Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the subensemble acceptance method for the search of QCD critical point

The critical point is one of the most important aspects of the QCD phase diagram of strongly interacting matter. The nonmonotonic behavior of the higher-order moments of conserved quantities like net-baryon (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi><a:mi>B</a:mi></a:math>), net-charge (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="normal">Δ</d:mi><d:mi>Q</d:mi></d:math>), and net-strangeness (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi mathvariant="normal">Δ</g:mi><g:mi>S</g:mi></g:math>) are believed to be the signatures of the QCD critical point as a function of energy. We study the effect of the QCD critical point on moments of net-baryon in the Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD with six-quark and eight-quark interactions for finite and infinite volume systems. The study is performed at energies similar to Relativistic Heavy-Ion Collider beam energy scan. Experimentally measuring conserved quantities is difficult due to systematic limitations. Therefore, net-proton, net-pion, and net-kaon are measured as the proxy of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi mathvariant="normal">Δ</j:mi><j:mi>B</j:mi></j:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="normal">Δ</m:mi><m:mi>Q</m:mi></m:math>, and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi mathvariant="normal">Δ</p:mi><p:mi>S</p:mi></p:math>. Recent studies in the subensemble acceptance method on the hadron resonance gas (HRG) model show the dependency of the measured higher-order moment on the experimental acceptance. We applied the subensemble acceptance method to analyze the behavior of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>κ</s:mi><s:msup><s:mi>σ</s:mi><s:mn>2</s:mn></s:msup></s:math> of net-baryon distribution within the subvolume system for various acceptance fractions. These results can be directly mapped to the subvolume (particle) percentage of the total volume (conserved quantities). Our findings are compared to the solenoidal tracker at RHIC (STAR) net-proton and proton data with different energies to investigate the presence of the critical point. Additionally, these results are also compared with the ultrarelativistic quantum molecular dynamics (UrQMD), HRG model, and available lattice data. Published by the American Physical Society 2024