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We consider the quarkonium diffusion, dissociation and recombination insidequark-gluon plasma. We compute scattering amplitudes in potentialnonrelativistic QCD for relevant processes. These processes include the gluonabsorption/emission at the order $gr$, inelastic scattering at the order $g^2r$and elastic scattering with medium constituents at the order $g^2r^2$. We showthese amplitudes satisfy the Ward identity. We also consider one-loopcorrections. The dipole interaction between the color singlet and octet is notrunning at the one-loop level. Interference between the tree-level gluonabsorption/emission and its thermal loop corrections cancels the collineardivergence in the $t$-channel inelastic scattering. The inelastic scatteringhas no soft divergence because of the finite binding energy of quarkonium. Wewrite out the diffusion, dissociation and recombination terms explicitly for aBoltzmann transport equation and define the dissociation and recombinationrates. Furthermore, we calculate the diffusion coefficient of quarkonium. Wefind our result of diffusion coefficient differs from a previous calculation bytwo to three orders of magnitude. We explain this and can reproduce theprevious result in a certain limit. Finally we discuss two mechanisms ofquarkonium energy loss inside quark-gluon plasma.

Quarkonium inside Quark-Gluon Plasma: Diffusion, Dissociation, Recombination and Energy Loss