Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations

I give an estimate for the skewness and the kurtosis of the baryon number distribution in two representative models; i.e., models of a hadron resonance gas and relativistic mean-field nuclear matter. I emphasize formal similarity between these two descriptions. The hadron resonance gas leads to a deviation from the Skellam distribution if quantum statistical correlation is taken into account at high baryon density, but this effect is not strong enough to explain fluctuation data seen in the beam-energy scan at RHIC/STAR. In the calculation of mean-field nuclear matter the density correlation with the vector $\omega$-field rather than the effective mass with the scalar $\sigma$-field renders the kurtosis suppressed at higher baryon density so as to account for the experimentally observed behavior of the kurtosis. We finally discuss the difference between the baryon number and the proton number fluctuations from correlation effects in isospin space. The numerical results suggest that such effects are only minor even in the case of complete randomization of isospin.