Quarkonium dissociation in perturbative QCD

For weakly bound quarkonia, we rederive the next-to-leading order cross sections of quarkonium dissociation by partons that include the hard thermal loop (HTL) resummation. Our results calculated with an effective vertex from the Bethe–Salpeter amplitude reduce to those obtained by potential nonrelativistic QCD (pNRQCD) in the relevant kinematical limit, and they can be used in a wide temperature range applicable to heavy-quark systems in heavy-ion collisions. Based on the lattice computation of the temperature-dependent binding energy, our numerical analysis on $\mathrm{{\rm Y}}\left(1S\right)$ indicates that at high temperature the dominant mechanism for quarkonium dissociation is inelastic parton scattering as expected in the quasifree approximation, while it is gluo-dissociation at low temperature. By comparing with the momentum diffusion coefficient of a heavy quark, we discuss possible $O\left(g\right)$ corrections to the next-to-leading-order thermal width.

Figure 1

The leading order gluon-quarkonium interactions. Thick solid lines denote quarkonium ($Q$) or heavy (anti)quarks ($P_1$, $P_2$), and wiggly lines are gluons.

Figure 2

The effective vertex derived from the sum of the leading processes shown in Fig. 1.

Figure 3

The inelastic parton scattering processes which contribute to quarkonium dissociation at next-to-leading order (NLO). Panel (b) gives $O\left(g\right)$ corrections to the NLO thermal width if all the gluons are soft.

Figure 4

The self-energy diagram of the quarkonium color singlet. At two-loop order, the cut diagram corresponds to the scattering processes of Fig. 3.

Figure 5

The binding energy of $\mathrm{{\rm Y}}\left(1S\right)$ from lattice computations [26] and the numerical fit. The black dashed line shows the temperature for reference and the gray band is for the Debye mass as a function of temperature.

Figure 6

The leading-order and next-to-leading-order results by gluo-dissociation [$g+\mathrm{{\rm Y}}\left(1S\right)\to b+\overline{b}]$ for ${\alpha }_s=0.4$. (a) $\mathrm{{\rm Y}}\left(1S\right)$ dissociation cross sections and (b) thermal widths.

Figure 7

The comparison of the numerically calculated cross section with the asymptotic formula for $p+\mathrm{{\rm Y}}\left(1S\right)\to p+b+\overline{b}$ with ${\alpha }_s=0.4$.

Figure 8

$\mathrm{{\rm Y}}\left(1S\right)$ dissociation cross sections by gluo-dissociation and inelastic parton scattering for $T=300,400$ MeV and ${\alpha }_s=0.4$.

Figure 9

(a) Temperature dependence of the $\mathrm{{\rm Y}}\left(1S\right)$ thermal widths by gluo-dissociation and inelastic parton scattering for ${\alpha }_s=0.4$. (b) The total thermal width as the sum of the contributions by two mechanisms for ${\alpha }_s=0.3,0.4$.

Figure 10

With soft gluons, $O\left(g\right)$ corrections to the next-to-leading order thermal width can be obtained.