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

Abstract

Abstract Original Georgi–Machacek model can preserve the custodial symmetry at tree level after the electroweak symmetry breaking. Unless additional $$SU(2)_c$$ S U ( 2 ) c custodial symmetry breaking effects are significant, the new physics contributions to $$\Delta m_W$$ Δ m W are always very small. Our numerical results show that ordinary GM model can contribute to $$\Delta m_W$$ Δ 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 $$\Delta m_W$$ Δ m W , which can give large new physics contributions to $$\Delta m_W$$ Δ m W . Such slightly misaligned triplet VEVs from custodial symmetry preserving scalar potential can still be allowed. Our numerical results indicate that the resulting $$\Delta m_W$$ Δ m W can easily reach the $$1\sigma $$ 1 σ range of CDF-II $$m_W$$ m W data and the splitting among the triplet VEVs $$\Delta v$$ Δ v ( $$\equiv v_\xi -v_\chi $$ ≡ v ξ - v χ ) can be as small as 0.8 GeV for $$v_\chi \lesssim 15$$ v χ ≲ 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 $$h_{ij}$$ h ij even for triplet VEVs of order GeV. With low scale RH neutrino mass scale of order $$10^2$$ 10 2 – $$10^4$$ 10 4 TeV, the new physics contribution to $$\Delta m_W$$ Δ m W can reach 0.03 GeV and is much larger than that of ordinary GM model. Combining both custodial $$SU(2)_c$$ S U ( 2 ) c symmetry breaking effects, the small misalignment among the triplet VEVs and the moderately large $$h_{ij}$$ h ij couplings allowed with RH neutrino sector, the value of $$\Delta m_W$$ Δ m W can still easily reach the $$1\sigma $$ 1 σ range of CDF-II $$m_W$$ m W data, with a minimum splitting (among the triplet VEVs) approximately 0.7 GeV for $$v_\chi \lesssim 15$$ v χ ≲ 15 GeV.