Thermally averaged Sommerfeld factors

Data for thermally averaged Sommerfeld factors

Simone Biondini, Seyong Kim, and Mikko Laine

If dark matter or its co-annihilation partners are pair-annihilating in the non-relativistic regime (T ≪ M), as happens in classic WIMP scenarios, the annihilation can be strongly affected by attractive interactions. For annihilation through scattering states, this is referred to as the Sommerfeld effect. Recently, it has been realized that the annihilation may be even more efficient if it proceeds via bound states. In fact, at finite temperature, both possibilities need to be considered simultaneously, and thermally averaged over the whole phase space. We refer to such results as thermally averaged Sommerfeld factors.

On this web page, we reproduce data for simple cases in which Sommerfeld factors are strongly modified by thermal corrections, including the contribution of bound states. The basic ideas, and numerical checks against non-perturbative lattice NRQCD, can be found in 1602.08105. The theoretical foundations and various applications were explored more extensively in 1609.00474. A first full model computation for a weakly interacting case, specifically the Inert Higgs Doublet Model, can be found in 1706.01894. More dramatic effects are found for strongly interacting co-annihilation partners, as shown in 1801.05821 and 1811.02581. Recently similar effects have also been demonstrated to originate from Higgs exchange, in 1805.00353.

QCD fundamental and antifundamental representations annihilating through the s-wave singlet channel

We start with the data denoted by S₃ in fig. 2(right) of 1801.05821. The columns are:

1: M / T
2: S₃ including only above-threshold states (i.e. scattering states)
3: S₃ including the full spectrum (both bound and scattering states)

The file name indicates the mass of the annihilating particles (M). Here are the files:

QCD fundamental and antifundamental representations annihilating through a p-wave channel

Next we consider data, similar to those denoted by S_p in fig. 2(right) of 1904.07882, but at higher masses and temperatures, as is normally relevant for cosmology. The columns are like above:

1: M / T
2: S_p including only above-threshold states (i.e. scattering states)
3: S_p including the full spectrum (both bound and scattering states)

The file name indicates the mass of the annihilating particles (M). Here are the files: