Observation of excess J/$\psi$ yield at very low transverse momenta in Au+Au collisions at $\sqrt{s_{\rm{NN}}} =$ 200 GeV and U+U collisions at $\sqrt{s_{\rm{NN}}} =$ 193 GeV

We report on the first measurements of J/$\psi$ production at very low transverse momentum ($p_{T} <$ 0.2 GeV/c) in hadronic Au+Au collisions at $\sqrt{s_{\rm{NN}}} =$ 200 GeV and U+U collisions at $\sqrt{s_{\rm{NN}}} =$ 193 GeV. Remarkably, the inferred nuclear modification factor of J/$\psi$ at mid-rapidity in Au+Au (U+U) collisions reaches about 24 (52) for $p_{T} <$ 0.05 GeV/c in the 60-80$\%$ collision centrality class. This noteworthy enhancement cannot be explained by hadronic production accompanied by cold and hot medium effects. In addition, the $dN/dt$ distribution of J/$\psi$ for the very low $p_{T}$ range is presented for the first time. The distribution is consistent with that expected from the Au nucleus and shows a hint of interference. Comparison of the measurements to theoretical calculations of coherent production shows that the excess yield can be described reasonably well and reveals a partial disruption of coherent production in semi-central collisions, perhaps due to the violent hadronic interactions. Incorporating theoretical calculations, the results strongly suggest that the dramatic enhancement of J/$\psi$ yield observed at extremely low $p_{T}$ originates from coherent photon-nucleus interactions. In particular, coherently produced J/$\psi$'s in violent hadronic collisions may provide a novel probe of the quark-gluon-plasma.