Baryon number fluctuations induced by hadronic interactions at low temperature and large chemical potential

We investigate the density fluctuations induced by hadronic interactions at low temperatures and large chemical potentials after the hadronization of quark-gluon plasma~(QGP). We analyze the structures of net-baryon number kurtosis and skewness and elaborate on their relations with the nuclear liquid-gas~(LG) phase transition and hadronic interactions above the critical temperature. Combining with the relevant experimental projects at RHIC/NICA/FAIR/J-PARC/HIAF with collision energies from $200\,$GeV to $1.8\,$GeV, we propose a double-peak structure of kurtosis (skewness) as a function of collision energy, which can be taken to identify the chiral phase transition and the nuclear liquid-gas phase transition. In particular, the fluctuation distributions at low temperatures provide a new method to explore hadronic interactions and nuclear liquid-gas transition.