A New State Of Hadronic Matter At High Density

We propose in this article that if the chemical potential exceeds a critical value in dense hadronic medium, a first-order phase transition to a new state of matter with Lorentz symmetry spontaneously broken (in addition to the explicit breaking) takes place. As a consequence, light vector mesons get excited as ``almost'' Goldstone bosons. Since the light vector mesons dominantly couple to photons, the presence of these new vector mesons could lead to an enhancement in the dilepton production from dense medium at an invariant mass lower than the free-space vector-meson mass. We provide a low-energy quark model which demonstrates that the above scenario is a generic case for quark theories with a strong interaction in the vector channel. We discuss possible relevance of this phase to the phenomenon of the enhanced dilepton production at low invariant masses in relativistic heavy-ion collisions.