<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

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

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

We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature <math><msub><mi>T</mi><mi>c</mi></msub></math>, allowing for its very precise determination, and extrapolate from imaginary chemical potential up to real <math><msub><mi>μ</mi><mi>B</mi></msub><mo>≈</mo><mn>300</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The definition of <math><msub><mi>T</mi><mi>c</mi></msub></math> adopted in this work is based on the observation that the chiral susceptibility as a function of the condensate is an almost universal curve at zero and imaginary <math><msub><mi>μ</mi><mi>B</mi></msub></math>. We obtain the parameters <math><msub><mi>κ</mi><mn>2</mn></msub><mo>=</mo><mn>0.0153</mn><mo>(</mo><mn>18</mn><mo>)</mo></math> and <math><msub><mi>κ</mi><mn>4</mn></msub><mo>=</mo><mn>0.00032</mn><mo>(</mo><mn>67</mn><mo>)</mo></math> as a continuum extrapolation based on <math><msub><mi>N</mi><mi>t</mi></msub><mo>=</mo><mn>10</mn></math>, 12, 16 lattices with physical quark masses. We also extrapolate the peak value of the chiral susceptibility and the width of the chiral transition along the crossover line. In fact, both of these are consistent with a constant function of <math><msub><mi>μ</mi><mi>B</mi></msub></math>. We see no sign of criticality in the explored range.

Szabolcs Borsanyi

Zoltan Fodor

Sandor D. Katz

Attila Pasztor

Kálman K. Szabó

QCD Crossover at Finite Chemical Potential from Lattice Simulations

We construct a family of equations of state for QCD in the temperature range <math><mrow><mn>30</mn><mspace width="0.16em"></mspace><mi>MeV</mi><mo>≤</mo><mi>T</mi><mo>≤</mo><mn>800</mn><mspace width="0.16em"></mspace><mi>MeV</mi></mrow></math> and in the chemical potential range <math><mrow><mn>0</mn><mo>≤</mo><msub><mi>μ</mi><mi>B</mi></msub><mo>≤</mo><mn>450</mn><mspace width="0.16em"></mspace><mi>MeV</mi></mrow></math>. These equations of state match available lattice QCD results up to <math><mrow><mi>O</mi><mo>(</mo><msubsup><mi>μ</mi><mi>B</mi><mn>4</mn></msubsup><mo>)</mo></mrow></math> and in each of them we place a critical point in the three-dimensional (3D) Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at the Relativistic Heavy Ion Collider. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density, and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.

Poland

Marcus Bluhm

Debora Mroczek

Marlene Nahrgang

J. Noronha-Hostler

Krishna Rajagopal

Thomas Schäfer

Mikhail Stephanov

QCD equation of state matched to lattice data and exhibiting a critical point singularity