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Phase structure and observables at high densities from first principles QCD

Christian S. Fischer, Jan M. Pawlowski

Abstract

We provide a short review of the progress made in the past decade with functional QCD in the description of the phase structure of QCD. We summarise the most important technical aspects of the framework, discuss strategies for truncations and address the problem of systematic error estimates. We detail efforts to gauge the approach systematically with lattice QCD at zero chemical potential, also including the physics of the Columbia plot at non-physical quark masses. Our main focus is, however, the high density regime of QCD. We address the predictive power of the functional approach for the appearance of new phases beyond the chiral crossover regime for chemical potentials $μ_B/T\geq 4.5$. The onset of this regime may be signalled by a critical end point of the crossover line but may also involve a moat regime or the emergence of an instability that indicates an inhomogeneous phase. Respective results include estimates for the location of the onset of new phases, and predictions for their experimental signatures.

Phase structure and observables at high densities from first principles QCD

Abstract

We provide a short review of the progress made in the past decade with functional QCD in the description of the phase structure of QCD. We summarise the most important technical aspects of the framework, discuss strategies for truncations and address the problem of systematic error estimates. We detail efforts to gauge the approach systematically with lattice QCD at zero chemical potential, also including the physics of the Columbia plot at non-physical quark masses. Our main focus is, however, the high density regime of QCD. We address the predictive power of the functional approach for the appearance of new phases beyond the chiral crossover regime for chemical potentials . The onset of this regime may be signalled by a critical end point of the crossover line but may also involve a moat regime or the emergence of an instability that indicates an inhomogeneous phase. Respective results include estimates for the location of the onset of new phases, and predictions for their experimental signatures.
Paper Structure (30 sections, 37 equations, 21 figures)

This paper contains 30 sections, 37 equations, 21 figures.

Table of Contents

  1. Introduction
  2. Functional approach to QCD
  3. Functional relations in QCD
  4. Systematic expansion schemes, error estimates and apparent convergence
  5. (i) Modular form of functional relations:
  6. (ii) Locality of correlation functions in gauge-fixed QCD
  7. QCD phase structure from functional QCD
  8. Chiral crossover and soft modes
  9. Confinement-deconfinement crossover and strong correlations
  10. Phase structure of QCD
  11. Critical end point: Estimates and predictions
  12. Pinning down the CEP
  13. Soft modes and the size of QCD critical regions
  14. Fluctuations of conserved charges and thermodynamics
  15. Columbia plot, isospin chemical potential, magnetic fields and more
  16. ...and 15 more sections

Figures (21)

  • Figure 1: DSE: Full propagators and vertices are indicated by grey blobs, the classical vertices are indicated by small black blobs. Gluons are represented by red spiral lines, ghosts by back dotted ones, and quark by straight black ones. In \ref{['fig:DSE-backA0']} we depict the background field DSE. In contradistinction to the fluctuation field DSE, it also hosts a two-loop ghost-gluon term with the four-point vertex $S^{(4)}_{ac\bar{c} \bar{A}_0}$. In \ref{['fig:QuarkGapDSE']} we depict the quark DSE.
  • Figure 2: fRG: Full propagators and vertices are indicated by grey blobs. Gluons are represented by red spiral lines, ghosts by back dotted ones, and quark by straight black ones, $\bigoplus$ accommodates symmetry factors and relative minus signs. In \ref{['fig:funfRG']} we depict the right hand side of the flow equation \ref{['eq:GenFlow']} of the effective action with $\dot \Phi=0$. A detailed account of the flow can be found in Ihssen:2024miv. In \ref{['fig:QuarkGapfRG']} we depict the flow equation for the quark propagator, for the respective DSE see \ref{['fig:QuarkGapDSE']}.
  • Figure 3: Flow of the four-quark scattering vertex: Diagrams in the blue-shaded areas in \ref{['fig:4quarkLego1']} are quark-gluon diagrams that source the four-quark vertex and dominate in the ultraviolet regime with $k \gtrsim 0.6$ GeV, see \ref{['fig:4quarkLego2']}. Diagrams in the red-shaded area in \ref{['fig:4quarkLego1']} are quark-gluon-meson diagrams and dominate in the interface regime with $0.3$ GeV $\lesssim k\lesssim 0.6$ GeV. Diagrams in the green-shaded area in \ref{['fig:4quarkLego1']} are quark-meson diagrams and dominate the infrared regime with $k \lesssim 0.3$ GeV, see \ref{['fig:4quarkLego2']}. The figures are modified from Ihssen:2024miv. The scale $k$ is the infrared cutoff scale in the fRG and is related to an average symmetric-point momentum. The chiral scale $k_\chi=388$ MeV is the onset scale of chiral symmetry breaking in the chiral limit, computed in Ihssen:2024miv.
  • Figure 4: Momentum scale (RG-scale)dependence of the strong couplings $\alpha_{i}$ for $N_f=2+1$ flavours with $i=l\bar{l} A, s\bar{s}A, A^3, A^4$ on a double-logarithmic scale in comparison to the running of the meson exchange couplings $\lambda^{(\pi)} = (h_\phi^2/2)\, G_\pi$ and $\lambda^{(\sigma)}=(h_\phi^2/2)\, G_\sigma$. The different colours reflect the dominance regimes of the different diagrammatic subsectors, see \ref{['fig:4quarkLego']}. Figure modified from Ihssen:2024miv.
  • Figure 5: DSE for the gluon propagator. Diagrams with grey background contain only internal gluon and ghost lines; the quark-loop diagram (blue background) is the explicit matter part.
  • ...and 16 more figures