  The late time limit of the power spectrum for heavy (principal series) fields
in de Sitter space yields a series of polynomial terms with complex scaling
dimensions. Such scaling behavior is expected to result from an associated
operator with a complex dimension. In a free theory, these complex dimensions
are known to match the constraints imposed by unitarity on the space of states.
Yet, perturbative corrections to the scaling behavior of operators are naively
inconsistent with unitary evolution of the quantum fields in dS. This paper
demonstrates how to compute one-loop corrections to the scaling dimensions that
appear in the two point function from the field theory description in terms of
local operators. We first show how to evaluate these anomalous dimensions using
Mellin space, which has the feature that it naturally accommodates a scaleless
regulator. We then explore the consequences for the Soft de Sitter Effective
Theory (SdSET) description that emerges in the long wavelength limit. Carefully
matching between the UV and SdSET descriptions requires the introduction of
novel non-dynamical "operators" in the effective theory. This is not only
necessary to reproduce results extracted from the K\"all\'en-Lehmann
representation (that use the space of unitary states directly), but it is also
required by general arguments that invoke positivity.
