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

he sign of higher order multiplicity fluctuations is a very important quantity in exploring the QCD phase transition. It is found that the kurtosis of net-baryon is typically negative in the simulations of the dynamics of conserved net-baryon density near the QCD critical point. This paper considers the effects of finite size on the multiplicity fluctuations with equilibrium critical fluctuations. It is found that the multiplicity fluctuations (or magnitude of correlation function $D_{ij}$) are dramatically suppressed with decreasing system size when the size of the system is small comparing 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 $(\sim D^4_{ij})$ in the four-point correlation function dominates over the one of positive term $(\sim D^5_{ij})$, and this finite size effects induces a dip structure near the QCD critical point.