Description
The region of large baryo-chemical potential of the QCD phase diagram represents one of the current frontiers in the exploration of strongly interacting matter. Experimentally, one of the most promising avenues is the study of rare probes of the Quark-Gluon Plasma (QGP) and the hadronic phase, as produced by colliding heavy nuclei in the center of mass energy range between 6 and 20 GeV. The NA60+ project aims at proposing an experiment at the CERN SPS devoted to the measurement of heavy quarks and electromagnetic processes. In the 2017 NuPECC Long Range Plan the project, at the time in its infancy, was briefly discussed among the possible developments. Five years later, it has strongly advanced towards the actual proposal of an experiment, with a well-defined and strong physics program, an R&D phase with first results already available and a definite plan. A detailed Letter of Intent is ready to be submitted by the end of 2022 to the CERN SPSC with the aim of having the experiment taking data after the CERN Long Shutdown 3 (currently foreseen in 2029). In this document, we will present a summary the current status of the activities related to the project and demonstrate how the NA60+ experiment can play a very relevant role among the currently existing and foreseen projects for the study of the QGP at high-$\mu_{\rm B}$.