The QCD critical point via Padé and multi-point Padé resummations

Detailed knowledge of the phase diagram of Quantum Chromodynamics (QCD) is of uttermost importance for our understanding of heavy ion collisions and is also relevant in the context of cosmology and astrophysics.

QCD exhibits a complex phase structure with various critical points that give rise to universal critical behaviour.

A promising and novel procedure to investigate this critical behaviour is through the analysis of Lee-Yang edge singularities (LYE), related to these critical points. Unfortunately direct lattice QCD calculations at real chemical potentials or genuine complex chemical potentials are prohibited by the infamous sign problem in QCD.

We propose here to calculate the LYE by a multi-point Padé interpolation of the net-baryon density obtained at imaginary chemical potential. This method allows for the combination of the Taylor expansion approach with calculations at imaginary chemical potential.

Current results on the LYE are promising: We observe an apparent approach to the real axis, which would indicate the position of the elusive QCD critical point. To further control the extrapolation we need higher precision in the LYE calculation and also smaller temperatures.