Net strangeness fluctuations and their experimental implications in the SU(3) PNJL model using the subensemble acceptance method for the search of QCD critical point

Abstract The critical end point (CEP) is a key feature of the quantum chromo dynamics (QCD) phase diagram. Near the CEP, critical phenomena lead higher-order moments of conserved charges, such as net baryon ( $$\Delta B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>B</mml:mi> </mml:mrow> </mml:math> ), net charge ( $$\Delta Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> ), and net strangeness ( $$\Delta S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> ), to exhibit non-monotonic behavior. These moments and their volume-independent products are sensitive to the correlation length, making them crucial observables in the search for the CEP. In this study, we investigate net strangeness fluctuations using the finite-volume Polyakov-loop extended Nambu–Jona-Lasinio (PNJL) model, incorporating six-quark and eight-quark interactions at energies similar to those of the RHIC beam energy scan. Since direct measurement of conserved charges is experimentally challenging, net proton, net pion, and net kaon are used as proxies for $$\Delta B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>B</mml:mi> </mml:mrow> </mml:math> , $$\Delta Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> , and $$\Delta S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> . Recent studies employing the sub-ensemble acceptance method in the Hadron resonance gas (HRG) model have shown that higher-order moments are dependent on experimental acceptance. We applied this method to study the behavior of $$\kappa \sigma ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>κ</mml:mi> <mml:msup> <mml:mi>σ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> of net strangeness distributions across varying acceptance fractions, corresponding to sub-volume percentages of the total system. Our results are compared to STAR kaon data and the HRG model to assess the existence of the CEP.