Probing the High Density Behaviour of Nuclear Symmetry Energy with High Energy Heavy-Ion Collisions

High energy heavy-ion collisions are proposed as a novel means to constrain stringently the high density (HD) behaviour of nuclear symmetry energy. Within an isospin-dependent hadronic transport model, it is shown for the first time that the isospin asymmetry of the HD nuclear matter formed in high energy heavy-ion collisions is uniquely determined by the HD behaviour of nuclear symmetry energy. Experimental signatures in two sensitive probes, i.e., $\pi^-$ to $\pi^+$ ratio and neutron-proton differential collective flow, are also investigated.