Data-Driven Refinement of an Analytical Holographic Model for the QCD Phase Transition

TL;DR

This paper refines an analytical holographic model for the QCD phase transition using lattice QCD data, accurately locating the critical endpoint and validating the model's predictions at finite chemical potentials.

Contribution

It introduces a gradient descent calibration method for the holographic model parameters based on lattice data, improving the model's accuracy in predicting the QCD phase diagram.

Findings

Calibrated the holographic model with lattice data for key thermodynamic quantities.

Validated the model's extension to finite chemical potentials against lattice QCD results.

Located the critical endpoint at specific temperature and chemical potential values.

Abstract

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 $T-\mu$ plane. Specifically, we calibrate the model using input data for the speed of sound at $\mu_B = 0$, the second-order baryon number susceptibility $\chi^B_2$, and the baryon number density at $\mu_B/T = 1$. 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 $T-\mu_B$ plane, finding it located at $(\mu_B = 0.678 \, \rm{GeV}, T = 0.110 \, \rm{GeV})$