Are 2HDMs with a gauged $U(1)$ symmetry alive?

TL;DR

This paper explores the phenomenology of 2HDMs with a new $U(1)_X$ gauge symmetry, analyzing constraints from collider data and proposing models with dark matter candidates that evade current experimental bounds.

Contribution

It introduces specific $U(1)_X$-extended 2HDMs with dark matter candidates, analyzing their parameter space and experimental constraints, especially from four-lepton searches at the LHC.

Findings

$Z'$ and extra Higgs bosons are constrained to be below TeV scale.

Current LHC data exclude minimal models without dark matter candidates.

Allowed parameter space is identified for $U(1)_H$ and $U(1)_R$ models.

Abstract

We investigate the phenomenology of 2 Higgs doublet models (2HDMs) with a new $U(1)$ gauge symmetry, $U(1)_X$, by which flavor changing neutral currents are forbidden at tree level. As an important consequence of the spontaneous breaking of both the $U(1)_X$ and electroweak symmetries by electroweak vacuum expectation values, upper limits appear on masses of an additional gauge boson $Z'$ and extra Higgs bosons which are less than the TeV scale. In addition, the standard model (SM) like Higgs boson $h$ and a heavier Higgs boson $H$ mainly decay into a pair of $Z'$ which induces four lepton final states. These new decay modes cannot be suppressed by taking no $Z$-$Z'$ mixing and/or the Higgs alignment limit. We find that the minimum setup of these 2HDMs has been excluded by current data for four lepton searches at LHC. Such severe constraints can, however, be avoided by introducing a pair of vector-like fermions $\chi$ which are singlet under the SM symmetry but charged under $U(1)_X$, and can be a candidate of dark matter. Thanks to the existence of $\chi$, $Z'$ can mainly decay into $\chi\bar{\chi}$ instead of SM leptons. As benchmark models, we consider the $U(1)_H$ and $U(1)_R$ models realized by fixing specific $U(1)_X$ charges, and find regions of parameter space allowed by theoretical and current experimental constraints. We clarify that $m_H \in [160, 220]$ GeV and $\tan \beta \in [3, 4.4]$ are allowed in the $U(1)_H$ model, while $m_H \in [160, 380]$ GeV and $\tan \beta \in [1.6, 4.4]$ are allowed in the $U(1)_R$ model. In both the models, the $Z'$ mass is constrained to be $100~\text{GeV} \lesssim m_{Z'} \lesssim 110$ GeV. Such a quite limited parameter space can further be explored at future collider experiments, e.g., High-Luminosity LHC and lepton colliders.