Data-driven Einstein-dilaton model for pure Yang-Mills thermodynamics and glueball spectrum

Using ( 2 + 1 )-flavor lattice QCD data, we refine the parameters of an analytical holographic model via gradient descent optimization to precisely locate the critical endpoint in the T − μ plane. Specifically, we calibrate the model using input data for the speed of sound at μ B = 0 , the second-order baryon number susceptibility χ 2 B , and the baryon number density at μ B / T = 1 . With these parameters fixed, we calculate pressure and energy density versus temperature at small chemical potentials and compare the results with lattice QCD data using Taylor expansion techniques. This comparison validates the robustness of our model upon extension to finite chemical potentials, as the results show broad consistency with lattice QCD data in this regime. Finally, we employ the calibrated model to determine the coordinates of the critical endpoint in the T − μ B plane, finding it located at ( μ B = 0.678 GeV , T = 0.110 GeV ) .