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$\%$ at a momentum of 1$\rm{ GeV}$. Specifically, we first investigate the difference between the longitudinal and transverse modes of both $J/\psi$ and $\chi_{ c1}$. We find that the transverse mode of the $J/\psi$ 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 $J/\psi$ 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 $\Upsilon$(1S) has negligible 3-momentum dependence compared to the charmonium states, e.g. less than 0.01$\%$ even at 1.4$T_c$ and at a momentum of 4$\rm{ GeV}$.
Categories: hep-ph hep-ex nucl-th