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

TL;DR

This paper identifies the unique class of higher-derivative operators based on $ox^2$ that can universally cancel vacuum-energy divergences and address the Higgs naturalness problem within Lorentz-invariant field theories.

Contribution

It demonstrates that the $ox^2$ operator class is uniquely suited for universal vacuum-energy divergence cancellation and explores its implications for Higgs mass naturalness using Lee--Wick higher-derivative structures.

Findings

The $ox^2$ operator class uniquely cancels all power divergences across spin sectors.

The Lee--Wick higher-derivative structure yields finite Higgs mass corrections.

A phenomenologically motivated scale of approximately 11.3 TeV is suggested for new physics.

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.