  We investigate the impact of operators of higher canonical dimension on the
lower Higgs mass consistency bound by means of generalized Higgs-Yukawa
interactions. Analogously to higher-order operators in the bare Higgs potential
in an effective field theory approach, the inclusion of higher-order Yukawa
interactions, e.g., $\phi^3\bar{\psi}\psi$, leads to a diminishing of the lower
Higgs mass bound and thus to a shift of the scale of new physics towards larger
scales by a few orders of magnitude without introducing a metastability in the
effective Higgs potential. We observe that similar renormalization group
mechanisms near the weak-coupling fixed point are at work in both
generalizations of the microscopic action. Thus, a combination of
higher-dimensional operators with generalized Higgs as well as Yukawa
interactions does not lead to an additive shift of the lower mass bound, but
relaxes the consistency bounds found recently only slightly. On the method
side, we clarify the convergence properties of different projection and
expansion schemes for the Yukawa potential used in the functional
renormalization group literature so far.
