  We study Active Model B+, a scalar field theory extending the paradigmatic
Model B for equilibrium coexistence through including terms that do not arise
from an underlying free energy functional and thus break detailed balance. In
the first part of the manuscript, we provide a pedagogical and self-contained
introduction to one-loop dynamic renormalization. We then address the technical
challenge of complex vertex functions through developing a symbolic computer
algebra code that allows us to obtain the graphical corrections of model
parameters. We argue that the additional terms of Active Model B+ imply the
generation of, potentially relevant, higher-order terms; strongly restricting
the parameter regime in which we can apply a perturbative renormalization
scheme. Moreover, we elucidate the role of the cubic coefficient, which, in
contrast to passive Model B, is incessantly generated by the new terms.
Analyzing its behavior with and without field shift near the Wilson-Fisher
fixed point, we find that additional fixed points in the one-loop flow
equations are likely artifacts. Additionally, we characterize the
renormalization flow of perturbatively accessible field theories derived from
Active Model B+.
