Finding the CP-Violating Higgs Bosons at e^+e^- Colliders

TL;DR

This paper addresses the possibility of CP violation in the Higgs sector within a general two-Higgs-doublet model (2HDM) where the three neutral Higgs states mix and lack definite CP. It derives a new sum rule tying Yukawa couplings to Higgs–$Z$ couplings, proving that any light neutral Higgs with suppressed $ZZh$ coupling cannot evade detection at $e^+e^-$ colliders because its Yukawa couplings to top or bottom quarks must be sizable, enabling production in $e^+e^- o far f h_i$. It also recalls and extends an existing sum rule ensuring at least one of $Zh_i$, $Zh_j$, or $h_ih_j$ is observable if two light Higgs bosons are accessible, and analyzes the impact for a two-doublet plus one-singlet (2D1S) extension, where Yukawa processes can guarantee discovery of at least one of three light Higgs bosons and, with four light states, Zh or hh channels become effective. The work provides guidance for Higgs searches at future linear colliders and highlights the complementary role of Yukawa-driven production channels with respect to Higgs-strahlung and pair production, while remaining consistent with precision electroweak constraints.

Abstract

We discuss a general two-Higgs-doublet model with CP violation in the Higgs sector. In general, the three neutral Higgs fields of the model all mix and the resulting physical Higgs bosons have no definite CP properties. We derive a new sum rule relating Yukawa and Higgs-Z couplings which implies that a neutral Higgs boson cannot escape detection at an e^+e^- collider if it is kinematically accessible in Z+Higgs, $b\anti b+$Higgs and $t\anti t+$Higgs production, irrespective of the mixing angles and the masses of the other neutral Higgs bosons. We also discuss modifications of the sum rules and their phenomenological consequences in the case when the two-doublet Higgs sector is extended by adding one or more singlets.

Figures (2)

• Figure 1: Contour lines for ${\rm min}[\sigma(e^+e^-\rightarrow h_1 h_2)]$ as functions of Higgs boson masses for the indicated $\sqrt{s}$ values. In scanning over mixing angles $\alpha_i$, we respect the experimental constraints listed in Section 4, and we assume that at any $\sqrt{s}$ the number of $e^+e^- \rightarrow Zh_1$ or $Zh_2$ events is less than 50 for total luminosity $L=500 ~{\rm fb}^{-1}$. The contour lines are plotted for $\tan \beta=0.5$; the plots are virtually unchanged for larger values of $\tan \beta$. The contour lines overlap in the inner corner of each plot as a result of excluding mass choices inconsistent with experimental constraints from LEP2 data.
• Figure 2: The minimal and maximal values (after requiring fewer than 50 $Zh_1$ events for $L=500~{\rm fb}^{-1}$) of the cross sections for $e^+e^- \rightarrow b\bar{b} h_1$ (a) and $e^+e^-\rightarrow t\bar{t} h_1$ (b) are plotted for $\sqrt{s}=500$ GeV. For a given value of $\tan \beta$, the same type of line (closely spaced dots for $\tan \beta=0.1$, widely spaced dots for $\tan \beta=1$, dashes for $\tan \beta=10$) is used for the minimal and maximal values of the cross sections. Solid lines denote cross sections for $e^+e^-\rightarrow f\bar{f}A^0$ in the CP-conserving limit of the general 2HDM with $m_{A^0}=m_{h_1}$. In the case of $b\bar{b} h_1$, the minimal and maximal values of the cross sections are almost the same and are almost hidden by the $A^0$ curves with the same $\tan \beta$ value. In the case of $t\bar{t}$, the minimal cross section curves are almost hidden by the $A^0$ curves with the same $\tan \beta$ value. Masses of the remaining Higgs bosons are assumed to be $1000\,{\rm GeV}$.