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Dark Matter interactions in an $S_4 \times Z_5$ flavor symmetry framework

The interactions of dark matter (DM) with the visible sector are often phenomenologically described in the framework of simplified models where the couplings of quarks to the new particles are generally assumed to be universal or have a simple structure motivated by observational benchmarks. They should, however, a priori be treated as free parameters. In this work we discuss one particular realization of the structure of DM couplings based on an $S_4 \times Z_5$ flavor symmetry, which has been shown to account reasonably well for fermion masses and mixing, and compare their effect on observational signals to universal as well as Yukawa-like couplings, which are motivated by minimal flavor violation. We will also comment on how these structures could be constrained in UV complete theories of DM and how DM observables, such as, e.g., relic density and direct detection, can potentially be used as a smoking gun for the underlying flavor symmetries.