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

TL;DR

This paper demonstrates that in non-supersymmetric GUTs, the expected decoupling of heavy fields does not occur due to a dimensionful coupling, leading to custodial symmetry violation at one loop.

Contribution

It reveals a violation of the Appelquist-Carazzone decoupling in non-SUSY GUTs caused by a dimensionful coupling in the Higgs sector.

Findings

Heavy gauge and Higgs fields contribute to triplet VEVs at one loop.

The triplet VEV remains unsuppressed as GUT scale VEV increases.

Custodial symmetry is violated due to non-decoupling effects.

Abstract

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 $V\to\infty$ and violates the custodial symmetry.