<p>The crossover from hadronic to quark matter is understood to be both a deconfinement as well as a chiral symmetry–restoring transition. The precise definition of these aspects may be ambiguous. Here we use the static quark free energy and its temperature derivative as proxies for deconfinement and the chiral condensate and its mass derivatives for the chiral transition. At zero baryochemical potential, and infinite volume, the chiral and deconfinement crossover temperatures almost agree. However, as we vary the spatial volume of the simulation, we observe that chiral and deconfinement-related observables have a qualitatively different chemical potential and volume dependence. In general, deconfinement-related observables have a milder volume dependence. Furthermore, while the deconfinement transition appears to get broader with increasing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math>, the width as well as the strength of the chiral transition is approximately constant. Our results are based on simulations at zero and imaginary chemical potentials using 4-stout-improved staggered fermions with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>12</mn></math> time slices and physical quark masses.</p>

Germany

Szabolcs Borsányi

United States

Hungary

Zoltán Fodor

Jana N. Guenther

Ruben Kara

Italy

Paolo Parotto

Attila Pásztor

Ludovica Pirelli

Chik Him Wong

Chiral versus deconfinement properties of the QCD crossover: Differences in the volume and chemical potential dependence from the lattice

The QCD crossover line in the temperature (<math><mi>T</mi></math>)-baryochemical potential (<math><msub><mi>μ</mi><mi>B</mi></msub></math>) plane has been computed by several lattice groups by calculating the chiral order parameter and its susceptibility at finite values of <math><msub><mi>μ</mi><mi>B</mi></msub></math>. In this work we focus on the deconfinement aspect of the transition between hadronic and quark gluon plasma phases. We define the deconfinement temperature as the peak position of the static quark entropy [<math><msub><mi>S</mi><mi>Q</mi></msub><mo>(</mo><mi>T</mi><mo>,</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>)</mo></math>] in <math><mi>T</mi></math>, which is based on the renormalized Polyakov loop. We extrapolate <math><msub><mi>S</mi><mi>Q</mi></msub><mo>(</mo><mi>T</mi><mo>,</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>)</mo></math> based on high statistics finite temperature ensembles on a <math><msup><mn>16</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math> lattice to finite density by means of a Taylor expansion to eighth order in <math><msub><mi>μ</mi><mi>B</mi></msub></math> (NNNLO) along the strangeness neutral line. For the simulations the 4HEX staggered action was used with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> flavors at physical quark masses. In this setup the phase diagram can be drawn up to unprecedentedly high chemical potentials. Our results for the deconfinement temperature are in rough agreement with phenomenological estimates of the freeze-out curve in relativistic heavy ion collisions. In addition, we study the width of the deconfinement crossover. We show that up to <math><msub><mi>μ</mi><mi>B</mi></msub><mo>≈</mo><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, the deconfinement transition gets broader at higher densities, disfavoring the existence of a deconfinement critical endpoint in this range. Finally, we examine the transition line without the strangeness neutrality condition and observe a hint for the narrowing of the crossover towards large <math><msub><mi>μ</mi><mi>B</mi></msub></math>.

Kálmán K. Szabó

QCD deconfinement transition line up to <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>=</mo><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> from finite volume lattice simulations

Fluctuations play a key role in the study of QCD phases. Lattice QCD is a valuable tool to calculate them, but going to high orders is challenging. Up to the fourth order, continuum results have been available since 2015. We present the first continuum results for sixth-order baryon fluctuations for temperatures between <math><mi>T</mi><mo>=</mo><mn>130</mn></math> and 200 MeV and eighth order at <math><mi>T</mi><mo>=</mo><mn>145</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> in a fixed volume. Comparison with earlier studies with imaginary chemical potential suggests that the volume effect is under control for <math><mi>T</mi><mo>&lt;</mo><mn>145</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Our results are in sharp contrast with well-known results in the literature obtained at finite lattice spacing.

Sándor D. Katz

Dávid Pesznyák

Continuum-extrapolated high-order baryon fluctuations

Research on the quantum chromodynamics (QCD) phase diagram with lattice field theory methods is dominated by the use of rooted staggered fermions, as they are the computationally cheapest discretization available. We show that rooted staggered fermions at a nonzero baryochemical potential <math><msub><mi>μ</mi><mi>B</mi></msub></math> predict a sharp rise in the baryon density at low temperatures and <math><msub><mi>μ</mi><mi>B</mi></msub><mo>≳</mo><mn>3</mn><msub><mi>m</mi><mi>π</mi></msub><mo>/</mo><mn>2</mn></math>, where <math><msub><mi>m</mi><mi>π</mi></msub></math> is the Goldstone pion mass. We elucidate the nature of the nonanalyticity behind this sharp rise in the density by a comparison of reweighting results with a Taylor expansion of high order. While at first sight this nonanalytic behavior becomes apparent at the same position where the pion condensation transition takes place in the phase-quenched theory, the nature of the nonanalyticity in the two theories appears to be quite different: While at nonzero isospin density the data are consistent with a genuine thermodynamic (branch-point) singularity, the results at nonzero baryon density point to an essential singularity at <math><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></math>. The effect is absent for four flavors of degenerate quarks, where rooting is not used. For the two-flavor case, we show numerical evidence that the magnitude of the effect diminishes on finer lattices. We discuss the implications of this technical complication on future studies of the QCD phase diagram.

Matteo Giordano

Can rooted staggered fermions describe nonzero baryon density at low temperatures?

The equation of state of the quark gluon plasma is a key ingredient of heavy-ion phenomenology. In addition to the traditional Taylor method, several novel approximation schemes have been proposed with the aim of calculating it at finite baryon density. In order to gain a pragmatic understanding of the limits of these schemes, we compare them to direct results at <math><msub><mi>μ</mi><mi>B</mi></msub><mo>&gt;</mo><mn>0</mn></math>, using reweighting techniques free from an overlap problem. We use 2stout improved staggered fermions with eight time slices and cover the entire Relativistic Heavy Ion Collider Beam Energy Scan range in the baryochemical potential, up to <math><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><mi>T</mi><mo>=</mo><mn>3</mn></math>.

Equation of state of a hot-and-dense quark gluon plasma: Lattice simulations at real <math><msub><mi>μ</mi><mi>B</mi></msub></math> vs extrapolations

We calculate a resummed equation of state with lattice QCD simulations at imaginary chemical potentials. This work presents a generalization of the scheme introduced in [Phys. Rev. Lett. 126, 232001 (2021) to the case of nonzero <math><msub><mi>μ</mi><mi>S</mi></msub></math>, focusing on the line of strangeness neutrality. We present results up to <math><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><mi>T</mi><mo>≤</mo><mn>3.5</mn></math> on the strangeness neutral line <math><mrow><mo>⟨</mo><mi>S</mi><mo>⟩</mo></mrow><mo>=</mo><mn>0</mn></math> in the temperature range <math><mn>130</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>≤</mo><mi>T</mi><mo>≤</mo><mn>280</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. We also extrapolate the finite baryon density equation of state to small nonzero values of the strangeness-to-baryon ratio <math><mi>R</mi><mo>=</mo><mrow><mo>⟨</mo><mi>S</mi><mo>⟩</mo></mrow><mo>/</mo><mrow><mo>⟨</mo><mi>B</mi><mo>⟩</mo></mrow></math>. We perform a continuum extrapolation using lattice simulations of the 4stout-improved staggered action with 8, 10, 12 and 16 time slices.

Claudia Ratti

Kálmán Szabó

Resummed lattice QCD equation of state at finite baryon density: Strangeness neutrality and beyond

We use the sign-reweighting method to simulate the QCD chiral transition at real baryon densities on phenomenologically relevant lattices. This avoids the severe limitations of extrapolating from zero or imaginary chemical potential and the overlap problem of traditional reweighting approaches, opening up a new window to reliably study hot and dense strongly interacting matter from first principle lattice simulations. We demonstrate that sign reweighting can reach up to a baryochemical potential-temperature ratio of <math><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><mi>T</mi><mo>=</mo><mn>2.7</mn></math>, covering most of the Relativistic Heavy Ion Collider Beam Energy Scan range.

Dániel Nógrádi

Lattice simulations of the QCD chiral transition at real baryon density

The hadron resonance gas (HRG) model is often believed to correctly describe the confined phase of QCD. This assumption is the basis of many phenomenological works on QCD thermodynamics and of the analysis of hadron yields in relativistic heavy ion collisions. We use first principle lattice simulations to calculate corrections to the ideal HRG model. Namely, we determine the subleading fugacity expansion coefficients of the grand canonical free energy, receiving contributions from processes like kaon-kaon or baryon-baryon scattering. We achieve this goal by performing a two dimensional scan on the imaginary baryon number chemical potential (<math><msub><mi>μ</mi><mi>B</mi></msub></math>)—strangeness chemical potential (<math><msub><mi>μ</mi><mi>S</mi></msub></math>) plane, where the fugacity expansion coefficients become Fourier coefficients. We carry out a continuum limit estimation of these coefficients by performing lattice simulations with temporal extents of <math><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>8</mn></math>, 10, 12 using the 4stout-improved staggered action. We then use the truncated fugacity expansion to extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials. Evaluating the fugacity expansion along the crossover line, we reproduce the trend seen in the experimental data on net-proton fluctuations by the STAR collaboration.

Rene Bellwied

France

Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density

The topological susceptibility of the SU(3) pure gauge theory is calculated in the deconfined phase at temperatures up to <math><mn>10</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>. At such large temperatures the susceptibility is suppressed, topologically non-trivial configurations are extremely rare. Thus, direct lattice simulations are not feasible. The density of states (DoS) method is designed to simulate rare events, we present an application of the DoS method to the problem of high temperature topological susceptibility. We reconstruct the histogram of the charge sectors that one could have obtained in a naive importance sampling. Our findings are perfectly consistent with a free instanton gas.

Austria

Dénes Sexty

Topological susceptibility of pure gauge theory using density of states

We study the correlators of Polyakov loops, and the corresponding gauge invariant free energy of a static quark-antiquark pair in 2+1 flavor QCD at finite temperature. Our simulations were carried out on N t = 6 , 8 , 10 , 12 , 16 lattices using a Symanzik improved gauge action and a stout improved staggered action with physical quark masses. The free energies calculated from the Polyakov loop correlators are extrapolated to the continuum limit. For the free energies we use a two step renormalization procedure that only uses data at finite temperature. We also measure correlators with definite Euclidean time reversal and charge conjugation symmetry to extract two different screening masses, one in the magnetic, and one in the electric sector, to distinguish two different correlation lengths in the full Polyakov loop correlator.

Sándor Katz

Csaba Török

Static Q ¯ Q $$ \overline{\mathrm{Q}}\mathrm{Q} $$ pair free energy and screening masses from correlators of Polyakov loops: continuum extrapolated lattice results at the QCD physical point