [Phys. Rev. D 79, 033012 (2009)]. In this paper we review the $J=0$ fixed-pole issue in deeply virtual Compton scattering. We employ the dispersive approach to derive the sum rule that connects the $J=0$ fixed-pole contribution and the subtraction constant, called the $D$-term form factor for deeply virtual Compton scattering. We show that in the Bjorken limit the $J=0$ fixed-pole universality hypothesis is equivalent to the conjecture that the $D$-term form factor is given by the inverse moment sum rule for the Compton form factor. This implies that the $D$-term is an inherent part of the corresponding generalized parton distribution (GPD). Any supplementary $D$-term added to a GPD results in an additional $J=0$ fixed-pole contribution and implies the violation of the universality hypothesis. We argue that there exists no theoretical proof for the $J=0$ fixed-pole universality conjecture.

• Received 14 September 2015

DOI:https://doi.org/10.1103/PhysRevD.92.074025