  Cosmological models describing the non-gravitational interaction between dark
matter and dark energy are based on some phenomenological choices of the
interaction rates between dark matter and dark energy. There is no such guiding
rule to select such rates of interaction. {\it In the present work we show that
various phenomenological models of the interaction rates might have a strong
field theoretical ground.} We explicitly derive several well known interaction
functions between dark matter and dark energy under some special conditions and
finally constrain them using the latest cosmic microwave background
observations from final Planck legacy release together with baryon acoustic
oscillations distance measurements. Our analyses report that one of the
interacting functions is able to alleviate the $H_0$ tension. We also perform a
Bayesian evidence analyses for all the models with reference to the
$\Lambda$CDM model. From the Bayesian evidence analyses, although the reference
scenario is preferred over the interacting scenarios, however, we found that
two interacting models are close to the reference $\Lambda$CDM model.
