Separating Equation-of-State Dynamics from Hadronic Rescattering in Low-Mass Dileptons

We investigate dilepton emission as a probe of the QCD equation of state and phase structure within non-equilibrium chiral fluid dynamics, comparing first-order phase transition and crossover scenarios at $\sqrt{s_{NN}}=2.20$--$6.20~\mathrm{GeV}$. The in-medium $\rho$ and $\omega$ spectral functions are evaluated from resonance-driven forward scattering with pions and nucleons, allowing hadronic in-medium broadening to be distinguished from the additional modification induced by first-order phase transition dynamics. While the phase transition scenario produces an early enhancement in the pole-mass region associated with the onset of EoS softening, the low-mass continuum is enhanced predominantly during the later evolution through reheating and the prolonged lifetime of the fireball. Both signatures remain identifiable after integration over the full evolution and produce a clear separation between the phase transition and crossover scenarios at low beam energies.