4D-TExS: A Novel 4D Lattice-based QCD Equation of State with Extended Density Range

First-principle lattice QCD calculations of thermodynamic properties are typically limited to zero net density or chemical potential $(\mu_i)$ due to the fermion sign problem. However, several techniques have been developed to extend the equation of state (EoS) to finite baryon (B), electric charge (Q), and strangeness (S) chemical potentials. A Taylor expansion around $\mu_i = 0$ (for $i = B, Q, S$) effectively covers the region up to $\mu_i/T < 2.5$. Recently, a novel Taylor expansion resummation method, the T'-expansion scheme (TExS), was developed to construct a 2D EoS in the $(T, \mu_B)$ plane, extending density coverage to $\mu_B/T \approx 3.5$. Here, we introduce the 4D-TExS EoS, a generalization of TExS that incorporates all three chemical potentials. This formulation provides broader coverage than the traditional 4D Taylor expansion EoS. We present this extension of the 2D TExS to four dimensions and discuss thermodynamic observables as functions of temperature and chemical potentials along any direction in the QCD phase diagram.