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 reexamine the issue of the time and normal ordering in the operator definition of GPDs. We demonstrate that the contribution of the anticommutator 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 anticommutator modifies likewise the so-called positivity constraint, i.e., the Cauchy-Bunyakovsky-Schwarz inequality, which is another important feature of the GPDs.

• Received 23 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.105023