4D lattice-based Equation of State: Generalization of $T^\prime$-Expansion scheme

First-principle lattice QCD calculations of thermodynamics are constrained to zero net density due to the fermion sign problem. To address this, various methods have been developed to extend the equation of state (EoS) to finite baryonic chemical potential $mu_B$, with Taylor expansion being the standard approach for $B$, $Q$, and $S$ chemical potentials. While the Taylor expansion around $mu_i = 0$ ($i = B, Q, S$) provides reliable results up to $mu_i/T < 2.5$, its range is limited.

We present a novel extension of a recently introduced expansion scheme, which successfully extends the $mu_B$ coverage up to $mu_B/T approx 3.5$. This generalization allows independent variations of the three chemical potentials, leveraging continuum-estimated fluctuations up to fourth order. Our approach significantly expands the accessible region of the four-dimensional QCD phase diagram compared to traditional Taylor expansion methods, offering enhanced predictive power for QCD thermodynamics at finite density.