Proton-neutron correlations in baryon-number fluctuations near the liquid-gas transition

We study net-baryon number density fluctuations in isospin-symmetric matter near the nuclear liquid-gas phase transition using the parity doublet model. We analyze second-order susceptibilities of net-proton and net-neutron numbers and their correlations. We show that proton-neutron correlations are nontrivial and lead to qualitative differences between net-proton and net-baryon fluctuations. We further investigate factorial cumulants and demonstrate that the differences between baryon- and proton-number factorial cumulants are governed by proton-neutron correlations. Our results highlight the importance of interaction-driven correlations for interpreting fluctuation measurements near the liquid-gas critical endpoint.