Speaker
Description
Our ability to predict thermodynamic observables and determine the QCD critical point at real values of chemical potentials is severely limited by the infamous sign problem. To address this issue, there are two common approaches: expanding the QCD partition function in a Taylor series with respect to the charge chemical potentials ($\mu_{B,Q,S}$) or analytically continuing from imaginary chemical potentials. However, both methods have limitations, particularly for larger values of the baryon chemical potential. Recently, we proposed a multi-point Pade approach[1] based on a (2+1)-flavor Lattice QCD simulation that uses multiple imaginary chemical potentials with temporal extents of $N_{\tau}=4,6,8$. This method combines the benefits of the aforementioned approaches and is expected to provide more reliable quantitative predictions for small to intermediate values of the baryon chemical potential. Another, advantage we can use this method to estimate different critical points of QCD by examining the singularities of the Pade series.
In this presentation, we will focus on two critical points, well known Roberge-Weiss critical point, which arises when the baryon chemical potential is purely imaginary, and the QCD critical point, which will emerge at a real value of the baryon chemical potential. We use the multi-point Pade approach to locate the Lee-Yang edge singularities in the complex chemical potential plane, which are obtained from lattice QCD simulated data. Our results demonstrate that the scaling of these singularities corresponds to the expected scaling of the well-known Roberge-Weiss transition. The universal scaling of singularities in the vicinity of the QCD critical endpoint is also investigated. Lee-Yang edge singularities associated with the QCD critical point at the real chemical potential for various temperatures are calculated. As the temperature decreases, the imaginary part of the singularities becomes smaller, hinting at a possible existence of a critical point at low temperatures. A machine learning technique is used to model the probability density of the singularities and interpolate the real and imaginary parts of the singularities between different temperatures. By employing a suitable scaling ansatz, the singularities are extrapolated towards the real axis, and the possible location of the QCD critical point is estimated. Preliminary results of ($T_{CEP},\mu_B^{CEP}$) are consistent with model predictions and other lattice QCD calculations.
[1] P. Dimopoulos et al., Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD, Phys. Rev. D 105 (2022) 034513 [2110.15933]
| Category | Theory |
|---|
