Saddle point approximation in Keldysh field theory

I want to integrate out the bosonic fields $d_{dcl,q}$ in my problem to obtain an effective action for my $c$ fields. For explanation, I wrote the Keldysh fields in terms of their real and imaginary part as:

$
a_{cl/q}=c_{cl,q}+i d_{cl,q}
$

The action I am looking at is mainly quadratic in the $d$ fields but there is also a contribution

$
U(c_{cl}^{2}+c_{q}^{2}+d_{cl}^{2}+d_{q}^{2})(c_{cl}c_{q}+d_{cl}d_{q})
$

Now I already found out that the quantum fields with powers $>2$ become irrelevant near the fixpoint but the classical fields become irrelevant only for powers $>5$. Is there a way to do a saddle point approximation in this case for the $d_{cl}$ fields because they appear as $d_{cl}^3 $? And how does this work?