Quark Mass and Volume Dependence of the QCD Phase Diagram with DSEs

Abstract

In this work, which is divided into three distinct analyses, we investigate the quark mass and volume dependence of the phase diagram of quantum chromodynamics. To this end, we employ two very similar sets of truncated Dyson-Schwinger equations in Landau gauge for 2 + 1 quark flavours in a combination with lattice Yang-Mills theory that have been studied extensively in the past. This system predicts a critical endpoint in the phase diagram at moderate temperature and large chemical potential. In the first analysis, we study the impact of a finite volume on the location of this critical endpoint. We investigate our system of Dyson-Schwinger equations at small and intermediate volumes and determine the dependence of the location of the critical endpoint on the boundary conditions and the volume of a three-dimensional cube with edge length L. We demonstrate that noticeable volume effects of more than five per cent occur only for L ≲ 5 fm and that volumes as large as L³ ≳ (8 fm)³ are very close to the infinite-volume limit. Additionally, we present results for the volume dependence of baryon-number fluctuations and ratios thereof up to fourth order in the vicinity of the critical endpoint. Due to the limitations of our truncation, the results are quantitatively meaningful only outside the critical scaling region of the endpoint. We find that the fluctuations are visibly affected by the finite volume, particularly for antiperiodic boundary conditions, whereas their ratios are practically invariant. In the second analysis, we examine the quality of the extrapolation procedure employed in Ref. [1] to extract the crossover line at real chemical potential from lattice data at imaginary potential. We determine the up/down-quark condensate and chiral susceptibility at imaginary chemical potentials and perform an analytic continuation along the lines described in Ref. [1]. We find that the analytically continued crossover line agrees very well (within one per cent) with the explicitly calculated one for chemical potentials up to about 80 % of the value of the critical endpoint. The method breaks down in the region where the chiral susceptibility as a function of the condensate can no longer be well described by a polynomial. In the final analysis, we investigate the order of the chiral transition of quantum chromodynamics in the limit of vanishing bare up/down-quark masses for variations of the bare strange-quark mass, 0 ≤ ms ≤ ∞. In this limit and due to universality, long-range correlations with the quantum numbers of pseudoscalar and scalar mesons may dominate the physics. In order to study the interplay between the microscopic quark and gluon degrees of freedom and these long-range correlations, we extend our set of Dyson-Schwinger equations with a meson-backcoupling approach. The latter has already been studied in the past but this is the first work in a full (2 + 1)-flavour setup. Starting from the physical point, we determine the chiral susceptibilities for decreasing up/down-quark masses and find good agreement with both lattice and functional-renormalization-group results. We then proceed to determine the order of the chiral transition along the left-hand side of the Columbia plot for chemical potentials in the range -(30 MeV)² ≤ μB² ≤ (30 MeV)². We find a second-order phase transition throughout and no trace of a first-order region in the Nf = 3 corner of the Columbia plot. This result remains unchanged when an additional Goldstone boson due to a restored axial UA(1) symmetry is taken into account.