$W$ mass in a model with vectorlike leptons and $U(1{)}^{\prime }$

We study the effects of vectorlike leptons on the $W$-boson mass in a model with a vectorlike $U(1{)}^{\prime }$ gauge symmetry. This model provides simultaneous explanations for the recent anomalies in the muon anomalous magnetic moment and the semileptonic decays of $B$ mesons. We find that the recent result of the $W$-boson mass’s precise measurement at CDF can be explained if the charged (neutral) vectorlike lepton is lighter than 250 (80) GeV. The light vectorlike leptons may not be excluded by collider experiments if these decay to a physical mode of the $U(1{)}^{\prime }$-breaking scalar field.

Figure 1

Scattering plots on the observables in our analysis. The cross and circle points are $100<m_{E_1}<175\mathrm{GeV}$ and $m_{E_1}>175\mathrm{GeV}$, respectively. All the points explain the $m_W$ and $\mathrm{\Delta }{a}_{\mu }$ within $1\sigma$. The error bars in the left panel are the $1\sigma$ uncertainties, and the dashed horizontal line in the right panel is the 95% C.L. limit on $R_{\mathrm{CCFR}}$. The central value of $R_{\gamma \gamma }=1.10$ is outside of the figure. The benchmark points (A), (B), (C), and (D) lie on top of each other in the left panel.

Figure 2

Scattering plots on the Yukawa couplings $({\lambda }_e^{\prime },{\lambda }_n^{\prime })$ and the VL lepton masses $(m_{E_1},m_{N_1})$. The cross and circle points are $100<m_{E_1}<175\mathrm{GeV}$ and $m_{E_1}>175\mathrm{GeV}$, respectively.

Figure 3

Scattering plots on the masses of the $Z^{\prime }$ boson and the VL leptons. The cross and circle points are $100<m_{E_1}<175\mathrm{GeV}$ and $m_{E_1}>175\mathrm{GeV}$, respectively. The diagonal lines are $m_{Z^{\prime }}=m_{E_1}$ and $m_{\chi }=m_{E_1}$ in the left and right panels, respectively.

Figure 4

Scattering plots on the oblique parameters. The cross and circle points are $100<m_{E_1}<175\mathrm{GeV}$ and $m_{E_1}>175\mathrm{GeV}$, respectively. The solid (dashed) lines are the $1\sigma$ ($2\sigma$) range of the $W$-boson mass measured by the CDF for $U=0$ and $S=0$ in the left and right panels, respectively.