  We continue investigation of the renormalization group and decoupling of the
quantized massive fields in curved space. In the present work we analyze a
theory, where fields gain their masses due to the Spontaneous Symmetry Breaking
(SSB), that is the case providing a remarkable exception from the
Appelquist-Carazzone theorem in the matter fields sector. In the vacuum sector,
already at the classical level, the theory with SSB includes, in the general
case an infinite number of the non-local terms in the induced vacuum action.
Despite this surprising property, we show that the theory is renormalizable and
moreover the low-energy decoupling in the higher-derivative gravitational
sector performs similar to the AC theorem.
