Strongly Interacting Higgs Sector Without Technicolor

The theoretical framework for the higher derivative O(N) scalar field theory is established and the theory is shown to be finite and unitary with the indefinite metric quantization. It has been shown that if the ghost states are represented by a complex conjugate pair, the theory is free of any logical inconsistencies and the ghost pair can easily evade the experimental tests. With an underlying hypercubic lattice structure, the higher derivative O(4) model is studied nonperturbatively in computer simulations. The Higgs mass bound problem is also studied within the framework of higher derivative theory. A much higher Higgs mass value in the TeV range is found with the ghost pair well-hidden in the multi-TeV range. Therefore, the higher derivative O(4) model can incorporate a strongly interacting Higgs sector without introducing more complicated structures, like technicolor, which was impossible for the conventional lattice scalar model. This means that, although the added higher derivative term is a higher dimensional operator, it changes the fundamental features (metric, energy spectrum, strength of interaction, etc.) of the theory so much that we can no longer view it as an irrelevant operator in the Lagrangian. Moreover, due to the strong interaction of the theory, it would be impossible to meaningfully define the scaling violation in the higher derivative O(4) model. This implies that we will not be able to set up the Higgs mass bound in this theory unless a new nonperturbative interpretation of the Higgs mass bound is developed.