Eur. Phys. J. C (2022) 82: 1135
https://doi.org/10.1140/epjc/s10052-022-11051-z

Regular Article - Theoretical Physics

The CDF W-mass, muon $g-2$, and dark matter in a $U{(1)}_{L_{\mu }-L_{\tau }}$ model with vector-like leptons

Department of Physics, Yantai University, 264005, Yantai, People’s Republic of China

^c leiwang@ytu.edu.cn

Received: 3 May 2022
Accepted: 18 November 2022
Published online: 15 December 2022

Abstract

We study the CDF W-mass, muon $g-2$, and dark matter observables in a local $U{(1)}_{L_{\mu }-L_{\tau }}$ model in which the new particles include three vector-like leptons ($E_1,E_2,N$), a new gauge boson $Z^{\prime }$, a scalar S (breaking $U{(1)}_{L_{\mu }-L_{\tau }}$), a scalar dark matter $X_I$ and its partner $X_R$. We find that the CDF W-mass disfavors $m_{E_1}=m_{E_2}=m_N$ or $s_L=s_R=0$ where $s_{L(R)}$ is mixing parameter of left (right)-handed fields of vector-like leptons. A large mass splitting between $E_1$ and $E_2$ is favored when the differences between $s_L$ and $s_R$ becomes small. The muon $g-2$ anomaly can be simultaneously explained for appropriate difference between $m_{E_1}$$(s_L)$ and $m_{E_2}$$(s_R)$, and some regions are excluded by the diphoton signal data of the 125 GeV Higgs. Combined with the CDF W-mass, muon $g-2$ anomaly and other relevant constraints, the correct dark matter relic density is mainly obtained in two different scenarios: (i) $X_I{X}_I\to Z^{\prime }{Z}^{\prime },SS$ for $m_{Z^{\prime }}(m_S)<m_{X_I}$ and (ii) the co-annihilation processes for $min(m_{E_1},m_{E_2},m_N,m_{X_R})$ close to $m_{X_I}$. Finally, we use the direct searches for $2\ell +E_T^{\mathit{miss}}$ event at the LHC to constrain the model, and show the allowed mass ranges of the vector-like leptons and dark matter.