  Dark matter that was once in thermal equilibrium with the Standard Model is
generally prohibited from obtaining all of its mass from the electroweak or QCD
phase transitions. This implies a new scale of physics and mediator particles
needed to facilitate dark matter annihilations. In this work, we consider
scenarios where thermal dark matter annihilates via scalar mediators that are
colored and/or electrically charged. We show how partial wave unitarity places
upper bounds on the masses and couplings on both the dark matter and mediators.
To do this, we employ effective field theories with dark matter as well as
three flavors of sleptons or squarks with minimum flavor violation. For Dirac
(Majorana) dark matter that annihilates via mediators charged as left-handed
sleptons, we find an upper bound around 45 TeV (7 TeV) for both the mediator
and dark matter masses, respectively. These bounds vary as the square root of
the number of colors times the number of flavors involved. Therefore the bounds
diminish by root two for right handed selectrons. The bounds increase by root
three and root six for right and left handed squarks, respectively. Finally,
because of the interest in natural models, we also focus on an effective field
theory with only stops. We find an upper bound around 32 TeV (5 TeV) for both
the Dirac (Majorana) dark matter and stop masses. In comparison to traditional
naturalness arguments, the stop bound gives a firmer, alternative expectation
on when new physics will appear. Similar to naturalness, all of the bounds
quoted above are valid outside of a defined fine-tuned regions where the dark
matter can co-annihilate. The bounds in this region of parameter space can
exceed the well-known bounds from Griest and Kamionkowski. We briefly describe
the impact on planned and existing direct detection experiments and colliders.
