Chemical freeze-out curve in heavy-ion collisions and the QCD critical point
Artemiy Lysenko, M. I. Gorenstein, Roman V. Poberezhnyuk, Volodymyr Vovchenko
Abstract
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> .