Higgs sector as a probe of supersymmetric grand unification with the Hosotani mechanism

The supersymmetric grand unified theory where the $SU(5)$ gauge symmetry is broken by the Hosotani mechanism predicts the existence of adjoint chiral superfields whose masses are at the supersymmetry breaking scale. The Higgs sector is extended with the $SU(2{)}_L$ triplet with hypercharge zero and neutral singlet chiral multiplets from that in the minimal supersymmetric standard model. Since the triplet and singlet chiral multiplets originate from a higher-dimensional vector multiplet, this model is highly predictive. Properties of the particles in the Higgs sector are characteristic and can be different from those in the Standard Model and other models. We evaluate deviations in coupling constants of the standard model-like Higgs boson and the mass spectrum of the additional Higgs bosons. We find that our model is discriminative from the others by precision measurements of these coupling constants and masses of the additional Higgs bosons. This model can be a good example of grand unification that is testable at future collider experiments such as the luminosity upgraded Large Hadron Collider and future electron-positron colliders.

Figure 1

Evolution of the gauge coupling constants in the MSSM (black lines), the MSSM with the adjoint multiplets (red lines), and the MSSM with the adjoint and additional chiral multiplets (blue lines) is plotted from the top to the bottom.

Figure 2

An example of running of the Higgs triplet and singlet coupling constants ${\lambda }_{\mathrm{\Delta }}$ (red line) and ${\lambda }_S^{\prime }$ (blue line) as well as the gauge coupling constants $g_3$, $g_2$, and $g_1$ (green lines) from the top to the bottom. The horizontal axis is the common logarithm of the energy scale in units of GeV. Here, we normalize the singlet and $U(1{)}_Y$ gauge couplings as ${\lambda }_S^{\prime }=(2\sqrt{5/3}){\lambda }_S$ and $g_1=(\sqrt{5/3})g^{\prime }$, respectively, and one loop RGEs are used.

Figure 3

The deviations in the Higgs boson coupling with the tau lepton ${\kappa }_{\tau }$ and that with the bottom quark ${\kappa }_b$ from the SM predictions are plotted. The predictions of the three benchmark points (A), (B), and (C) in the SGGHU are shown with green blobs. The MSSM and NMSSM predictions are shown with red and blue lines, respectively. For the purpose of illustration, the NMSSM line is slightly displaced from ${\kappa }_{\tau }={\kappa }_b$.

Figure 4

The deviations in the Higgs boson coupling with the weak gauge bosons ${\kappa }_V$ and that with the bottom quark ${\kappa }_b$ from the SM predictions are plotted. The predictions of the three benchmark points (A), (B), and (C) in the SGGHU are shown with green blobs. The MSSM predictions are shown with red lines for $\tan \beta =10$ (thick line) and $\tan \beta =3$ (dashed line). The NMSSM predictions are shown with blue grid lines, which indicate mixings between the SM-like and singletlike Higgs bosons of 10%, 20%, and 30% from the right to the left.

Figure 5

The deviations in the Higgs boson coupling with the charm quark ${\kappa }_c$ and that with the bottom quark ${\kappa }_b$ from the SM predictions are plotted. See the caption of Fig. 4 for details.

Figure 6

The deviation parameter ${\delta }_{H^{\pm }}$ of the MSSM-like charged Higgs boson mass $m_{H^{\pm }}$ as a function of the MSSM-like $CP$-odd Higgs boson mass $m_A$ in the large soft mass scenario. The black, blue, and green lines correspond to the triplet contribution, the singlet contribution, and the sum of the singlet and triplet contributions, respectively. Here, we choose ${\lambda }_{\mathrm{\Delta }}=1.1$ and ${\lambda }_S=0.25$.