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Effects of nuclear symmetry energy on eta meson production and its rare decay to the dark U-boson in heavy-ion reactions

Using a relativistic transport model ART1.0, we explore effects of nuclear symmetry energy on eta meson production and its rare decay to the dark U-boson in heavy-ion reactions from 0.2 to 10 GeV/nucleon available at several current and future facilities. The yield of eta mesons at sub-threshold energies is found to be very sensitive to the density dependence of nuclear symmetry energy. Above a beam energy of about 5 GeV/nucleon in Au+Au reactions, the sensitivity to symmetry energy disappears. Using the branching ratio of the rare eta decay (eta->gamma U) available in the literature, we estimate the maximum cross section for the U-boson production in the energy range considered, providing a useful reference for future U-boson search using heavy-ion reactions.