Explaining The CDF-II W-Boson Mass Anomaly in the Georgi-Machacek Extension Models

Original Georgi-Machacek model can preserve the custodial symmetry at tree level after the electroweak symmetry breaking. Unless additional $SU(2)_c$ custodial symmetry breaking effects are significant, the new physics contributions to $\Delta m_W$ are 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 anomaly on W boson mass. We propose firstly to introduce small misalignment among the triplet VEVs to increase $\Delta m_W$, which can give large new physics contributions to $\Delta m_W$. Such slightly misaligned triplet VEVs from custodial symmetry preserving scalar potential can still be allowed. Our numerical results indicate that the resulting $\Delta m_W$ can easily reach the $1\sigma$ range of CDF-II $m_W$ data and the splitting among the triplet VEVs $\Delta v$($\equiv v_\xi-v_\chi$) can be as small as $0.8$ GeV for $v_\chi\lesssim 15$ GeV. We also propose to introduce an additional custodial symmetry breaking source by extending the GM model with a low scale RH neutrino sector, which can adopt the leptogenesis mechanism and allow moderately large coupling strength $h_{ij}$ even for triplet VEVs of order GeV. With low scale RH neutrino mass scale of order $10^2\sim 10^4$ TeV, the new physics contribution to $\Delta m_W$ can reach $0.03$ GeV and is much larger than that of ordinary GM model. Combining both custodial $SU(2)_c$ symmetry breaking effects, the small misalignment among the triplet VEVs and the moderately large $h_{ij}$ couplings allowed with RH neutrino sector, the value of $\Delta m_W$ can still easily reach the $1\sigma$ range of CDF-II $m_W$ data, with a minimum splitting (among the triplet VEVs) approximately $0.7$ GeV for $v_\chi\lesssim 15$ GeV.