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

Abstract

We study the CDF W-mass, muon $$g-2$$ g - 2 , and dark matter observables in a local $$U(1)_{L_\mu -L_\tau }$$ U ( 1 ) L μ - L τ model in which the new particles include three vector-like leptons ($$E_1,~ E_2,~ N$$ E 1 , E 2 , N ), a new gauge boson $$Z'$$ Z ′ , a scalar S (breaking $$U(1)_{L_\mu -L_\tau }$$ U ( 1 ) L μ - L τ ), a scalar dark matter $$X_I$$ X I and its partner $$X_R$$ X R . We find that the CDF W-mass disfavors $$m_{E_1}= m_{E_2}={m_N}$$ m E 1 = m E 2 = m N or $$s_L=s_R=0$$ s L = s R = 0 where $$s_{L(R)}$$ s L ( R ) is mixing parameter of left (right)-handed fields of vector-like leptons. A large mass splitting between $$E_1$$ E 1 and $$E_2$$ E 2 is favored when the differences between $$s_L$$ s L and $$s_R$$ s R becomes small. The muon $$g-2$$ g - 2 anomaly can be simultaneously explained for appropriate difference between $$m_{E_1}$$ m E 1 $$(s_L)$$ ( s L ) and $$m_{E_2}$$ m E 2 $$(s_R)$$ ( s R ) , and some regions are excluded by the diphoton signal data of the 125 GeV Higgs. Combined with the CDF W-mass, muon $$g-2$$ g - 2 anomaly and other relevant constraints, the correct dark matter relic density is mainly obtained in two different scenarios: (i) $$X_IX_I\rightarrow Z'Z',~ SS$$ X I X I → Z ′ Z ′ , S S for $$m_{Z'}(m_S)<m_{X_I}$$ m Z ′ ( m S ) < m X I and (ii) the co-annihilation processes for $$min(m_{E_1},m_{E_2},m_N,m_{X_R})$$ m i n ( m E 1 , m E 2 , m N , m X R ) close to $$m_{X_I}$$ m X I . Finally, we use the direct searches for $$2\ell +E_T^{miss}$$ 2 ℓ + E T miss event at the LHC to constrain the model, and show the allowed mass ranges of the vector-like leptons and dark matter.