Constructing the equation of state of QCD in a functional QCD based scheme

We construct the equation of state (EOS) of QCD based on the finite chemical potential information from the functional QCD approaches with the results at zero chemical potential being calibrated by lattice QCD simulations. Specifically, the construction is achieved by parametrizing the order parameters from the functional QCD data into the EOS, namely, the dynamical quark mass for the chiral phase transition and the Polyakov loop for the deconfinement phase transition. The obtained EOS is consistent with the up-to-date results of the QCD phase diagram, including a phase transition temperature at zero chemical potential of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi><a:mo>=</a:mo><a:mn>155</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>MeV</a:mi></a:math>, the curvature of the transition line <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>κ</c:mi><c:mo>=</c:mo><c:mn>0.016</c:mn></c:math>, and also a critical end point at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo stretchy="false">(</e:mo><e:mi>T</e:mi><e:mo>,</e:mo><e:msub><e:mi>μ</e:mi><e:mi>B</e:mi></e:msub><e:mo stretchy="false">)</e:mo><e:mo>=</e:mo><e:mo stretchy="false">(</e:mo><e:mn>118</e:mn><e:mo>,</e:mo><e:mn>600</e:mn><e:mo stretchy="false">)</e:mo><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>MeV</e:mi></e:math>. We also implement the EOS in hydrodynamic simulations to compute the particle yields and ratios and find that our obtained EOS agrees well with the commonly used one based on the combination of lattice QCD simulation and hadron resonance gas model. Published by the American Physical Society 2024