Abstract
The annihilation of heavy particles close to thermal equilibrium, which plays a prominent role in the chemical equilibration of heavy quarks in the Quark-Gluon Plasma (QGP) as well as in many classic dark matter scenarios, is reexamined. We derive a scattering amplitude that resums near-threshold attractive interaction of the annihilating particles in terms of the non-relativistic scattering $T$-matrix and Green's function, thereby capturing the pertinent Sommerfeld enhancement from both nonperturbative scattering state and bound state solutions. The derived formula is of such generality that it applies to arbitrary partial wave processes of two-particle annihilation, and enables to incorporate finite widths of the annihilating particles. In a screened potential model, the non-perturbative scattering amplitude is computed and the Sommerfeld enhancement is identified for heavy quark-antiquark annihilation in the QGP.
Highlights
Heavy particle annihilation near threshold represents a phenomenon that is encountered in different context
Concerning the pair annihilation of a heavy quark and an antiquark (QQ ) in near-thermal equilibrium at typical temperatures (∼ a few hundred MeV) of the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions [13,14,15,16], it was shown [2,3] that the Sommerfeld enhancement factor can be defined within the nonrelativistic QCD framework [17] in terms of an imaginary-time twopoint correlator of the heavy quark singlet operators, whose spectral function has been measured on lattice [3]
We have reexamined the nonperturbative enhancement in the pair annihilation of nonrelativistic particles that is of direct relevance for determining the abundance of heavy weakly interacting dark matter particles [9,10,11]
Summary
Heavy particle annihilation near threshold represents a phenomenon that is encountered in different context. Concerning the pair annihilation of a heavy quark and an antiquark (QQ ) in near-thermal equilibrium at typical temperatures (∼ a few hundred MeV) of the QGP created in relativistic heavy-ion collisions [13,14,15,16], it was shown [2,3] that the Sommerfeld enhancement factor can be defined within the nonrelativistic QCD framework [17] in terms of an imaginary-time twopoint correlator of the heavy quark singlet operators, whose spectral function has been measured on lattice [3]. We derive a formula for the heavy quark-antiquark scattering amplitude that resums the attractive interaction in the color-singlet channel into a T matrix, from which the Sommerfeld enhancement factor from both nonperturbative scattering state and bound state solutions can be extracted. Within a screened potential model, we compute the pertinent enhancement factor as a function of energy as well as the thermally averaged enhancement that is shown to agree with the lattice results [3]
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