The Gildener-Weinberg two-Higgs doublet model at two loops

Abstract

The Gildener-Weinberg two-Higgs doublet model (GW-2HDM) provides a naturally light and aligned Higgs boson, $H=H(125)$. It has been studied in the one-loop approximation of its effective potential, $V_1$. An important consequence is that the masses of the model's BSM Higgs bosons ($H^{\prime },A,H^{\pm }$) are bounded by the sum rule ${\left(M_{H^{\prime }}^4+M_A^4+2M_{H^{\pm }}^4\right)}^{1/4}=540\mathrm{GeV}$. Although they are well within reach of the LHC, searches for them have been stymied by large QCD backgrounds. Another consequence is that $H$ is highly aligned, i.e., $H$--$H^{\prime }$ mixing is small and $H$ has only Standard Model couplings. A corollary of this alignment is that search modes such as $H^{\prime },A\leftrightarrow W^{+}{W}^{-},ZZ,HZ$ and $H^{\pm }\leftrightarrow W^{\pm }Z,W^{\pm }H$ are greatly suppressed. To assess the accuracy of the sum rule and Higgs alignment, we study this model in two loops. This calculation is complicated by having many new contributions. We present two formulations of it to calculate the $H$--$H^{\prime }$ mass matrix, its eigenvectors $H_1,H_2$, and the mass $M_{H_2}$ while fixing $M_{H_1}=125\mathrm{GeV}$. They give similar results, in accord with the one-loop results. Requiring $M_A=M_{H^{\pm }}$, we find $180\mathrm{GeV}<M_{A,H^{\pm }}<380$--$425\mathrm{GeV}$ and $550$--$700\mathrm{GeV}>M_{H_2}>125\mathrm{GeV}$, with $M_{H_2}$ decreasing as $M_{A,H^{\pm }}$ increase. The corrections to $H$-alignment are below $\mathcal{O}(1\%)$. So, the BSM searches above will remain fruitless. Finding the BSM Higgses requires improved sensitivity to their low masses. We discuss two possible searches for this.

arXiv comment48 pages, 13 figures. Revisions are: correction of title; a dedication is added on page 1; the abstract is slightly modified and shortened; the discussion in Section IV on $gg\to H_2\to W^{\pm }{H}^{\mp }$ is sharpened; two acknowledgements are added

References in corpus (29)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Theory and phenomenology of two-Higgs-doublet models
• The CP-conserving two-Higgs-doublet model: the approach to the decoupling limit
• A portrait of the Higgs boson by the CMS experiment ten years after the discovery
• A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery
• Two-loop effective potential for a general renormalizable theory and softly broken supersymmetry
• Impersonating the Standard Model Higgs Boson: Alignment without Decoupling
• Search for a charged Higgs boson in pp collisions at sqrt(s) = 8 TeV
• A Higgslike Dilaton
• Vacuum Topology of the Two Higgs Doublet Model
• Search for charged Higgs bosons decaying into a top quark and a bottom quark at $\sqrt{s}$=13 TeV with the ATLAS detector
• Search for production of four top quarks in final states with same-sign or multiple leptons in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Search for charged Higgs bosons decaying into top and bottom quarks at $\sqrt{s}$ = 13 TeV with the ATLAS detector
• Search for heavy Higgs bosons decaying to a top quark pair in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Search for a heavy Higgs boson decaying into a $Z$ boson and another heavy Higgs boson in the $\ell \ell bb$ final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Search for charged Higgs bosons decaying into a top and a bottom quark in the all-jet final state of pp collisions at $\sqrt{s}=$ 13 TeV
• Measurements of the SUSY Higgs self-couplings and the reconstruction of the Higgs potential
• On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential
• Radiative Corrections to Scalar Masses and Mixing in a Scale Invariant Two Higgs Doublet Model
• Search for new neutral Higgs bosons through the H $\to$ ZA $\to$ ${\ell }^{+}{\ell }^{-}\mathrm{b}\bar{\mathrm{b}}$ process in pp collisions at $\sqrt{s}=$ 13 TeV
• Search for a heavy Higgs boson decaying into a $Z$ boson and another heavy Higgs boson in the $\ell \ell bb$ and $\ell \ell WW$ final states in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector
• Search for a charged Higgs boson decaying into top and bottom quarks in events with electrons or muons in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Two-loop analysis of classically scale-invariant models with extended Higgs sectors
• Natural Stabilization of the Higgs Boson's Mass and Alignment
• A natural mechanism for approximate Higgs alignment in the 2HDM
• Phenomenology of the new light Higgs bosons in Gildener-Weinberg model
• Exceptional regions of the 2HDM parameter space
• Higgs alignment and the top quark

Cited by in corpus (2)

• ATLAS searches for additional scalars and exotic Higgs boson decays with the LHC Run 2 dataset
• Systematic analysis of 3HDM symmetries