On the universality of the $J=0$ fixed pole contribution in DVCS

TL;DR

This paper examines the universality hypothesis of the $J=0$ fixed pole in DVCS, linking it to the $D$-term form factor sum rule, and discusses how additional $D$-terms can violate this universality, which remains unproven.

Contribution

It demonstrates the equivalence between the $J=0$ fixed pole universality hypothesis and the inverse moment sum rule for the $D$-term form factor, and shows potential violations in models.

Findings

Universality hypothesis is equivalent to the $D$-term sum rule.

Additional $D$-terms can violate the fixed pole universality.

The hypothesis remains an unproven external assumption.

Abstract

S. Brodsky, F.J. Llanes-Estrada, and A. Szczepaniak formulated the $J=0$ fixed pole universality hypothesis for (deeply) virtual Compton scattering. We show that in the Bjorken limit this hypothesis is equivalent to the validity of the inverse moment sum rule for the $D$-term form factor. However, any supplementary $D$-term added to a generalized parton distribution (GPD) results in an additional $J=0$ fixed pole contribution that violates universality. Unfortunately, one can not provide any reliable theoretical argument excluding the existence of such supplementary $D$-term. Moreover, the violation of $J=0$ fixed pole universality was revealed in field theoretical GPD models. Therefore, $J=0$ fixed pole universality hypothesis remains just an external assumption and probably will never be proven theoretically.