Violation of the Appelquist-Carazzone decoupling in non-SUSY GUT

We point out that in non supersymmetric GUTs, in which the SU(5) gauge symmetry is broken down to the Standard Model gauge group by a $\mathbf{24}$ Higgs multiplet the Appelquist-Carazzone decoupling is violated. This is because the $SU(2{)}_L$ Higgs triplet contained in the $\mathbf{24}$ acquires a dimensionfull coupling to the $SU(2{)}_L$ Higgs doublets which is proportional to the GUT breaking vacuum expectation value (VEV) $V$. As a result, at one loop heavy gauge and Higgs fields contribution to tadpoles generate a VEV of the triplet which is not suppressed for $V\to \mathrm{\infty }$ and violates the custodial symmetry.