A lattice-based equation of state to study the matter at the Bean Energy Scan.*

We construct a novel equation of state (EoS) describing QCD (Quantum Chromodynamic) matter at finite temperature and baryon B, electric Q and strangeness S chemical potentials by utilizing the alternate expansion scheme from the lattice QCD results [Phys.Rev.Lett. 126 (2021) 23, 232001]. This procedure allows to reliably estimate the baryon and strangeness densities at larger values of the baryon chemical potential μ_B in comparison to the usual Taylor expansion in terms of susceptibilities. We use the latter only to incorporate the μ_Q and μ_S dependence into thermodynamic quantities, which is sufficient for studying the matter as produced in relativistic heavy-ion collisions. We then smoothly match this lattice-based EoS at high temperature with the thermodynamics of the Hadron-Resonance Gas (HRG) model at low temperature. Finally we employ this newly constructed EoS to illustrate the trajectories of the matter produced at the Beam Energy Scan (BES) program by coarse-graining the Parton-Hadron-String Dynamics (PHSD) transport approach which consistently describes the whole non-equilibrium dynamics of heavy-ion collisions, from the early nucleon hard scatterings, to the partonic phase based on the Dynamical QuasiParticle Model (DQPM), and up to the final hadron rescatterings.