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The chiral phase transition in the 3D Columbia plot

Alessandro Sciarra

TL;DR

Addresses the chiral phase transition problem in QCD by leveraging a sign-problem-free extension with purely imaginary chemical potential $\mu=i\mu_i$ to map the 3D Columbia plot. The paper builds on the framework from Ref. Cuteri_2021 to propose a concrete extension with an intermediate $\mu_i$ value in the range $-(\pi/3)^2 < (i\mu_i/T)^2 < 0$, detailing data production, analysis, and software workflow (CL2QCD, BaHaMAS, MCC++, etc.). It discusses lattice artefacts that produce a chiral first-order region at coarse lattices for $N_f=2$ and $N_f=3$ and argues this region vanishes in the continuum, shaping two possible continuum scenarios (3D-seculation-1 and 3D-seculation-2) for how the first-order surface evolves near the Roberge-Weiss plane. The work emphasizes a fully specified numerical program with publicly released tools to systematically test these scenarios and clarify the phase structure at nonzero density, with implications for locating or excluding critical points in the QCD phase diagram.

Abstract

The nature of the chiral phase transition of QCD continues to represent a fundamental open problem in the study of strongly interacting matter. In recent years, significant progress has been achieved by exploiting systematic variations of theory parameters in regimes free of the sign problem. In this work, the idea of a follow-up investigation that extends a previous study at zero chemical potential is presented. A concrete programme for such an extension is discussed, outlining the required numerical steps, from data production to final analysis, and pointing to all the software tools that have been released to support these studies.

The chiral phase transition in the 3D Columbia plot

TL;DR

Addresses the chiral phase transition problem in QCD by leveraging a sign-problem-free extension with purely imaginary chemical potential to map the 3D Columbia plot. The paper builds on the framework from Ref. Cuteri_2021 to propose a concrete extension with an intermediate value in the range , detailing data production, analysis, and software workflow (CL2QCD, BaHaMAS, MCC++, etc.). It discusses lattice artefacts that produce a chiral first-order region at coarse lattices for and and argues this region vanishes in the continuum, shaping two possible continuum scenarios (3D-seculation-1 and 3D-seculation-2) for how the first-order surface evolves near the Roberge-Weiss plane. The work emphasizes a fully specified numerical program with publicly released tools to systematically test these scenarios and clarify the phase structure at nonzero density, with implications for locating or excluding critical points in the QCD phase diagram.

Abstract

The nature of the chiral phase transition of QCD continues to represent a fundamental open problem in the study of strongly interacting matter. In recent years, significant progress has been achieved by exploiting systematic variations of theory parameters in regimes free of the sign problem. In this work, the idea of a follow-up investigation that extends a previous study at zero chemical potential is presented. A concrete programme for such an extension is discussed, outlining the required numerical steps, from data production to final analysis, and pointing to all the software tools that have been released to support these studies.

Paper Structure

This paper contains 2 sections, 3 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The 3D Columbia plot

Figures (2)

  • Figure 1: Known sketches of the Columbia plot and its 3D extension. Sketch \ref{['fig:3D-1st']} was taken from ref. Philipsen_2020 and depicts the scenario realized on coarse lattices. Sketch \ref{['fig:CP']} was taken from ref. Cuteri_2021; there it has been shown that the chiral first-order region at zero baryon chemical potential is a lattice artefact for $\text{N}_\text{f}=2$ and $\text{N}_\text{f}=3$ which vanishes in the continuum limit.
  • Figure 2: Possible realizations of the 3D Columbia plot in the continuum limit sciarra_2024_10599969. Sketch \ref{['fig:3D-seculation-1']} had already been suggested in ref. sciarra_PhD as a speculation, while \ref{['fig:3D-seculation-2']} represents the most natural scenario, given how the chiral first-order region seems to shrink approaching the continuum limit. Grey lines and points denote a possibly more complex type of phase transition, still to be determined. For instance, it is still an open question how the Roberge-Weiss transition across different sectors interplays with the thermal transition along the $m_{u,d}=0$ line in the Roberge-Weiss plane.