  We revisit the dissociation of heavy quarkonia by thermal partons at the
next-to-leading order (NLO, also known as inelastic parton scattering
dissociation) in the Quark-Gluon Plasma (QGP). Utilizing the chromo-electric
dipole coupling from QCD multipole expansion as an effective Hamiltonian, this
has been conducted in the approach of second-order quantum mechanical
perturbation theory, which allows us to systematically incorporate the bound
state wave functions. Employing the quarkonium wave functions and binding
energies obtained from an in-medium potential model, we then numerically
evaluate the dissociation cross sections and rates for various charmonia and
bottomonia, where the infrared and collinear divergences are regularized by the
thermal masses of medium partons. We demonstrate that distinct from the leading
order (LO, also known as gluo-dissociation) counterparts peaking at relatively
low gluon energy and falling off thereafter, the NLO cross sections first grow
and then nearly saturate as the incident parton energy increases, as a result
of the outgoing parton carrying away the excess energy. The resulting NLO
dissociation rates increase with temperature and take over from the LO
counterparts toward high temperatures, similar to pertinent findings from
previous studies. We also evaluate the in-medium second-order transition
between different bound states, which may contribute to the total thermal decay
widths of heavy quarkonia in the QGP.
