  The role of higher derivative operators in 4D effective field theories is
discussed in both non-supersymmetric and supersymmetric contexts. The approach,
formulated in the Minkowski space-time, shows that theories with higher
derivative operators do not always have an improved UV behaviour, due to
subtleties related to the analytical continuation from the Minkowski to the
Euclidean metric. This continuation is further affected at the dynamical level
due to a field-dependence of the poles of the Green functions of the
particle-like states, for curvatures of the potential of order unity in ghost
mass units. The one-loop scalar potential in lambda*phi^4 theory with a single
higher derivative term is shown to have infinitely many counterterms, while for
a very large mass of the ghost the usual 4D renormalisation is recovered. In
the supersymmetric context of the O'Raifeartaigh model of spontaneous
supersymmetry breaking with a higher derivative (supersymmetric) operator, it
is found that quadratic divergences are present in the one-loop self-energy of
the scalar field. They arise with a coefficient proportional to the amount of
supersymmetry breaking and suppressed by the scale of the higher derivative
operator. This is also true in the Wess-Zumino model with higher derivatives
and explicit soft breaking of supersymmetry. In both models, the UV logarithmic
behaviour is restored in the decoupling limit of the ghost.
