Constraining models with a large scalar multiplet

Abstract

Models in which the Higgs sector is extended by a single electroweak scalar multiplet $X$ can possess an accidental global U(1) symmetry at the renormalizable level if $X$ has isospin $T\ensuremath{\ge}2$. We show that all such models with an accidental U(1) symmetry are excluded by the interplay of the cosmological relic density of the lightest (neutral) component of $X$ and its direct-detection cross section via $Z$ exchange. The sole exception is the $T=2$ multiplet, whose lightest member decays on a few-day to few-year time scale via a Planck-suppressed dimension-5 operator.