Do precision electroweak constraints guarantee $e^+e^-$ collider discovery of at least one Higgs boson of a two-Higgs-doublet model?

Abstract

We consider a CP-conserving two-Higgs-doublet type II model with a light scalar or pseudoscalar neutral Higgs boson ($\h=\hl$ or $\h=\ha$) that has no $ZZ/WW$ coupling and, thus, cannot be detected in $\epem\to Z\h$ (Higgs-strahlung) or $ν\antiν\h$ (via $WW$ fusion). Despite sum rules which ensure that the light $\h$ must have significant $t\anti t$ or $b\anti b$ coupling, for a wedge of moderate $\tanb$, that becomes increasingly large as $\mh$ increases, the $\h$ can also escape discovery in both $b\anti b \h$ and $t\anti t \h$ production at a $\rts=500-800\gev$ $\epem$ collider (for expected luminosities). If the other Higgs bosons happen to be too heavy to be produced, then no Higgs boson would be detected. We demonstrate that, despite such high masses for the other Higgs bosons, only the low-$\tanb$ portion of the no-discovery wedges in $[\mh,\tanb]$ parameter space can be excluded due to failure to fit precision electroweak observables. In the $\tanb\gsim 1$ regions of the no-discovery wedges, we find that the 2HDM fit to precision electroweak observables has small $Δχ^2$ relative to the best minimal one-doublet SM fit.

Figures (4)

• Figure 1: For $\sqrt s=500\,{\rm GeV}$ and $\sqrt s=800\,{\rm GeV}$, the solid lines show as a function of $m_{A^0}$ the maximum and minimum $\tan \beta$ values between which $t\overline t A^0$, $b\overline b A^0$ final states will both have fewer than 50 events assuming $L=2500~{\rm fb}^{-1}$. The different types of bars indicate the best $\chi^2$ values obtained for fits to precision electroweak data after scanning: over the masses of the remaining Higgs bosons subject to the constraint they are too heavy to be directly produced; and over the mixing angle in the CP-even sector.
• Figure 2: The same as for Fig. \ref{['wedgeha']}, except for $h=h^0$. The CP-even sector mixing angle is fixed by the requirement $\sin(\beta-\alpha)=0$.
• Figure 3: For the case of $m_{A^0}=90\,{\rm GeV}$, $\tan \beta=2.3$ and $m_{h^0}=490\,{\rm GeV}$ (that yields the minimum $\Delta\chi^2$ for $\sqrt s=500\,{\rm GeV}$ when requiring that $b\overline bh^0$ production is forbidden), we plot $m_{H^{\pm}}$ as a function of $m_{H^0}$ for various ranges of $\Delta\chi^2$. Scans in $m_{H^0}$ and $m_{H^{\pm}}$ were done using 10 GeV steps, which leads to some incompleteness in the points for each $\Delta\chi^2$ range. The scan in $m_{H^0}$ was limited to $m_{H^0}<980\,{\rm GeV}$. Multiple entries at the same $m_{H^0},m_{H^{\pm}}$ location correspond to different $\alpha$ values.
• Figure 4: For the case of $m_{A^0}=90\,{\rm GeV}$ and $\tan \beta=2.3$, we plot as a function of $m_{h^0}\in[410,980]\,{\rm GeV}$: a) the minimum $\Delta\chi^2$ found after scanning over all values of $m_{H^0},m_{H^{\pm}}>m_{h^0}$ and over all scalar sector mixing angles; b) the corresponding values of $m_{H^0}$ and $m_{H^{\pm}}$; c) the values of $m_{H^0}$ for which $\Delta\chi^2<\Delta\chi^2_{\rm min}+0.05$ is achieved; d) the closely correlated values of $m_{H^{\pm}}$ for which $\Delta\chi^2<\Delta\chi^2_{\rm min}+0.05$ is achieved. For this case, $\Delta\chi^2_{\rm min}$ is always achieved for $\alpha=-0.1\pi$ (our scan is in units of $0.1\pi$), which roughly corresponds to $\beta-\alpha=\pi/2$, i.e. maximal $h^0$ coupling to $ZZ$.