Femtoscopy as a New Probe of the Nuclear Equation of State
Femtoscopic correlations are widely regarded as precision probes of hadronic interactions through vacuum final-state interactions after kinetic freeze-out. Here we demonstrate that, in baryon-rich heavy-ion collisions, the nuclear mean field generates an additional dynamical contribution to femtoscopic correlations during the transport evolution. Using the Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) transport approach, we investigate proton-proton, proton-$\Lambda$, three-proton, and proton-proton-$\Lambda$ correlations in Au+Au collisions at $\sqrt{s_{\rm NN}}=3$, 4.5, 7.7, and 19.6 GeV. We find that the nuclear mean field produces a characteristic low-$k^*$ enhancement that is strongest at the lowest beam energies and gradually disappears with increasing collision energy. Furthermore, both the stiffness and the momentum dependence of the nuclear equation of state leave distinct signatures in the femtoscopic correlation functions, with higher-order correlations exhibiting substantially enhanced sensitivity compared with conventional two-particle observables. Our results demonstrate that femtoscopy extends beyond its traditional role as a tool for studying hadronic interactions and serve as a new class of microscopic observables for the nuclear equation of state, complementary to collective flow and subthreshold strangeness production, thereby opening a new avenue for exploring dense baryonic matter in low-energy heavy-ion collisions.