Second-Order Dissociation and Transition of Heavy Quarkonia in the Quark-Gluon Plasma

TL;DR

This paper investigates the next-to-leading order dissociation of heavy quarkonia in the quark-gluon plasma using quantum mechanical perturbation theory and in-medium potential models, revealing how NLO effects dominate at high temperatures.

Contribution

It introduces a systematic NLO calculation of heavy quarkonium dissociation in QGP using quantum perturbation theory and in-medium potentials, extending beyond leading order gluo-dissociation models.

Findings

NLO cross sections grow and saturate with incident energy.

NLO dissociation rates increase with temperature and surpass LO rates at high temperatures.

Second-order transitions between bound states contribute to quarkonium decay widths.

Abstract

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.