Heavy quarkonium dissociation by thermal gluons at next-to-leading order in the Quark–Gluon Plasma

Abstract

Using the chromo-electric dipole coupling Hamiltonian from QCD multipole expansion, we derive the dissociation cross sections of heavy quarkonia by thermal gluons at next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the Quark-Gluon Plasma (QGP) in the framework of second order quantum mechanical perturbation theory. While suffering divergence (infrared and soft-collinear divergences) in vacuum, the cross sections thus derived become finite in the QGP as rendered by the finite thermal gluon masses. In contrast to the leading order (LO, also known as gluo-dissociation) counterparts rapidly dropping off with increasing incident gluon energy, the NLO cross sections exhibits finite value toward high energies because of new phase space being opened up. We then carry out a full calculation of the dissociation rates for various charmonia and bottomonia within a non-relativistic in-medium potential model. The NLO process is shown to dominate the dissociation rate toward high temperatures when the binding energies of heavy quarkonia become smaller relative to the Debye screening mass.

Magnetic field induced hair structure in charmonium gluon-dissociation

“…Following the procedure in Refs. [41,42], the cross sections via transition processes E1 and M 1 read…”

“…Like usual treatment [40][41][42], we have neglected in the relative equation the potential V 2 in color octet state. In vacuum the potential V 1 in color singlet state is often taken as the Cornell form,…”

“…Peskin's perturbative analysis can be represented by a gaugeinvariant effective action from which one can get a nonrelativistic Hamiltonian for heavy quark systems via QCD multipole expansion [37][38][39]. Based on this effective Hamiltonian, the cross section of gluon dissociation in hot medium are derived in the frame of perturbation theory of quantum mechanics [40][41][42]. The result in the Coulomb approximation is in consistent with the OPE .…”

Heavy flavors under extreme conditions in high energy nuclear collisions

“…Considering that the quarkonium mass m ψ is finite, the relativistic correction leads to a shift of the threshold energy for the dissociation process [155]. In contrast to the leading order counterparts which rapidly drop off with increasing incident gluon energy, the NLO cross sections exhibit finite value toward high energies, because of the new phase space opened up [156].…”

Heavy quarkonium dissociation in the finite space of heavy-ion collisions

“…The properties of heavy quarkonia have also been studied in the framework of effective field theory [16] and lattice QCD [17]. The theories are still under development recent years [18][19][20][21][22][23][24][25][26][27][28][29][30].…”