Positivity and unitarity constraints on dipole gluon distributions

TL;DR

This paper explores how positivity and unitarity constraints shape the behavior of dipole gluon distributions in high-energy QCD, using mathematical properties of Fourier-positive functions.

Contribution

It provides a detailed analysis of the mathematical constraints on dipole gluon distributions, informing better model building in high-energy nuclear physics.

Findings

Derived constraints from Fourier-positive functions on gluon distributions

Clarified the impact of positivity and unitarity on dipole models

Guided the formulation of physically consistent dipole distributions

Abstract

In the high-energy domain, gluon transverse-momentum dependent distributions in nuclei obey constraints coming from positivity and unitarity of the colorless QCD dipole distributions through Fourier-Bessel transformations. Using mathematical properties of Fourier-positive functions, we investigate the nature of these constraints which apply to dipole model building and formulation