Uniqueness of the $\Box^2$ Higher-Derivative Operator Class for Universal Vacuum-Energy Cancellations and Higgs Naturalness
Masayuki Note
TL;DR
The paper argues that among dimension-6, four-derivative operators, the isotropic Box^2 class uniquely enables universal cancellation of vacuum-energy power divergences while preserving Lorentz and gauge symmetries. Introducing a higher-derivative Lee-Wick extension, it shows how a negative-norm LW ghost with mass M yields a finite, calculable Higgs mass correction when combined with a Real-Time Negative-Norm Prescription. The analysis demonstrates the cancellation of the Λ^4 term and identifies sector-dependent coefficients that remove residual divergences, culminating in a predictive scale M ≈ 11.3 TeV. This framework offers a structurally motivated approach to Higgs naturalness and provides concrete targets for experimental tests at high-energy scales.
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 $Λ^4$ and $m^2Λ^2$ 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.