On the addition of a large scalar multiplet to the Standard Model

Abstract

We consider the addition of a single $SU(2)$ multiplet of complex scalar fields to the Standard Model (SM). We explicitly consider the various possible values of the weak isospin $J$ of that multiplet, up to and including $J=7/2$. We allow the multiplet to have arbitrary weak hypercharge. The scalar fields of the multiplet are assumed to have no vacuum expectation value; the mass differences among the components of the multiplet originate in its coupling, present in the scalar potential (SP), to the Higgs doublet of the SM. We derive exact bounded-from-below and unitarity conditions on the SP, thereby constraining those mass differences. We compare those constraints to the ones that may be derived from the oblique parameters.

30 pages, 6 figures; v2: added references, few additional equations and footnotes; v3: added subsection 2.4, two figures and references

References in corpus (6)

• $W$-Boson Mass Anomaly from a General $SU(2{)}_L$ Scalar Multiplet
• $W$-boson Mass Anomaly from High-Dimensional Scalar Multiplets
• Unitarity constraints on large multiplets of arbitrary gauge groups
• Oblique corrections when $m_W\ne m_Z\cos {\theta }_W$ at tree level
• Oblique corrections from leptoquarks
• On the extension of the SM through a scalar quadruplet

Cited by in corpus (1)

• Vacuum Stability Conditions for New $SU(2)$ Multiplets