<p>The sign of higher-order multiplicity fluctuations is a very important parameter for exploring QCD phase transitions. The kurtosis of the net-baryon is typically negative in simulations of the dynamics of the conserved net-baryon density near the QCD critical point. This paper considers the effects of finite size on multiplicity fluctuations with equilibrium critical fluctuations. It is found that the multiplicity fluctuations (or the magnitude of the correlation function <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1721_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$D_{ij}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mrow> <mi mathvariant="italic">ij</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) are dramatically suppressed with decreasing system size when the size of the system is small compared with the correlation length, which is the so-called acceptance dependence. Consequently, the small correlation function of the small system size results in the magnitude of the negative contribution <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1721_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">$(\sim D^4_{ij})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>∼</mo> <msubsup> <mi>D</mi> <mrow> <mi mathvariant="italic">ij</mi> </mrow> <mn>4</mn> </msubsup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in the four-point correlation function dominating the positive term <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1721_Article_IEq3.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">$(\sim D^5_{ij})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>∼</mo> <msubsup> <mi>D</mi> <mrow> <mi mathvariant="italic">ij</mi> </mrow> <mn>5</mn> </msubsup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and this finite-size effect induces a dip structure near the QCD critical point.</p>

The sign of kurtosis within finite system near the QCD critical point

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发表日期：

2025年6月5日

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Shanjin Wu

摘要

The sign of higher-order multiplicity fluctuations is a very important parameter for exploring QCD phase transitions. The kurtosis of the net-baryon is typically negative in simulations of the dynamics of the conserved net-baryon density near the QCD critical point. This paper considers the effects of finite size on multiplicity fluctuations with equilibrium critical fluctuations. It is found that the multiplicity fluctuations (or the magnitude of the correlation function $D_{ij}$ $D_{ij}$ ) are dramatically suppressed with decreasing system size when the size of the system is small compared with the correlation length, which is the so-called acceptance dependence. Consequently, the small correlation function of the small system size results in the magnitude of the negative contribution $(\sim D^4_{ij})$ $(\sim D_{ij}^{4})$ in the four-point correlation function dominating the positive term $(\sim D^5_{ij})$ $(\sim D_{ij}^{5})$ , and this finite-size effect induces a dip structure near the QCD critical point.