Chemical freeze-out parameters via a functional renormalization group approach

We study the freeze-out parameters in a QCD-assisted effective theory that accurately captures the quantum and in-medium effects of QCD at low energies. The functional renormalization group approach is implemented in our work to incorporate the nonperturbative quantum, thermal, and density fluctuations. By analyzing the calculated baryon number susceptibility ratios <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>χ</a:mi><a:mn>2</a:mn><a:mi>B</a:mi></a:msubsup><a:mo>/</a:mo><a:msubsup><a:mi>χ</a:mi><a:mn>1</a:mn><a:mi>B</a:mi></a:msubsup></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msubsup><c:mi>χ</c:mi><c:mn>3</c:mn><c:mi>B</c:mi></c:msubsup><c:mo>/</c:mo><c:msubsup><c:mi>χ</c:mi><c:mn>2</c:mn><c:mi>B</c:mi></c:msubsup></c:math>, we determine the chemical freeze-out temperatures and baryon chemical potentials in cases of hard thermal or dense loop improved <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>μ</e:mi></e:math>-dependent gluon potential and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>μ</g:mi></g:math>-independent gluon potential. We calculate the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>χ</i:mi><i:mn>4</i:mn><i:mi>B</i:mi></i:msubsup><i:mo>/</i:mo><i:msubsup><i:mi>χ</i:mi><i:mn>2</i:mn><i:mi>B</i:mi></i:msubsup><i:mo stretchy="false">(</i:mo><i:mi>κ</i:mi><i:msup><i:mi>σ</i:mi><i:mn>2</i:mn></i:msup><i:mo stretchy="false">)</i:mo></i:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi>χ</m:mi><m:mn>6</m:mn><m:mi>B</m:mi></m:msubsup><m:mo>/</m:mo><m:msubsup><m:mi>χ</m:mi><m:mn>2</m:mn><m:mi>B</m:mi></m:msubsup></m:math> along the freeze-out line for both cases. It is found that <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>κ</o:mi><o:msup><o:mi>σ</o:mi><o:mn>2</o:mn></o:msup></o:math> exhibits a nonmonotonic behavior in a low collision energy region and approaches one for lower collision energy. <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msubsup><q:mi>χ</q:mi><q:mn>6</q:mn><q:mi>B</q:mi></q:msubsup><q:mo>/</q:mo><q:msubsup><q:mi>χ</q:mi><q:mn>2</q:mn><q:mi>B</q:mi></q:msubsup></q:math> shows a similar complicated behavior in our calculation. Published by the American Physical Society 2024