Use of the Husimi distribution for nucleon tomography

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-$x$.

12 pages, 6 figures; improved discussion about the positivity of the Husimi distribution, to be published in Nuclear Physics A