Abstract
We compute the decay spectrum for dark matter (DM) with masses above the scale of electroweak symmetry breaking, all the way to the Planck scale. For an arbitrary hard process involving a decay to the unbroken standard model, we determine the prompt distribution of stable states including photons, neutrinos, positrons, and antiprotons. These spectra are a crucial ingredient in the search for DM via indirect detection at the highest energies as being probed in current and upcoming experiments including IceCube, HAWC, CTA, and LHAASO. Our approach improves considerably on existing methods, for instance, we include all relevant electroweak interactions.
Highlights
Calculation of the resulting prompt spectra is a central ingredient in testing the hypothesis of heavy dark matter (DM)
The problem is to determine the probability that X and Xevolve to produce S carrying a fraction x of the initial energy. This process is described by a fragmentation function (FF) Dab(x; μQ, μ0), which determines the probability of an initial particle a at a scale μQ evolving to produce a particle b at μ0 carrying a momentum fraction x; in the absence of any evolution we would have Dab (x; μQ, μ0) = δabδ(1 − x)
The difference between our results and those of Pythia is driven by the lack of the full electroweak interactions in the latter
Summary
The flux of an observable particle S produced from DM decay depends centrally on the prompt spectrum, defined as. This process is described by a fragmentation function (FF) Dab(x; μQ, μ0), which determines the probability of an initial particle a at a scale μQ evolving to produce a particle b at μ0 carrying a momentum fraction x; in the absence of any evolution we would have Dab (x; μQ, μ0) = δabδ(1 − x) In this language, we can write the spectrum as. We perform a matching by evolving across a parametrically small region through the weak scale, removing all particles with electroweak scale masses These results are matched onto Pythia below qW , where it is used to calculate the subsequent showering, hadronization, and light particle decays in a regime where it has been extensively vetted. A simplified depiction of the full evolution is given in figure 2, and we flesh out the details involved at each stage
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