Reconstructing particle number distributions with convoluting volume fluctuations

We propose the methods to reconstruct the net-particle distributions with and without excluding the initial volume fluctuations. It enables us to correct for detector effects and initial volume fluctuations simultaneously under the assumption of the independent particle production (IPP) model or any particle production mechanism. Our study suggests a tool to investigate possible two-component structure of net-proton distribution in Au+Au collisions at $\sqrt{s_{\rm NN}}=$7.7 GeV as signature of the first-order phase transition or critical end point [arXiv:1804.04463,arXiv:1811.04456].