We show that dimensional regularization of a generic self-interacting field theory inducesan infrared mass scale, when the running spacetime dimension approaches the criticalvalue �� = 4. The mechanism is universal and does not rely on spontaneous symmetrybreaking alone. Instead, it arises from logarithmic corrections generated byrenormalization group (RG) flow near the bifurcation point at �� ≡ 4 − �� → 0. Weexplicitly indicate how dimensional transmutation converts marginal couplings intodynamically generated mass scales. This framework unifies the origin of the Higgsvacuum expectation value and electroweak boson masses with the Yang—Mills mass gapand the QCD scale ΛQCD. Step-by-step derivations are provided, without appealing tononperturbative assumptions beyond RG consistency. The paper focuses on the regimebordering relativistic quantum field theory and complex dynamics.