Prescription for finite oblique parameters $S$ and $U$ in extensions of the SM with $m_W\ne m_Z\cos {\theta }_W$

Abstract

We consider extensions of the Standard Model with neutral scalars in multiplets of $SU(2)$ larger than doublets. When those scalars acquire vacuum expectation values, the resulting masses of the gauge bosons $W^{\pm }$ and $Z^0$ are not related by $m_W=m_Z\cos {\theta }_W$. In those extensions of the Standard Model the oblique parameters $S$ and $U$, when computed at the one-loop level, turn out to be either gauge-dependent or divergent. We show that one may eliminate this problem by modifying the Feynman rules of the Standard Model for some vertices containing the Higgs boson; the modifying factors are equal to $1$ in the limit $m_W=m_Z\cos {\theta }_W$. We give the result for $S$ in a model with arbitrary numbers of scalar $SU(2)$ triplets with weak hypercharges either $0$ or $1$.

Comments: 33 pages, 2 figures