$pp\to A\to Zh$ and the wrong-sign limit of the two-Higgs-doublet model

We point out the importance of the decay channels $A\to Zh$ and $H\to VV$ in the wrong-sign limit of the two-Higgs-doublet model (2HDM) of type II. They can be the dominant decay modes at moderate values of $\tan \beta$, even if the (pseudo)scalar mass is above the threshold where the decay into a pair of top quarks is kinematically open. Accordingly, large cross sections $pp\to A\to Zh$ and $pp\to H\to VV$ are obtained and currently probed by the LHC experiments, yielding conclusive statements about the remaining parameter space of the wrong-sign limit. In addition, mild excesses—as recently found in the ATLAS analysis $b\overline{b}\to A\to Zh$—could be explained. The wrong-sign limit makes other important testable predictions for the light Higgs boson couplings.

Figure 1

Gluon-fusion cross section (black, solid) and bottom-quark annihilation cross section (red, dashed) and their sum (blue, dot-dashed) for a pseudoscalar with mass 440 GeV at a center-of-mass energy of 13 TeV as a function of $\tan \beta$.

Figure 2

Scatter plots for the 2HDM of type II showing (a) $\mathrm{BR}(A\to Zh)$ as a function of the pseudoscalar mass $m_A$ in GeV and (b) $\mathrm{BR}(A\to Zh)$ as a function of $\tan \beta$. All relevant constraints are imposed and $h$ rates are within 20% of their SM values. Red points are in the wrong-sign limit.

Figure 3

Scatter plots for the 2HDM of type II showing (a) $\tan \beta$ versus $\cos (\beta -\alpha )$ and (b) the cross section for $pp\to A$ in pb as a function of $\tan \beta$. All relevant constraints are imposed and $h$ rates are within 20% of their SM values. Red points further satisfy $400\le m_A\le 500\mathrm{GeV}$ and $\sigma (pp\to A\to Zh\to Zb\overline{b})\ge 0.1\mathrm{pb}$.

Figure 4

Scatter plots for the 2HDM of type II showing (a) the cross section $\sigma (b\overline{b}\to A)\mathrm{BR}(A\to Zh\to Zb\overline{b})$ in pb as a function of $m_A$ in GeV and (b) the cross section $\sigma (gg\to A)\mathrm{BR}(A\to Zh\to Zb\overline{b})$ in pb as a function of $m_A$ in GeV. All relevant constraints are imposed and $h$ rates are within 20% of their SM values. Red, yellow and green points represent those parameters satisfying the wrong-sign limit and distinguish different regions of $\tan \beta$: $1<\tan \beta <5$ (red), $5<\tan \beta <7.5$ (yellow) and $\tan \beta >7.5$ (green). The black lines indicate the experimental bounds from Ref. [31].

Figure 5

Scatter plots for the 2HDM of type II showing (a) the charged Higgs mass $m_{H^{\pm }}$ versus the heavier $CP$-even Higgs mass $m_H$, both in GeV, and (b) the gluon-fusion induced cross section for $gg\to H\to ZZ$ as a function of $m_H$ in GeV. All relevant constraints are imposed and $h$ rates are within 20% of their SM values. In (a) red points further satisfy $400\le m_A\le 500\mathrm{GeV}$ and $\sigma (pp\to A\to Zh\to Zb\overline{b})\ge 0.1\mathrm{pb}$. In (b) red, yellow and green points are in the wrong-sign limit and distinguish different regions of $\tan \beta$: $1<\tan \beta <5$ (red), $5<\tan \beta <7.5$ (yellow) and $\tan \beta >7.5$ (green). The black line in (b) corresponds to the upper $2\text{−}\sigma$ bound from the ATLAS analysis [22] based on an integrated luminosity of $36{\mathrm{fb}}^{-1}$.

Figure 6

Di-photon decay rate ${\mu }_{\gamma \gamma }$ versus $ZZ$ production and decay rate ${\mu }_{ZZ}$ for the lightest $CP$-even Higgs boson in the 2HDM of type II. It applies the same color code as in Fig. 3, highlighting in yellow points where the rates of the lightest $CP$-even Higgs-boson deviate from the SM values by at most 10%.