Exploring the Critical Points in QCD with Multi-Point Pad\'e and Machine Learning Techniques in (2+1)-flavor QCD

TL;DR

This paper combines multi-point Padé approximants and machine learning to analyze critical points in (2+1)-flavor QCD, identifying singularities and estimating their density to extrapolate the critical point.

Contribution

It introduces a novel approach integrating Padé approximants and MADE machine learning to study QCD critical phenomena and singularities.

Findings

Padé approximants reveal singularities consistent with Lee-Yang edge scaling.

MADE model effectively interpolates singularity densities across temperatures.

Extrapolation suggests the location of the QCD critical point.

Abstract

Using simulations at multiple imaginary chemical potentials for $(2+1)$-flavor QCD, we construct multi-point Pad\'e approximants. We determine the singularties of the Pad\'e approximants and demonstrate that they are consistent with the expected universal scaling behaviour of the Lee-Yang edge singularities. We also use a machine learning model, Masked Autoregressive Density Estimator (MADE), to estimate the density of the Lee-Yang edge singularities at each temperature. This ML model allows us to interpolate between the temperatures. Finally, we extrapolate to the QCD critical point using an appropriate scaling ansatz.