Chemical freeze-out curve in heavy-ion collisions and the QCD critical point

The chemical freeze-out curve in heavy-ion collisions is investigated in the context of a quantum chromodynamics (QCD) critical point (CP) search at finite baryon densities. Taking the hadron resonance gas picture at face value, chemical freeze-out points at a given baryochemical potential provide a lower bound on the possible temperature of the QCD CP. We first verify that the freeze-out data in heavy-ion collisions are well described by a constant energy per particle curve, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>E</a:mi><a:mo>/</a:mo><a:mi>N</a:mi><a:mo>=</a:mo><a:mi>const</a:mi></a:mrow></a:math>, under strangeness neutrality conditions (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>μ</b:mi><b:mi>S</b:mi></b:msub><b:mo>≠</b:mo><b:mn>0</b:mn></b:mrow></b:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>μ</c:mi><c:mi>Q</c:mi></c:msub><c:mo>≠</c:mo><c:mn>0</c:mn></c:mrow></c:math>). We then evaluate the hypothetical lower bound on the freeze-out curve based on this criterion in the absence of strangeness neutrality (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>μ</d:mi><d:mi>S</d:mi></d:msub><d:mo>=</d:mo><d:mn>0</d:mn></d:mrow></d:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>μ</e:mi><e:mi>Q</e:mi></e:msub><e:mo>=</e:mo><e:mn>0</e:mn></e:mrow></e:math>) and confront it with recent predictions on the CP location. We find that recent estimates based on Yang-Lee edge singularities from lattice QCD data on coarse lattices (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:msub><f:mi>N</f:mi><f:mi>τ</f:mi></f:msub><f:mo>=</f:mo><f:mn>6</f:mn></f:mrow></f:math>) place the CP significantly below the freeze-out curve, hinting at the importance of performing continuum extrapolation within this method. Predictions based on functional methods and holography place the CP slightly above the freeze-out curve, indicating that the QCD CP may be located very close to the chemical freeze-out in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>A</g:mi><g:mo>+</g:mo><g:mi>A</g:mi></g:mrow></g:math> collisions at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msqrt><h:msub><h:mi>s</h:mi><h:mrow><h:mi>N</h:mi><h:mi>N</h:mi></h:mrow></h:msub></h:msqrt><h:mo>=</h:mo><h:mn>3.5</h:mn><h:mo>−</h:mo><h:mn>6</h:mn><h:mspace width="0.16em"/><h:mi>GeV</h:mi></h:mrow></h:math>.