A Higher-Derivative Lee-Wick Standard Model
  The Lee-Wick Standard Model assumes a minimal set of higher-derivative quadratic terms that produce a negative-norm partner for each Standard Model particle. Here we introduce additional terms of one higher order in the derivative expansion that give each Standard Model particle two Lee-Wick partners: one with negative and one with positive norm. These states collectively cancel unwanted quadratic divergences and resolve the hierarchy problem as in the minimal theory. We show how this next-to-minimal higher-derivative theory may be reformulated via an auxiliary field approach and written as a Lagrangian with interactions of dimension four or less. This mapping provides a convenient framework for studies of the formal and phenomenological properties of the theory. 
Christopher D. Carone, Richard F. Lebed