Study of hard and electromagnetic processes at CERN-SPS energies: an investigation of the high-$\mu_{\mathbf{B}}$ region of the QCD phase diagram with NA60+

The exploration of the phase diagram of Quantum ChromoDynamics (QCD) is carried out by studying ultrarelativistic heavy-ion collisions. The energy range covered by the CERN SPS (\(\sqrt{s_{\text{NN}}} \sim 5\unicode{x2013}17\) GeV) is ideal for the investigation of the region of the phase diagram corresponding to finite baryochemical potential (\(\mu _{\text{B}}\)), and has been little explored up to now. In this paper we describe a new experiment, NA60+, that would address several observables which are fundamental for investigating the possible existence of a first phase transition between hadronic matter and a Quark–Gluon Plasma (QGP) at finite \(\mu _{\text{B}}\). In particular, we propose to study the production of thermal dimuons in Pb–Pb collisions at different energies, from which one would obtain a caloric curve of the QCD phase diagram that is sensitive to the order of the phase transition. In addition, the measurement of the \(\rho \unicode{x2013}\text{a}_{1}\) chiral mixing would provide crucial insight into the restoration of the chiral symmetry of QCD. In parallel, studies of heavy quark and quarkonium production would also be carried out, providing sensitivity for transport properties of the QGP and the investigation of the onset of the deconfinement transition. Results of physics performance studies for most observables accessible by NA60+ are discussed, showing that the results of the experiment would lead to a significant advance of our understanding of (non-perturbative) strong interaction physics.