Heavy quarkonium with finite three momentum near Tc

We investigate the nontrivial 3-momentum effects on the masses of heavy quarkonium states that are moving in a hot medium using QCD sum rules. For all charmonium states, we observe a negative mass shift near Tc that is less than 3% at a momentum of 1 GeV. Specifically, we first investigate the difference between the longitudinal and transverse modes of both J/ψ and χc1. We find that the transverse mode of the J/ψ experiences larger modification than the longitudinal mode, while the χc1 has the opposite behavior. By comparing the ηc and χc0, and also the unpolarized J/ψ and χc1, we recognize that the P-wave particles have stronger momentum dependencies on their masses than the S-wave ones. We also find (1S) has negligible 3-momentum dependence compared to the charmonium states, e.g., less than 0.01% even at 1.4Tc and at a momentum of 4 GeV.