Exploring the critical points in QCD with multi-point Padé and machine learning techniques in (2+1)-flavor QCD

¹ RIKEN Center for Computational Science, Kobe 650-0047, Japan
² Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, United States
³ Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma and INFN, Gruppo Collegato di Parma I-43100 Parma, Italy
⁴ Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
⁵ Dipartimento di Fisica dell’Università di Pisa and INFN–Sezione di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy

^* e-mail: jishnu.goswami@riken.jp

Published online: 26 June 2024

Abstract

Using simulations at multiple imaginary chemical potentials for (2 + 1)-flavor QCD, we construct multi-point Padé approximants. We determine the singularties of the Padé 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.