Bayesian Inference of the Critical Endpoint in 2+1-Flavor System from Holographic QCD

TL;DR

This paper develops a Bayesian holographic model to precisely locate the critical endpoint in 2+1-flavor QCD, integrating lattice data and providing confidence intervals for the CEP's position, aiding understanding of QCD phase transitions.

Contribution

It introduces a novel Bayesian framework for holographic QCD modeling, accurately estimating the CEP position with error analysis and validation against other theoretical models.

Findings

Critical endpoint position at (0.0859 GeV, 0.742 GeV) via MAP estimation.

CEP confidence intervals: 68 ext{--}0.0889 GeV, 0.71 ext{--}0.77 GeV.

Model validated by comparison with other theoretical predictions.

Abstract

We present a Bayesian holographic model constructed by integrating the equation of state and baryon number susceptibility at zero chemical potential from lattice QCD. The model incorporates error estimates derived from lattice data. With this model, we systematically investigate the thermodynamic properties of the 2+1-flavor QCD system. Using Bayesian Inference, we perform precise calibration of the model parameters and determined the critical endpoint (CEP) position under the maximum a posterior (MAP) estimation to be $(T^{c},\mu_{B}^{c})=(0.0859\;\mathrm{GeV},0.742\;\mathrm{GeV})$. Additionally, we predict the CEP positions within 68\% and 95\% confidence levels, yielding $(T^{c},\; \mu_{B}^{c})_{68\%}$=$(0.0820\text{--}0.0889, 0.71\text{--}0.77)\;\mathrm{GeV}$ and $(T^{c},\; \mu_{B}^{c})_{95\%}$=$(0.0816\text{--}0.0898,\; 0.71\text{--}0.79)\;\mathrm{GeV}$, respectively. Moreover, to validate the reliability and predictive power of our approach, we conduct a comprehensive comparison between our predictions and potential CEP locations proposed by other theoretical models. This work not only establishes a novel Bayesian framework for holographic modeling but also provides valuable insights and theoretical support for exploring phase transitions in strongly-interacting matter under extreme conditions.