Probing wrong-sign Yukawa couplings at the LHC and a future linear collider

We consider the two-Higgs-doublet model as a framework in which to evaluate the viability of scenarios in which the sign of the coupling of the observed Higgs boson to down-type fermions (in particular, $b$-quark pairs) is opposite to that of the Standard Model (SM), while at the same time all other tree-level couplings are close to the SM values. We show that, whereas such a scenario is consistent with current LHC observations, both future running at the LHC and a future $e^{+}{e}^{-}$ linear collider could determine the sign of the Higgs coupling to $b$-quark pairs. Discrimination is possible for two reasons. First, the interference between the $b$-quark and the $t$-quark loop contributions to the $ggh$ coupling changes sign. Second, the charged-Higgs loop contribution to the $\gamma \gamma h$ coupling is large and fairly constant up to the largest charged-Higgs mass allowed by tree-level unitarity bounds when the $b$-quark Yukawa coupling has the opposite sign from that of the SM (the change in sign of the interference terms between the $b$-quark loop and the $W$ and $t$ loops having negligible impact).

Figure 1

Ratio of the lightest Higgs couplings to down quarks in the 2HDM relative to the SM as a function of $\tan \beta$. Left: Type-I and right: type-II. All ${\mu }_f^h(\mathrm{LHC})$ are within 20% of the SM value.

Figure 2

Allowed regions for 2HDM type-II with all ${\mu }_f^h(\mathrm{LHC})$ within 20% (blue/black), 10% (green/light grey) and 5% (red/dark grey) of the SM value of unity. Left: In the $\tan \beta$ vs $\sin \alpha$ plane. Right: In $\tan \beta$ vs $\cos (\beta -\alpha )$ space.

Figure 3

Left panel: The Yukawa coupling ratio ${\kappa }_D=h_D^{2\mathrm{HDM}}/h_D^{\mathrm{SM}}$ as a function of $\sin (\beta -\alpha )$ in the type-II 2HDM, with all ${\mu }_f^h(\mathrm{LHC})$ within 20% (blue/black) and 10% (green/light grey) of their SM values. Right panel: Same ratio as a function of $\tan \beta$. If one demands consistency at the 5% level, no points survive.

Figure 4

For the 2HDM type-II, we show regions in ${\kappa }_D$ vs $\tan \beta$ space having $\sin \alpha >0$ that are allowed when ${\mu }_{\gamma \gamma }^h(\mathrm{LHC})$ (cyan/grey) and ${\mu }_{bb}^h(\mathrm{LHC})$ (black) are within 5% of the SM prediction of unity.

Figure 5

Assuming that the $WW,ZZ$ rates are measured to be within 5% of the SM prediction, we plot ${\mu }_{\gamma \gamma }^h(\mathrm{LHC})$ and ${\mu }_{bb}^h(\mathrm{LHC})$ vs $\tan \beta$ (left) and ${\mu }_{\gamma \gamma }^h(\mathrm{LHC})$ vs ${\mu }_{bb}^h(\mathrm{LHC})$ (right).

Figure 6

Allowed regions for 2HDM type-II with all ${\mu }_f^h(\mathrm{LHC})$ within 20% (blue/black), 10% (green/light grey) and 5% (red/dark grey) of their SM values in ${\kappa }_{\gamma }$ vs ${\kappa }_D$ space (left); ${\kappa }_g$ vs ${\kappa }_D$ space (right).

Figure 7

${\kappa }_g^2=\mathrm{\Gamma }(h\to gg{)}^{2\mathrm{HDM}}/\mathrm{\Gamma }(h_{\mathrm{SM}}\to gg)$ as a function of ${\kappa }_D=h_D^{2\mathrm{HDM}}/h_D^{\mathrm{SM}}$ in type-II, with all ${\mu }_f^h(\mathrm{LHC})$ within 20% (blue/black), 10% (green/light grey) and 5% (red/dark grey) of their SM values. Left panel: $\sin \alpha <0$. Right panel: $\sin \alpha >0$.

Figure 8

Left panel: ${\mu }_{gg}^h(\mathrm{ILC})$ as a function $\tan \beta$. Right panel: ${\mu }_{bb}^h(\mathrm{ILC})$ as a function of $\tan \beta$. The model is type-II, requiring $\sin \alpha >0$, with all ${\mu }_f^h(\mathrm{LHC})$ within 20% of the SM values in blue (black) and 10% of the SM values in green (light grey).

Figure 9

We show points in the $v^2{g}_{h{H}^{+}{H}^{-}}/m_{H^{\pm }}^2$ vs ${\kappa }_D$ plane with the standard color scheme of Fig. 2.

Figure 10

We show points in the $m_{H^{\pm }}$ vs ${\kappa }_D$ plane with the standard color scheme of Fig. 2. Note: 900 GeV is the largest $m_{H^{\pm }}$ considered in the scans—the ${\kappa }_D\sim +1$ region would extend to arbitrarily large $m_{H^{\pm }}$ corresponding to the decoupling limit.

Figure 11

In the left panel we plot ${\lambda }_3$ vs ${\kappa }_D$ using the color scheme of Fig. 2; in the right panel we plot $|{\lambda }_3|$ vs $m_{H^{\pm }}$ for ${\kappa }_D<0$ (blue/black) and ${\kappa }_D>0$ (green/light gray) points with all ${\mu }_f^h(\mathrm{LHC})$ within 20% of unity.

Figure 12

In the left panel we plot $|a^{+}|$ vs ${\kappa }_D$ using the color scheme of Fig. 2; in the right panel we plot $|a^{+}|$ vs $m_{H^{\pm }}$ for ${\kappa }_D<0$ (blue/black) and ${\kappa }_D>0$ (green/light gray) points with all ${\mu }_f^h(\mathrm{LHC})$ within 20% of unity.