Thermal pair annihilation of heavy particles, such as dark matter or its co-annihilation partners, can be strongly influenced by attractive interactions. We investigate the case that pair annihilation proceeds through a velocity-suppressed p-wave operator, in the presence of an SU(3) gauge force. Making use of a non-relativistic effective theory, the thermal average of the pair-annihilation rate is estimated both through a resummed perturbative computation and through lattice simulation, in the range M/T ∼ 10...30. Bound states contribute to the annihilation process and enhancement factors of up to ∼ 100 can be found.Inelastic processes between a dilute ensemble of heavy particles moving slowly in a thermal environment are encountered in many physical situations. A classic example is given by nuclear reactions taking place within the electromagnetic plasma of stars [1]. In particle physics, we may consider heavy dark matter particles pair-annihilating into Standard Model particles in the early universe, or a heavy quark and anti-quark pair-annihilating into light quarks and gluons in a quark-gluon plasma generated in heavy ion collision experiments.The theoretical treatment of slow annihilation processes is facilitated by noting that the average kinetic energy of the annihilating particles is small compared with their rest mass, M v 2 ∼ T ≪ M . Such a scale separation permits for a factorized description of annihilation processes in terms of a series of long-distance matrix elements times short-distance Wilson coefficients [2]. In particular, the thermal average of an annihilation rate can be expanded as σv = a + b v 2 + · · · , where v denotes the relative velocity. The term a is said to originate from "s-wave" matrix elements, whereas b may be associated with "p-wave" ones.In the presence of long-range interactions, the coefficients a and b may get large corrections compared with a tree-level treatment. For scattering states, this is known as the "Sommerfeld (-Gamow-Sakharov) effect" [3][4][5][6]. Sommerfeld factors are nowadays routinely included in Boltzmann equations for dark matter pair annihilation (cf., e.g., refs. [7][8][9][10][11]).Long-range interactions may also lead to the appearance of bound states in the dark sector, which opens up a fast pair-annihilation channel (cf., e.g., refs. [12, 13]). Bound states are particularly important if the dark sector contains particles charged under QCD, as is the case for instance in a prototypical model in which dark matter is a singlet Majorana fermion and the mediator is a slightly heavier strongly coupled scalar (cf. refs. [14, 15] for reviews).Recently, we have developed a framework which permits to estimate the thermally averaged pair annihilation rate, including bound-state effects, beyond perturbation theory [16]. The framework can be applied to a number of cosmological models [17], particularly the prototypical framework mentioned above [18,19], where bound-state effects have been seen to be important from other considerations as well [20][21][22][23].Th...