Freeze-in as a complementary process to freeze-out

There are many extensions of the Standard Model with a dark matter (DM) candidate
obtained via the freeze-out mechanism. It can happen that after all experimental and the-
oretical constraints are taken into account, all parameter points have a relic density below
the experimentally measured value. This means that the models solve only partially the DM
problem, and at least one more candidate is needed. In this work we show that it is possible
to further extend the model with a DM candidate obtained via the freeze-in mechanism to
be in agreement with the relic density experimental measurement. Once the relic density
problem is solved with this addition, new questions are raised. This new model with at least
two DM candidates could have a freeze-out undetectable DM particle both in direct and
indirect detection. This could happen if the freeze-out DM particle would have a very low
density. Hence, a collider DM hint via excess in the missing energy with no correspondence
in direct and indirect detection experiments, could signal the existence of a Feebly Interact-
ing Massive Particle (FIMP). Conversely, if a DM particle is found and a particular model
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can explain all observables except the correct relic density, an extension with an extra FIMP
would solve the problem. The freeze-in DM candidate, due to the small portal couplings,
will not change the remaining phenomenology.