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We study the higher derivative chiral models with four supercharges and BPSstates in these models. The off-shell Lagrangian generically includes higherpowers of the auxiliary fields F which causes distinct on-shell branchesassociated with the solutions to the auxiliary fields equation. We point outthat the model admits a supersymmetric completion of arbitrary higherderivative bosonic models of a single complex scalar field and an arbitraryscalar potential can be introduced even without superpotentials. As an example,we present a supersymmetric extension of the Faddeev-Skyrme model without fourtime derivatives, in contrast to the previously proposed supersymmetricFaddeev-Skyrme-like model containing four time derivatives. In general, higherderivative terms together with a superpotential result in deformed scalarpotentials. We find that higher derivative corrections to 1/2 BPS domain wallsand 1/2 BPS lumps are exactly canceled out while the 1/4 BPS lumps (as compactbaby Skyrmions) depend on a characteristic feature of the higher derivativemodels. We also find a new 1/4 BPS condition for domain wall junctions whichgenerically receives higher derivative corrections.

BPS States in Supersymmetric Chiral Models with Higher Derivative Terms