Indirect constraints on the Georgi-Machacek model and implications for Higgs boson couplings

We update the indirect constraints on the Georgi-Machacek model from $B$-physics and electroweak precision observables, including new constraints from $b\to s\gamma$ and $B_s^0\to {\mu }^{+}{\mu }^{-}$. We illustrate the effect of these constraints on the couplings of the Standard-Model-like Higgs boson by performing scans using the most general scalar potential, subject to vacuum stability and perturbativity constraints. We find that simultaneous enhancements of all the Higgs production cross sections by up to 39% are still allowed after imposing these constraints. LHC rate measurements on the Higgs pole could be blind to these enhancements if unobserved nonstandard Higgs decays are present.

Figure 1

Constraints on $m_3$ and $v_{\chi }$ in the GM model from $R_b$, $B_s^0–{\overline{B}}_s^0$ mixing, $\overline{\mathrm{BR}}(B_s^0\to {\mu }^{+}{\mu }^{-})$, and $\mathrm{BR}(b\to s\gamma )$. The region above each curve is excluded. Left: Tight constraints requiring that each observable lies within $2\sigma$ of the experimental central value. Right: Loose constraints requiring that $R_b$, $\overline{\mathrm{BR}}(B_s^0\to {\mu }^{+}{\mu }^{-})$, and $\mathrm{BR}(b\to s\gamma )$ lie within $2\sigma$ of the value at the best-fit point within the GM model.

Figure 2

Effect of the experimental constraints on $\mathrm{BR}(b\to s\gamma )$ and the $S$ parameter on $v_{\chi }$, as a function of $m_3$ (left) and $m_5$ (right). The black points are allowed. The red (medium gray) $+$-shaped points are eliminated by the $S$ parameter constraint. The light green (light gray) $\times$-shaped points are eliminated by the loose $b\to s\gamma$ constraint, in which we require that $\mathrm{BR}(b\to s\gamma )$ is within $2\sigma$ of the best-fit point in the GM model. The dark green (dark gray) $\times$-shaped points would be eliminated by the tight $b\to s\gamma$ constraint, in which we require that $\mathrm{BR}(b\to s\gamma )$ lies within $2\sigma$ of the experimental central value.

Figure 3

Effect of the experimental constraints on $\mathrm{BR}(b\to s\gamma )$ and the $S$ parameter as a function of $m_5$. The color codes are the same as in Fig. 2.

Figure 4

Effect of the experimental constraints on $\mathrm{BR}(b\to s\gamma )$ and the $S$ parameter on the couplings of the 125 GeV Higgs boson $h$ to $W$ and $Z$ boson pairs (left) and fermion pairs (right), shown as a function of $v_{\chi }$. ${\kappa }_V$ (${\kappa }_f$) is defined as the coupling of $h$ to $VV$ ($f\overline{f}$) normalized to the corresponding SM Higgs boson coupling. The color codes are the same as in Fig. 2.

Figure 5

The allowed correlations between ${\kappa }_V$ and ${\kappa }_f$ after applying the constraints from $\mathrm{BR}(b\to s\gamma )$ and the $S$ parameter. The color codes are the same as in Fig. 2.

Figure 6

${\kappa }_V$ as a function of the mass of the lightest new scalar, after imposing the constraint from the $S$ parameter and the loose (left) and tight (right) constraint from $b\to s\gamma$. Points for which $|{\kappa }_f/{\kappa }_V-1|<5\%$ are shown in red (medium gray), points for which $|{\kappa }_f/{\kappa }_V-1|<10\%$ are shown in blue (dark gray), and the remaining points are shown in green (light gray).