Space-time structure of polynomiality and positivity for GPDs

TL;DR

This paper investigates the space-time structure of GPDs, revealing that anti-commutator contributions are essential for satisfying polynomiality and positivity constraints, thus refining the theoretical understanding of GPD properties.

Contribution

It demonstrates the necessity of including anti-commutator matrix elements in GPD definitions to ensure polynomiality and positivity, challenging previous assumptions.

Findings

Anti-commutator contributions are essential for polynomiality.

Anti-commutator modifies the positivity constraints.

Re-examination of time- and normal-ordering in GPDs.

Abstract

We study the space-time structure of polynomiality and positivity---the most important properties which are inherent to the generalized parton distributions (GPDs). In this connection, we re-examine the issue of the time- and normal- ordering in the operator definition of GPDs. We demonstrate that the contribution of the anti-commutator matrix element in the collinear kinematics, which was previously argued to vanish, has to be added in order to satisfy the polynomiality condition. Furthermore, we schematically show that a new contribution due to the anti-commutator modifies likewise the so-called positivity constraint, i.e., the Cauchy-Bunyakovsky-Schwarz inequality, which is another important feature of the GPDs.