One-loop renormalization and $\boldsymbolρ$ parameter in the Georgi-Machacek model

Abstract

We study the one-loop renormalization of the Georgi-Machacek model. At one loop, the renormalization of the model is phenomenologically important when triggered by operators that are absent at the tree level due to the global $SU(2)_R$ symmetry. By computing all the tree-level parameters from the standard input parameters $α_e$, $G_μ$, and $m_Z$, we show the ultraviolet divergent nature of the electroweak $ρ$ parameter when one-loop corrections are incorporated. In this model, four input parameters are required to completely parametrize the electroweak precision observables at one loop. We study the quantitative impact of the model parameters on the one-loop corrections to the $ρ$ parameter. At one loop, the $ρ$ parameter shows a mild dependence on the mass differences between the custodial fiveplet and the heavy custodial singlet, and mainly depends on the ratio of the doublet and triplet vacuum expectation values, and on the mixing angle between the custodial singlet CP-even scalars.

Figures (6)

• Figure 1: Feynman diagrams for the $H_5^+$-$G^+$ mixing, where the scalars $S=\{G^+,G^0,H_5^0,H_5^+,H_5^{++}\}$.
• Figure 2: Feynman diagrams for the $H_5^+$-$H_3^+$ mixing, where the scalars $S=\{H_3^+,H_3^0,H_5^0,H_5^+,H_5^{++}\}$.
• Figure 3: One-loop Feynman diagrams for the vector boson self-energies involving scalar fields.
• Figure 4: Dependence of $\tan\beta$ on $\Delta\rho^{\text{NS}}$ for various values of $m_{H_1}$ and $m_{H_5}$. The CP-even scalar mixing angle $\alpha$ is fixed at $0.01$. We choose the values of $m_{H_1}$, $m_{H_5}$, and $\alpha$ that are allowed by the theoretical constraints and the latest Run-II Higgs signal strength data from the CMS and ATLAS detectors (taken from Ref. Chowdhury:2024mfu).
• Figure 5: The contours of $\Delta\rho^{\text{NS}}$ (shown in blue color) in the $v_\Delta$ vs. $\alpha$ plane. We denote the value of $\Delta\rho^{\text{NS}}\cdot 10^4$ for each contour in the red color. We choose the values of $m_{H_1}$ and $m_{H_5}$ that are allowed by the theoretical constraints and the latest Run-II Higgs signal strength data from the CMS and ATLAS detectors (taken from Ref. Chowdhury:2024mfu). The magenta dashed contour represents the allowed region from the latest Run-II Higgs signal strength data (taken from Ref. Chowdhury:2024mfu).