(Non)decoupling of the Higgs triplet effects

We consider the electroweak theory with an additional Higgs triplet at one loop using the hybrid renormalization scheme based on ${\alpha }_{\mathrm{E}\mathrm{M}}$, $G_F$ and $M_Z$ as input observables. We show that in this scheme loop corrections can be naturally split into the Standard Model part and corrections due to new physics''. The latter, however do not decouple in the limit of infinite triplet mass parameter, if the triplet trilinear coupling to SM Higgs doublets grows along with the the triplet mass. In electroweak observables computed at one loop this effect can be attributed to radiative generation in this limit of a nonvanishing vacuum expectation value of the triplet. We also point out that whenever tree level expressions for the electroweak observables depend on vacuum expectation values of scalar fields other than the Standard Model Higgs doublet, tadpole contribution to the oblique’’ parameter $T$ should in principle be included. In the Appendix the origin of nondecoupling is discussed on the basis of symmetry principles in a simple scalar field theory.