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S.~Brodsky, F.~J.~Llanes-Estrada, and A.~Szczepaniak emphasized theimportance of the $J=0$ fixed pole manifestation in real and (deeply) virtualCompton scattering measurements and argued that the $J=0$ fixed pole isuniversal, {\it i.e.}, independent on the photon virtualities\cite{Brodsky:2008qu}. In this paper we review the $J=0$ fixed pole issue indeeply virtual Compton scattering. We employ the dispersive approach to derivethe sum rule that connects the $J=0$ fixed pole contribution and thesubtraction constant, called the $D$-term form factor for deeply virtualCompton scattering. We show that in the Bjorken limit the $J=0$ fixed poleuniversality hypothesis is equivalent to the conjecture that the $D$-term formfactor is given by the inverse moment sum rule for the Compton form factor.This implies that the $D$-term is an inherent part of corresponding generalizedparton distribution (GPD). Any supplementary $D$-term added to a GPD results inan additional $J=0$ fixed pole contribution and implies the violation of theuniversality hypothesis. We argue that there exists no theoretical proof forthe $J=0$ fixed pole universality conjecture.

$J=0$ fixed pole and $D$-term form factor in deeply virtual Compton scattering