Heavy quarkonium with finite three momentum near $T_c$

We investigate the non-trivial 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 $T_c$ that is less than 3$\mathrm{\%}$ at a momentum of 1$\mathrm{G}\mathrm{e}\mathrm{V}$. Specifically, we first investigate the difference between the longitudinal and transverse modes of both $J\mathrm{/}\psi$ and ${\chi }_{c1}$. We find that the transverse mode of the $J\mathrm{/}\psi$ experiences larger modification than the longitudinal mode, while the ${\chi }_{c1}$ has the opposite behavior. By comparing the ${\eta }_c$ and ${\chi }_{c0}$, and also the unpolarized $J\mathrm{/}\psi$ and ${\chi }_{c1}$, we recognize that the P-wave particles have stronger momentum dependencies on their masses than the S-wave ones. We also find $\mathrm{{\rm Y}}$(1S) has negligible 3-momentum dependence compared to the charmonium states, e.g. less than 0.01$\mathrm{\%}$ even at 1.4$T_c$ and at a momentum of 4$\mathrm{G}\mathrm{e}\mathrm{V}$.