Use of the Husimi distribution for nucleon tomography

TL;DR

This paper introduces the Husimi distribution as a positive, probabilistic alternative to the Wigner distribution for nucleon tomography, demonstrating its advantages and potential connections to saturation physics.

Contribution

The paper presents the Husimi distribution as a new tool for nucleon tomography, offering a positive phase-space distribution in QCD, unlike the Wigner distribution.

Findings

Husimi distribution is positive and probabilistic.

Demonstrated advantages via a one-loop example.

Discussed connection to saturation physics at small-x.

Abstract

In the context of nucleon structure, the Wigner distribution has been commonly used to visualize the phase-space distribution of quarks and gluons inside the nucleon. However, the Wigner distribution does not allow for a probabilistic interpretation because it takes negative values. In pursuit of a positive phase-space distribution in QCD, we introduce the Husimi distribution and demonstrate its advantages via a simple one-loop example. We also comment on a possible connection to the semiclassical approach to saturation physics at small-$x$.