Letter of Intent: the NA60+ experiment

We propose a new fixed-target experiment for the study of electromagnetic and hard probes of the Quark-Gluon Plasma (QGP) in heavy-ion collisions at the CERN SPS. The experiment aims at performing measurements of the dimuon spectrum from threshold up to the charmonium region, and of hadronic decays of charm and strange hadrons. It is based on a muon spectrometer, which includes a toroidal magnet and six planes of tracking detectors, coupled to a vertex spectrometer, equipped with Si MAPS immersed in a dipole field. High luminosity is an essential requirement for the experiment, with the goal of taking data with 10$^6$ incident ions/s, at collision energies ranging from $\sqrt{s_{\rm NN}} = 6.3$ GeV ($E_{\rm lab}= 20$ A GeV) to top SPS energy ($\sqrt{s_{\rm NN}} = 17.3$ GeV, $E_{\rm lab}= 158$ A GeV). This document presents the physics motivation, the foreseen experimental set-up including integration and radioprotection studies, the current detector choices together with the status of the corresponding R&D, and the outcome of physics performance studies. A preliminary cost evaluation is also carried out.