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

TL;DR

This work analyzes 2HDMs with a gauged U(1)_X that suppresses tree-level FCNCs and yields a Z' boson in the electroweak-scale spectrum. The authors show that the minimal model is excluded by current 4-lepton LHC searches because $h$ and $H$ can decay to Z' pairs, producing observable $4\ell$ final states even at the Higgs alignment limit; introducing vector-like fermions $\chi$ (SM-singlets charged under U(1)_X) allows $Z'$ to predominantly decay invisibly to $\chi\bar{\chi}$, thereby evading these constraints. They study two benchmarks, U(1)_H and U(1)_R, and map the viable parameter space under theoretical (stability and unitarity) and experimental (EWPO, flavor, Higgs decays, and direct Z' searches) constraints. The surviving regions require a Z' mass around $m_{Z'}\sim$ 100 GeV and tightly coordinated couplings, yielding $m_H$ in the range of roughly 160–220 GeV (U(1)_H) or 160–380 GeV (U(1)_R) with $\tan\beta$ between about 3 and 4.4, offering concrete targets for HL-LHC and future lepton colliders to probe this class of 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 $χ$ 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 $χ$, $Z'$ can mainly decay into $χ\barχ$ 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 $\tan β\in [3, 4.4]$ are allowed in the $U(1)_H$ model, while $m_H \in [160, 380]$ GeV and $\tan β\in [1.6, 4.4]$ 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.

Figures (11)

• Figure 1: Left and right plots respectively show the $Z'$ mass as a function of $\epsilon$ and $x_R g_X^{}$ for fixed values of $\tan\beta$ in the $U(1)_H$ and $U(1)_R$ models.
• Figure 2: Left and right plots respectively show the BRs of $Z'$ as a function of $R_1$ and $R_2$ in the $U(1)_H$ and $U(1)_R$ models. For $q \bar{q}$ ($q\neq t$), $\ell^+ \ell^-$ and $\nu \bar{\nu}$ final states, we summed all the flavors.
• Figure 3: Left and right plots respectively show the BRs of $h \to Z' Z'^* \to Z' f_{} \bar{f}$ as a function of $m_{Z'}$ in the $U(1)_H$ model with $R_1=20$ and the $U(1)_R$ model with $R_2=20$ as a function of $m_{Z'}$. All the flavors are summed up (except for the top quark) for $f \bar{f}$ final states.
• Figure 4: Left: BRs of $H$ as a function of $m_{Z'}$ for $m_H = 240$ GeV, $m_{H^\pm}=190$ GeV and $\tan\beta = 3$. Right: BRs of $H^\pm$ as a function of $m_{Z'}$ for $m_H = 190$ GeV, $m_{H^\pm}=240$ GeV and $\tan\beta = 3$.
• Figure 5: Left and right panels respectively show the BRs of $H$ as a function of $m_{Z'}$ in the $U(1)_{H}$ model with $R_1=30$ and $U(1)_R$ model with $R_2 = 30$. In both the plots, we take $m_H = 180$ GeV, $m_{H^\pm} = 160$ GeV and $\tan\beta =3$.