How Can a Heavy Higgs Boson be Consistent with the Precision Electroweak Measurements?

TL;DR

The paper investigates whether a heavy Higgs can be reconciled with precision electroweak measurements by organizing beyond-MSM physics around oblique corrections. Using the $S$ and $T$ parameters, it identifies three universal mechanisms—negative $oldsymbol{igDelta S}$, new vector bosons ($Z'$), and positive $oldsymbol{igDelta T}$—and analyzes explicit models illustrating each route. It demonstrates that, although heavy-Higgs scenarios are viable, they require distinctive new physics with testable collider signatures, such as light electroweak-charged states, $Z'$ resonances, or sizable isospin-symmetry breaking. The work provides a framework to discriminate MSM from heavy-Higgs theories with future high-precision measurements and collider data.

Abstract

The fit of precision electroweak data to the Minimal Standard Model currently gives an upper limit on the Higgs boson mass of 170 GeV at 95% confidence. Nevertheless, it is often said that the Higgs boson could be much heavier in more general models. In this paper, we critically review models that have been proposed in the literature that allow a heavy Higgs boson consistent with the precision electroweak constraints. All have unusual features, and all can be distinguished from the Minimal Standard Model either by improved precision measurements or by other signatures accessible to next-generation colliders.

Figures (5)

• Figure 1: Fit of the precision electroweak data to the MSM plus the $S$, $T$ parameters described in the text. The fit is based on the values of $m_W$, ${\sin^2\theta_w^{\rm eff}}$, and $\Gamma_\ell$ shown in Table \ref{['tab:data']}. The ellipse shows the 68% two-dimensional confidence region (1.5 $\sigma$). The banana-shaped figure shows the central value of a fit to the MSM for $m_t = 174.3 \pm 5.1$ GeV and $m_h$ varying from 100 to 1000 GeV, with $m_h = 200$, 300, 500 GeV marked with vertical bands. An active version of this figure can be obtained by downloading the additional files deposited with the eprint.
• Figure 2: Shift in $S$ induced by the vacuum polarization of various multiplets in the Dugan-Randall scenerio described in the text. The curves assume that the lightest state in the multiplet is split in mass from the other states by 100 GeV. The various Dugan-Randall multiplets are labeled by $(j_L,j_R)$, and the corresponding shifts in $S$ are plotted against the mass of the lightest state.
• Figure 3: Fit of the precision electroweak data to the MSM with $m_h = 500$ GeV and shifts of the electroweak parameters due to a $Z^{0\prime}$, plus the effects of the $S$, $T$ parameters. The four darker ellipses correspond to fits with $M = 1.5$, 2.0, 2.5 TeV and $\infty$. The lighter ellipse and the grid are those plotted in Fig. \ref{['fig:STfit']}. This diagram shows how the centers of the various fits with different values of $M$ (symbolized by $\circ$) can be plotted as shifts of $(S,T)$ with respect the Standard Model ellipse (symbolized by $*$). These shifts represent the combined contribution of the $Z^{0\prime}$ and the heavy Higgs boson, and fall on a line which tends to the heavy Higgs boson prediction for $M \to \infty$. We see almost complete compensation of the heavy Higgs boson effect for $M \sim 2$ TeV.
• Figure 4: Contributions to $S$ and $T$ from a Higgs boson with $m_h = 500$ GeV, plus a heavy $Z^{0\prime}$. The contributions are computed and displayed as indicated in Fig. \ref{['fig:STfitZpC']}. Four different models are considered: ($\delta$): model of Fig. \ref{['fig:STfitZpC']}, with $\gamma =1$, $q_{L,R} = 0$; (u): rank-1 $E_6$ models with mixing due to a Higgs field $H_u$; (d): rank-1 $E_6$ models with mixing due to a Higgs field $H_d$; (KK): extra-dimension model of ref. rizzowells. The numbers indicate the values of the $Z^{0\prime}$ mass $M$, always in TeV, and the star symbols represent the $(S,T)$ shifts, as in Fig. 3, for the variously labeled values of $M$. For the $E_6$ models, there are two parameters to vary, the mass $M$ and the mixing angle $\theta$. For these models, we have plotted the contours swept out as one changes the mixing angle for fixed values of $M$. All of the $Z^{0\prime}$ predictions tend to the 500 GeV MSM point as $M \to \infty$.
• Figure 5: Future improvements in the determination of precision electroweak parameters. The lighter ellipse and grid are those plotted in Fig. \ref{['fig:STfit']}. The heavier ellipses, both centered at $(S,T) = (0.11, 0.11)$, correspond to an improved $W$ mass measurement with an error of 15 MeV, as would be expected from the LHC, and measurements of $m_W$, ${\sin^2\theta_w^{\rm eff}}$, and $\Gamma_\ell$ with errors of 6 MeV, 0.00002, and 0.04 MeV, respectively, as would be expected from the precision electroweak program at an $e^+e^-$ linear collider TESLAEWWilsonErlerRowson.