The analysis of the statistical and dynamical fluctuations in nucleus-nucleus collisions on an event-by-event basis strongly relies on a comparison with specially constructed artificial events where statistical fluctuations and kiuematical correlations are under control. In this paper, we present a novel, analytical method of constructing reference events based on independent emission, modified by the energy/momentum constraint, which can lead to a better understanding of the nature of the observed final-state fluctuations. This approach can be easily used in the analysis of other topics in the heavy ion field (e.g. flow, HBT etc.) allowing more precise measurements.

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document.