Illuminating the 1/x moment of parton distribution functions

TL;DR

This paper explores the Weisberger relation linking high-energy parton distribution moments to low-energy nucleon properties, highlighting current limitations in determining the 1/x moment and proposing new insights via deeply virtual Compton scattering.

Contribution

It introduces a novel F_{1/x}(t) form factor to better understand the 1/x moment and reveals issues with high Q^2 factorization in exclusive processes, suggesting directions for future experiments.

Findings

Contemporary fits fail to determine the 1/x moment.

Deeply virtual Compton scattering can be described by a new form factor.

High Q^2 factorization breaks down at low t in exclusive processes.

Abstract

The Weisberger relation, an exact statement of the parton model, elegantly relates a high-energy physics observable, the 1/x moment of parton distribution functions, to a nonperturbative low-energy observable: the dependence of the nucleon mass on the value of the quark mass or its corresponding quark condensate. We show that contemporary fits to nucleon structure functions fail to determine this 1/x moment; however, deeply virtual Compton scattering can be described in terms of a novel F_{1/x}(t) form factor which illuminates this physics. An analysis of exclusive photon-induced processes in terms of the parton-nucleon scattering amplitude with Regge behavior reveals a failure of the high Q^2 factorization of exclusive processes at low t in terms of the Generalized Parton-Distribution Functions which has been widely believed to hold in the past. We emphasize the need for more data for the DVCS process at large t in future or upgraded facilities.