Abstract
We use the framework of relativistic and non-relativistic conformal field theories (CFT) to derive general results relevant for the production of weakly coupled and strongly coupled dark sectors through thermal interactions. Our result reproduce trivially known formulas for 2 → n processes and extend to general m → n processes as well as interacting dark sectors. As concrete examples we consider freeze-in of a relativistic CFT coupled to the SM with contact interactions and derive Sommerfeld enhancement of non-relativistic cross-sections from the theory of fermions at unitarity.
Highlights
Determined by 2-point functions of the conformal field theories (CFT) whose structure is fixed up to the overall coefficient
As concrete examples we consider freeze-in of a relativistic CFT coupled to the SM with contact interactions and derive Sommerfeld enhancement of non-relativistic cross-sections from the theory of fermions at unitarity
After presenting general formulae for n → m processes we will show that Sommerfeld enhancement can be derived from the interacting CFT of fermions at unitarity
Summary
We consider DS that are singlets under SM gauge interactions. At sufficiently high temperatures they can be approximated by a CFT. For example the operator fLHfR allows to produce the DS from 3 SM particles or from 2 SM particles in association with a SM, see figure 1) In the latter case, thanks to the approximate conformal symmetry of both the dark and visible sector, we can think of the final state as excited by a composite operator build up with O and SM fields. Thanks to the approximate conformal symmetry of both the dark and visible sector, we can think of the final state as excited by a composite operator build up with O and SM fields All these contributions are of the same order so they must be added to obtain the total production
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