Uniqueness of the $\Box^2$ Higher-Derivative Operator Class for Universal Vacuum-Energy Cancellations and Higgs Naturalness

Abstract

Within the framework of local, Lorentz-invariant, and Hermitian field theories, we investigate the classification of dimension-6 operators that facilitate the dynamical cancellation of vacuum-energy divergences. We demonstrate that the operator class based on the $\Box^2$ d'Alembertian is uniquely singled out by the requirement of universal power-divergence subtraction across all spin sectors. By explicitly evaluating the modified propagators and one-loop vacuum integrals, we show that only this structure consistently removes $\Lambda^4$ and $m^2\Lambda^2$ terms while preserving gauge covariance. Adopting the Real-Time Negative-Norm Prescription (RTNNP) as a consistent contour selection, we find that the higher-derivative Lee--Wick (HDLW) structure leads to a finite, calculable Higgs mass correction. Our results suggest a phenomenologically preferred scale of $M \approx 11.3$ TeV, offering a predictive and structurally motivated resolution to the hierarchy problem.