Using the PCAC relation, we derive a compact formula for the pion decay constant Fπ in the nonlocal chiral quark model. For practical calculations this formula may be used both in the Minkowski and in the Euclidean space. For the pion momentum Pμ ← 0 it reduces to the well known expression derived earlier by other authors. Using a generalized dipole Ansatz for the momentum dependence of the constituent quark mass in the Minkowski space, we express Fπ2 in terms of a single integral over the quark momentum fraction μ. We interpret the integrand as a pion distribution amplitude φ(u). We discuss its properties and compare with the πDA's obtained in other models.

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.