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

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 Dij\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{ij}$$\end{document}) 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 (similar to Dij4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sim D<^>4_{ij})$$\end{document} in the four-point correlation function dominating the positive term (similar to Dij5)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sim D<^>5_{ij})$$\end{document}, and this finite-size effect induces a dip structure near the QCD critical point.