  We present for the first time a ghost-free higher-derivative chiral model
with a propagating auxiliary F-term field (highest component of the chiral
multiplet). We obtain this model by removing a ghost in a higher derivative
chiral model, with Higgsing it in terms of an auxiliary vector superfield.
Depending on the sign of the quadratic derivative term of the chiral
superfield, the model contains two ghost free branches of the parameter
regions. We find that supersymmetry is spontaneously broken in one branch while
it is preserved in the other branch. As a consequence of dynamical F-term
field, a conserved U(1) charge corresponding to the number density of $F$
appears, which can be regarded as a generalization of the R-symmetry.

High Energy Physics - Theory