Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter

Abstract

We compute the cross-sections for the radiative capture of non-relativistic particles into bound states, in unbroken perturbative non-Abelian theories. We find that the formation of bound states via emission of a gauge boson can be significant for a variety of dark matter models that feature non-Abelian long-range interactions, including multi-TeV scale WIMPs, dark matter co-annihilating with coloured partners and hidden-sector models. Our results disagree with previous computations, on the relative sign of the Abelian and non-Abelian contributions. In particular, in the case of capture of a particle-antiparticle pair into its tightest bound state, we find that these contributions add up, rather than partially canceling each other. We apply our results to dark matter co-annihilating with particles transforming in the (anti)fundamental of SU p3q c , as is the case in degenerate stop-neutralino scenarios in the MSSM. We show that the radiative formation and decay of particle-antiparticle bound states can deplete the dark matter density by p40´240q%, for dark matter heavier than 500 GeV. This implies a larger mass difference between the co-annihilating particles, and allows for the dark matter to be as heavy as 3.3 TeV.ArXiv ePrint: 1805.01200

Dark matter bound state formation via emission of a charged scalar

“…The formation of metastable bound states in the early universe has been shown to deplete the DM abundance [7], with the effect being generally more pronounced if the bound states have a sizeable binding energy. In such a case, they can form and decay efficiently already at high temperatures, when the DM density is large [2,7,8]. In the present case we find that, because of the largeness of the BSF cross-sections, shallow bound states are able to bring about a second period of rapid DM depletion at low temperatures (of the order of their binding energy), much later than the traditional freeze-out.…”

“…2 and 3. BSF V has been computed in [4,10] (see [8] for non-Abelian generalisations), and a number of papers have considered its effects on the DM relic density [2,7,8,[13][14][15][16] and indirect signals [13][14][15][17][18][19][20]. Here, the coupling of DM to the light scalar gives rise to an additional contribution to the BSF V amplitude at leading order, shown in fig.…”

“…4. Because these diagrams are not fully connected, the virtuality of the X, X † fields has to be integrated out as described in [10] (see [8] for a more recent summary). Adapting the result of [10], we find the leading order contributions to be Amplitudes of this type can be computed by expanding in powers of P Φ · r/2 [4].…”

“…They are readily generalisable to unbroken perturbative non-Abelian theories: as in ref. [8], the appropriate colour factors arising in the amplitudes (2.22) upon projection of the initial and final states onto states of definite colour must be included, α S and α B have to be chosen according to the initial and final colour representations [9], and the (anti)symmetrisation of the wavefunctions in the case of identical particles must be taken into account. Considering the couplings (2.27), we illustrate eq.…”

“…As in refs. [4,8,10], we shall use the Fourier transforms Applying the operator d 3 p/(2π) 3 exp(ip · r) on eq. (A.1), we obtain…”