We consider the quarkonium diffusion, dissociation, and recombination inside quark-gluon plasma. We compute scattering amplitudes in potential nonrelativistic QCD for relevant processes. These processes include the gluon absorption/emission at the order $gr$, inelastic scattering at the order $g^{2}r$, and elastic scattering with medium constituents at the order $g^2{r}^2$. We show these amplitudes satisfy the Ward identity. We also consider one-loop corrections. The dipole interaction between the color singlet and octet is not running at the one-loop level. Interference between the tree-level gluon absorption/emission and its thermal loop corrections cancels the collinear divergence in the $t$-channel inelastic scattering. The inelastic scattering has no soft divergence because of the finite binding energy of quarkonium. We write out the diffusion, dissociation, and recombination terms explicitly for a Boltzmann transport equation and define the dissociation and recombination rates. Furthermore, we calculate the diffusion coefficient of quarkonium. We find our result of the diffusion coefficient differs from a previous calculation by 2 to 3 orders of magnitude. We explain this and can reproduce the previous result in a certain limit. Finally, we discuss two mechanisms of quarkonium energy loss inside quark-gluon plasma.

• Received 12 December 2018

DOI:https://doi.org/10.1103/PhysRevD.100.014008

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Published by the American Physical Society