Reappraisal of the wrong-sign $hb\overline{b}$ coupling and the study of $h\to Z\gamma$

It has been pointed out recently that current experiments still allow for a two Higgs doublet model where the $hb\overline{b}$ coupling ($k_D{m}_b/v$) is negative; a sign opposite to that of the Standard Model. Due to the importance of delayed decoupling in the $h{H}^{+}{H}^{-}$ coupling, $h\to \gamma \gamma$ improved measurements will have a strong impact on this issue. For the same reason, measurements or even bounds on $h\to Z\gamma$ are potentially interesting. In this article, we revisit this problem, highlighting the crucial importance of $h\to VV$, which can be understood with simple arguments. We show that the impacts on $k_D<0$ models of both $h\to b\overline{b}$ and $h\to {\tau }^{+}{\tau }^{-}$ are very sensitive to input values for the gluon fusion production mechanism; in contrast, $h\to \gamma \gamma$ and $h\to Z\gamma$ are not. We also inquire if the search for $h\to Z\gamma$ and its interplay with $h\to \gamma \gamma$ will impact the sign of the $hb\overline{b}$ coupling. Finally, we study these issues in the context of the flipped two Higgs doublet model.

Figure 1

Left panel: Assuming that all ${\mu }_f$ are within 20% of the SM prediction we plot ${\mu }_{b\overline{b}}$ (red/dark gray) and ${\mu }_{\gamma \gamma }$ (black). Right panel: Assuming now that ${\mu }_{VV}$ are within 5% of the SM prediction we plot the same quantities. For comparison we also plot ${\mu }_{b\overline{b}}$ (cyan/light gray) for the assumed production of Ref. [7].

Figure 2

Left panel: Plot of $\tan \beta$ as a function of $\sin \alpha$ for all the points that obey Eq. (10) with $0.8\le {\mu }_{VV}\le 1.2$. Right panel: Plot of ${\sin }^2(\beta -\alpha )$ as a function of $\tan \beta$ for the points that obey Eq. (10) with $0.8\le {\mu }_{VV}\le 1.2$ and have $k_D<0$.

Figure 3

Fractional variation of ${\sin }^2(\beta -\alpha )$ as a function of $\tan \beta$ for all points with $k_D<0$ that obey Eq. (10) with $0.8\le {\mu }_{VV}\le 1.2$.

Figure 4

Left panel: $k_D^2$ as a function of ${\sin }^2(\beta -\alpha )$ for all points with $k_D<0$ that obey Eq. (10) with $0.8\le {\mu }_{VV}\le 1.2$ (black) or with $0.95\le {\mu }_{VV}\le 1.05$ (cyan/light gray). Right panel: The same but for generated data obeying the model constraints.

Figure 5

Allowed region for $k_D^2$ as a function of ${\sin }^2(\beta -\alpha )$ for all points with $k_D<0$ that obey $0.8\le {\mu }_{VV}\le 1.2$ (black). The region in cyan (light gray) is obtained by imposing in addition that $0.8\le {\mu }_{\tau \tau }\le 1.2$, while in the region in red (dark gray) we further impose $0.8\le {\mu }_{\gamma \gamma }\le 1.2$.

Figure 6

Same as in Fig. 5, but for the assumed production rates in Ref. [7]. See text for details.

Figure 7

Left panel: Prediction for ${\mu }_{{\tau }^{+}{\tau }^{-}}$ (red/dark gray) and ${\mu }_{\gamma \gamma }$ (black) as a function of $\tan \beta$ for the LHC at 14 TeV with the constraint of 20% errors at 8 TeV. Right panel: Assuming now that ${\mu }_{VV}$ are within 5% of the SM prediction at 14 TeV, we plot the same quantities. Also shown (cyan/light gray) is the prediction for ${\mu }_{b\overline{b}}(Vh)$ from associated production.

Figure 8

Prediction for ${\mu }_{{\tau }^{+}{\tau }^{-}}$ (red/dark gray), ${\mu }_{Z\gamma }$ (cyan/light gray), and ${\mu }_{\gamma \gamma }$ (black) as a function of $\tan \beta$, for the LHC at 14 TeV, with a measurement of ${\mu }_{VV}$ within 5% of the SM at 14 TeV.

Figure 9

Predictions for ${\mu }_{Z\gamma }$ versus ${\mu }_{\gamma \gamma }$ at 14 TeV, for $k_D<0$. In black, we have the points in the SET (obeying theoretical constraints and $S,T,U$, only). In red/dark gray (cyan/light gray), the points satisfying, in addition, $VV$ within 20% (5%) of the SM, at 14 TeV.

Figure 10

Predictions for ${\mu }_{Z\gamma }$ versus ${\mu }_{\gamma \gamma }$ at 14 TeV, for $k_D>0$. In black, we have the points in the SET (obeying theoretical constraints and $S,T,U$, only). In red/dark-gray (cyan/light gray), the points satisfying, in addition, $VV$ within 20% (5%) of the SM, at 14 TeV.

Figure 11

Left panel: Allowed region for $k_D^2$ as a function of ${\sin }^2(\beta -\alpha )$ in the flipped 2HDM, for all points with $k_D<0$ that obey $0.8\le {\mu }_{VV}\le 1.2$ (black). The region in cyan (light gray) is obtained by imposing, in addition, that $0.8\le {\mu }_{\tau \tau }\le 1.2$, while in the region in red (dark gray) we further impose $0.8\le {\mu }_{\gamma \gamma }\le 1.2$. Right panel: Predictions for ${\mu }_{Z\gamma }$ versus ${\mu }_{\gamma \gamma }$ at 14 TeV, for $k_D<0$, in the flipped 2HDM. In black, we have the points in the SET (obeying theoretical constraints and $S,T,U$, only). In red/dark gray (cyan/light gray), the points satisfying, in addition, $VV$ within 20% (5%) of the SM, at 14 TeV. Shown in green/light gray are the points satisfying ${\mu }_{{\tau }^{+}{\tau }^{-}}$ at 20% of the SM, which lie on a line going diagonally from the origin with almost unit slope.