Formulation of Scale-Gauge Theory and Its Cosmological Consequences Part II

This work presents a hybrid mechanism for addressing both the Higgs hierarchy problem and the cosmological constant problem within a unified theoretical framework. We introduce the concept of Hierarchical Local Stability, in which the effective potential of the dilaton field in Scale Gauge Theory exhibits locally stable points for each hierarchy index. By extending the stability condition to the Renormalization Group flow, we derive fixed-point conditions that naturally resolve the two hierarchy problems. The resolution emerges through a combination of coarse adjustment via a large non-minimal coupling and ultra-fine tuning through the dynamic suppression of the effective self-coupling. The resulting parameter values are consistent with current observations in particle physics and cosmology, offering a novel perspective on the interplay between fundamental constants and spacetime geometry.