  There is an ambiguity in choosing field-strength renormalization factors in
the $ \overline{\text{MS}} $ scheme starting from the 3-loop order in
perturbation theory. More concerning, trivially choosing Hermitian factors has
been shown to produce divergent renormalization group functions, which are
commonly understood to be finite quantities. We demonstrate that the
divergences of the RG functions are such that they vanish in the RG equation
due to the Ward identity associated with the flavor symmetry. It turns out that
any such divergences can be removed using the renormalization ambiguity and
that the use of the flavor-improved $ \beta $-function is preferred. We show
how our observations resolve the issue of divergences appearing in previous
calculations of the 3-loop SM Yukawa $ \beta $-functions and provide the first
calculation of the flavor-improved 3-loop SM $ \beta $-functions in the
gaugeless limit.
