Explaining the CDF-II W-boson mass anomaly in the Georgi–Machacek extension models

Abstract

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 1sigma 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 10^2–10^4 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 1sigma 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.