Dark clouds to silver linings over the hyperchargeless scalar triplets

Abstract

A real scalar triplet with zero hypercharge offers a minimal non-trivial extension of the Standard Model (SM) with a charged Higgs and a possible dark matter or custodial symmetry breaking signature. The $Z_2$-odd inert triplet model (ITM) provides a dark matter, while the non-inert Higgs triplet model (HTM) breaks the custodial symmetry, enabling rich collider signatures. Both these models also promise the viability of a first-order phase transition (FOPT). This letter revisits both models under various theoretical and current experimental constraints, revealing a trade-off between DM and FOPT viability, and explores the resulting gravitational wave signals and collider prospects.