Explaining The New CDF II W-Boson Mass Data In The Georgi-Machacek Extension Models

Georgi-Machacek model can hardly account for the new CDF II data on W-boson mass in its original form. As anticipated, unless additional tree level $SU(2)_c$ custodial symmetry breaking effects are non-negligible, the new physics contributions to $\Delta m_W$ is always very small. Our numerical results show that ordinary GM model can contribute to $\Delta m_W$ a maximal amount $0.0012$ GeV, which can not explain the new CDF II data on W boson mass. We propose to introduce small misalignment among the triplet VEVs to increase $\Delta m_W$, which can reach 0.06 GeV for $v_\xi-v_\chi\sim 6$ GeV, marginally explain the new data in $2\sigma$ range. We also propose to extend the GM model with low scale RH neutrino sector, which can adopt the leptogenesis mechanism and act as a large $SU(2)_c$ breaking source because of its correlation with $h_{ij}$. With low scale RH neutrino mass scale of order $10^2\sim 10^4$ TeV, the new physics contributions to $\Delta m_W$ can reach $0.03$ GeV. Combining both small $SU(2)_c$ breaking effects, the small misalignment among the triplet VEVs and large $h_{ij}$ couplings, the $1\sigma$ range of CDF II data on W boson mass can be obtained even for small splitting among the triplet VEVs with $v_\xi-v_\chi\approx 1 $ GeV.Comment: 12 pages, 3 figures; Major changes, numerical results correcte