  In 4D renormalisable theories, integrating out massive states generates in
the low energy effective action higher dimensional operators (derivative or
otherwise). Using a superfield language it is shown that a 4D N=1
supersymmetric theory with higher derivative operators in either the Kahler or
the superpotential part of the Lagrangian and with an otherwise arbitrary
superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without
higher derivatives) with additional superfields and renormalised interactions.
We provide examples where a free theory with trivial supersymmetry breaking
provided by a linear superpotential becomes, in the presence of higher
derivatives terms and in the second order version, a non-trivial interactive
one with spontaneous supersymmetry breaking. The couplings of the equivalent
theory acquire a threshold correction through their dependence on the scale of
the higher dimensional operator(s). The scalar potential in the second order
theory is not necessarily positive definite, and one can in principle have a
vanishing potential with broken supersymmetry. We provide an application to
MSSM and argue that at tree-level and for a mass scale associated to a higher
derivative term in the TeV range, the Higgs mass can be lifted above the
current experimental limits.
