Constraining Type II 2HDM in Light of LHC Higgs Searches

We study the implication of the LHC Higgs search results on the Type II Two Higgs-Doublet Model. In particular, we explore the scenarios in which the observed 126 GeV Higgs signal is interpreted as either the light CP-even Higgs $h^0$ or the heavy CP-even Higgs $H^0$. Imposing both theoretical and experimental constraints, we analyze the surviving parameter regions in $m_H$ ($m_h$), $m_A$, $m_{H^{\pm }}$, $\tan \beta$ and $\sin (\beta -\alpha )$. We further identify the regions that could accommodate a 126 GeV Higgs with cross sections consistent with the observed Higgs signal. We find that in the $h^0$-126 case, we are restricted to narrow regions of $\sin (\beta -\alpha )\approx \pm 1$ with $\tan \beta$ up to 4, or an extended region with $0.55 < \sin(\beta-\alpha) < 0.9$and$1.5 < \tan\beta < 4$\mathrm{.}Thevaluesof$m_H$,$m_A$and$m_{H^\pm}$, however, are relatively unconstrained. In the $H^0$-126 case, we are restricted to a narrow region of $\sin (\beta -\alpha )\sim 0$ with $\tan \beta$ up to about 8, or an extended region of $\sin (\beta -\alpha )$ between $-0.8$ to $-0.05$, with $\tan \beta$ extended to 30 or higher. $m_A$ and $m_{H^{\pm }}$ are nearly degenerate due to $\mathrm{\Delta }\rho$ constraints. Imposing flavor constraints shrinks the surviving parameter space significantly for the $H^0$-126 case, limiting $\tan \beta \lesssim 10$, but has little effect in the $h^0$-126 case. We also investigate the correlation between $\gamma \gamma$, $VV$ and $bb\mathrm{/}\tau \tau$ channels. $\gamma \gamma$ and $VV$ channels are most likely to be highly correlated with $\gamma \gamma :VV\sim 1$ for the normalized cross sections.