Capture and decay of electroweak WIMPonium

Abstract

Abstract. The spectrum of Weakly-Interacting-Massive-Particle (WIMP) dark matter generically possesses bound states when the WIMP mass becomes sufficiently large relative to the mass of the electroweak gauge bosons. The presence of these bound states enhances the annihilation rate via resonances in the Sommerfeld enhancement, but they can also be produced directly with the emission of a low-energy photon. In this work we compute the rate for SU(2) triplet dark matter (the wino) to bind into WIMPonium -which is possible via single-photon emission for wino masses above 5 TeV for relative velocity v < O(10 −2 ) -and study the subsequent decays of these bound states. We present results with applications beyond the wino case, e.g. for dark matter inhabiting a nonabelian dark sector; these include analytic capture and transition rates for general dark sectors in the limit of vanishing force carrier mass, efficient numerical routines for calculating positive and negative-energy eigenstates of a Hamiltonian containing interactions with both massive and massless force carriers, and a study of the scaling of bound state formation in the short-range Hulthén potential. In the specific case of the wino, we find that the rate for bound state formation is suppressed relative to direct annihilation, and so provides only a small correction to the overall annihilation rate. The soft photons radiated by the capture process and by bound state transitions could permit measurement of the dark matter's quantum numbers; for wino-like dark matter, such photons are rare, but might be observable by a future ground-based gamma-ray telescope combining large effective area and a low energy threshold.

Complementarity for dark sector bound states

“…These charged partners can always form Coulombic bound states; when the DM is sufficiently heavy, W and Z exchange may also support bound states including the DM itself (e.g., Ref. [23]). Numerical calculations indicate that for wino DM there is a crossover point at a DM mass of around 5 TeV, where the ground state transitions from being primarily composed of χ þ χ − , bound by photon exchange, to being composed of an admixture of χ 0 χ 0 and χ þ χ − , bound by the gauge bosons of an approximately unbroken SUð2Þ L symmetry.…”

“…Since the mediator to the DM is an EW gauge boson, the bound state dominantly produced at colliders has L ¼ 0 and S ¼ 1; these are true bound states, not pseudobound, and cannot decay rapidly to pairs of identical DM particles. In particular, in the pure wino case, the χ þ χ − bound state with L ¼ 0, S ¼ 1, denoted B w , decays dominantly via an s-channel γ=Z to SM fermion pairs or through a t-channel exchange of a χ 0 into a W þ W − final state [23]; final states involving the DM are suppressed. We will see this behavior arise again in our example dark sector models.…”

“…Furthermore, we have included an extra factor of 1=2 to account for the fact that our annihilating particles are identical fermions, and thus only spin-singlet configurations contribute to this s-wave process (yielding a factor of 1=4), but the overall cross section is increased by a factor of 2, as discussed in Ref. [23].…”

“…To estimate the contribution from bound-state formation, we numerically calculate the cross section for capture into the ground state by dipole photon emission and also add the contribution from an s-wave initial state transitioning into the first excited state by the emission of a dipole photon. The former process dominates when the mediator mass can be neglected [23] but is suppressed in the very-low-velocity regime as it corresponds to a p-wave initial state [99]; thus, we add the latter process to properly include the leading contribution at very small velocities. We follow the numerical method described in Ref.…”

Wino dark matter annihilation through the radiative formation of bound states

“…Previous work on the formation of bound states of dark matter particles is summarized in Ref. [1]. Much of the previous work focused on wimps coupling to dark sector mediators, such as a light scalar or dark photon.…”