Radiative Symmetry Breaking and the Hierarchy Problem in Cryptic Noncommutative Dark Sectors

We resolve the dark scalar mass hierarchy problem in the non‑Abelian dark sector Adark=H4⊕H5Adark=H4⊕H5 introduced in our companion paper. By imposing the classical scale invariance condition STr⁡(E)=0STr(E)=0 at the Planck cutoff, the quadratic divergences that would drive the scalar mediator mass to the cutoff are eliminated. The dark gauge symmetry SU(2)4×SU(2)5SU(2)4×SU(2)5 is broken radiatively via the Coleman–Weinberg mechanism, generating a vacuum expectation value vD≈14.1 GeVvD≈14.1GeV and a light scalar mediator mϕ≈100 MeVmϕ≈100MeV without fine‑tuning. The predicted dark gauge coupling is αD≈0.010αD≈0.010, which together with the dark matter mass mΨ≈5 GeVmΨ≈5GeV yields the correct self‑interacting dark matter cross‑section σT/m≈0.18 cm2/gσT/m≈0.18cm2/g. The large Yukawa coupling yD=0.5yD=0.5 required by the radiative mechanism forces the model into the Asymmetric Dark Matter paradigm. The model also predicts a massive dark gauge boson W′W′ with mass mW′≈3.55 GeVmW′≈3.55GeV, accessible to future collider experiments. This work completes the UV‑consistent framework for a cryptic dark sector in noncommutative geometry.