Eur. Phys. J. C (2023) 83: 139
https://doi.org/10.1140/epjc/s10052-023-11297-1

Regular Article - Theoretical Physics

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

¹ School of Physics, Zhengzhou University, 450000, Zhengzhou, People’s Republic of China
² Institute of Physics, Henan Academy of Sciences, 450046, Zhengzhou, People’s Republic of China

^c feiwang@zzu.edu.cn

Received: 25 June 2022
Accepted: 6 February 2023
Published online: 11 February 2023

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 $\mathrm{\Delta }{m}_W$ are always very small. Our numerical results show that ordinary GM model can contribute to $\mathrm{\Delta }{m}_W$ 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 $\mathrm{\Delta }{m}_W$, which can give large new physics contributions to $\mathrm{\Delta }{m}_W$. Such slightly misaligned triplet VEVs from custodial symmetry preserving scalar potential can still be allowed. Our numerical results indicate that the resulting $\mathrm{\Delta }{m}_W$ can easily reach the $1\sigma$ range of CDF-II $m_W$ data and the splitting among the triplet VEVs $\mathrm{\Delta }v$($\equiv v_{\xi }-v_{\chi }$) 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 $h_{\mathit{ij}}$ 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 $\mathrm{\Delta }{m}_W$ 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 $h_{\mathit{ij}}$ couplings allowed with RH neutrino sector, the value of $\mathrm{\Delta }{m}_W$ 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.