Fingerprinting nonminimal Higgs sectors

After the discovery of the standard model-like Higgs boson at the LHC, the structure of the Higgs sector remains unknown. We discuss how it can be determined by the combination of direct and indirect searches for additional Higgs bosons at future collider experiments. First of all, we evaluate expected excluded regions for the mass of additional neutral Higgs bosons from direct searches at the LHC with the 14 TeV collision energy in the two Higgs doublet models with a softly broken $Z_2$ symmetry. Second, precision measurements of the Higgs boson couplings at future experiments can be used for the indirect search of extended Higgs sectors if the measured coupling constant with the gauge boson slightly deviates from the standard model value. In particular, in the two Higgs doublet model with the softly broken discrete symmetry, there are four types of Yukawa interactions, so that they can be discriminated by measuring the pattern of deviations in Yukawa coupling constants. Furthermore, we can fingerprint various extended Higgs sectors with future precision data by detecting the pattern of deviations in the coupling constants of the standard model-like Higgs boson. We demonstrate how the pattern of deviations can be different among various Higgs sectors that predict the electroweak rho parameter to be unity, such as models with additional an isospin singlet, a doublet, triplets, or a septet. We conclude that, as long as the gauge coupling constant of the Higgs boson slightly differs from the standard model prediction but is enough to be detected at the LHC and its high-luminosity run or at the International Linear Collider, we can identify the nonminimal Higgs sector even without direct discovery of additional Higgs bosons at the LHC.

Figure 1

Upper limit of $1-{\kappa }_V$ as a function of $m_A$ for each value of $\tan \beta$ from the constraints of unitarity and vacuum stability in the case in which $M$ is scanned over the range of $m_A\pm 500\mathrm{GeV}$ and $m_{H^{+}}=m_A$. The left and right panels, respectively, show the results with $\cos (\beta -\alpha )>0$ and $\cos (\beta -\alpha )<0$. The solid curves show the case with $m_H=m_A$, while the dotted curves show the result with $m_H$ to be scanned over the range of $m_A\pm 500\mathrm{GeV}$.

Figure 2

Upper limit of $m_A$ as a function of $\tan \beta$ for each value of $1-{\kappa }_V$ from the constraints of unitarity and vacuum stability in the case in which $M$ is scanned over the range of $m_A\pm 500\mathrm{GeV}$ and $m_{H^{+}}=m_A$. The left and right panels, respectively, show the results with $\cos (\beta -\alpha )>0$ and $\cos (\beta -\alpha )<0$. The solid curves show the result with $m_H=m_A$, while the dotted curves show the result with $m_H$ to be scanned over the range of $m_A\pm 500\mathrm{GeV}$.

Figure 3

Total widths for $H$, $A$, and $H^{\pm }$ as a function of $\tan \beta$ in the case of $\sin (\beta -\alpha )=1$. The solid and dashed curves, respectively, show the results with $m_{\mathrm{\Phi }}=M=200\mathrm{GeV}$ and $m_{\mathrm{\Phi }}=M=400\mathrm{GeV}$.

Figure 4

Decay branching ratios for $H$, $A$, and $H^{\pm }$ as a function of $\tan \beta$ in the case of $m_{\mathrm{\Phi }}=M=200\mathrm{GeV}$ and $\sin (\beta -\alpha )=1$.

Figure 5

Decay branching ratios for $H$, $A$, and $H^{\pm }$ as a function of $\tan \beta$ in the case of $m_{\mathrm{\Phi }}=M=400\mathrm{GeV}$ and $\sin (\beta -\alpha )=1$.

Figure 6

Decay branching ratios for $h$ as a function of $\tan \beta$ in the case of $m_{\mathrm{\Phi }}=M=200\mathrm{GeV}$ and $\sin (\beta -\alpha )=0.99$. The solid and dashed curves respectively show the cases with $\cos (\beta -\alpha )<0$ and $\cos (\beta -\alpha )>0$.

Figure 7

Decay branching ratios for $H$, $A$, and $H^{\pm }$ as a function of $\tan \beta$ in the case of $m_{\mathrm{\Phi }}=M=200\mathrm{GeV}$ and $\sin (\beta -\alpha )=0.99$. For the $H$ decay, the solid and dashed curves, respectively, show the cases with $\cos (\beta -\alpha )<0$ and $\cos (\beta -\alpha )>0$.

Figure 8

Decay branching ratios for $H$, $A$, and $H^{\pm }$ as a function of $\tan \beta$ in the case of $m_{\mathrm{\Phi }}=M=400\mathrm{GeV}$ and $\sin (\beta -\alpha )=0.99$. For the $H$ decay, the solid and dashed curves, respectively, show the cases with $\cos (\beta -\alpha )<0$ and $\cos (\beta -\alpha )>0$.

Figure 9

Expected excluded regions on the $\tan \beta$-$m_A$ plane at the 95% C.L. from the $gg\to {\varphi }^0\to {\tau }^{+}{\tau }^{-}$ and $gg\to b\overline{b}{\varphi }^0\to b\overline{b}{\tau }^{+}{\tau }^{-}$ processes by using Eqs. (33) and (34) in the case of $m_A=m_H$ and $\sin (\beta -\alpha )=1$. The left and right panels show the results in the type-II and type-X THDMs, respectively. The blue (red) shaded regions are excluded regions assuming the integrated luminosity to be $300{\mathrm{fb}}^{-1}$ ($3000{\mathrm{fb}}^{-1}$). In the right panel, the constraint from the $q\overline{q}\to HA\to {\tau }^{+}{\tau }^{-}{\tau }^{+}{\tau }^{-}$ processes is also shown by the light colored regions in the type-X THDM.

Figure 10

The scaling factors for the Yukawa interaction of the SM-like Higgs boson in THDMs in the case of $\cos (\beta -\alpha )<0$.

Figure 11

The scaling factors for the Yukawa interaction of the SM-like Higgs boson in THDMs in the case of $\cos (\beta -\alpha )>0$.

Figure 12

The scaling factors ${\kappa }_f$ and ${\kappa }_V$ in models with universal Yukawa coupling constants.