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 mW data and the splitting among the triplet VEVs A(v)(equivalent to v(xi) - v(chi)) can be as small as 0.8 GeV for v(chi) ? 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 hijeven for triplet VEVs of order GeV. With low scale RH neutrino mass scale of order 10(2)-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) ? 15 GeV.