A model of vector-like leptons for the muon $$g-2$$ and the W boson mass

Abstract

Abstract We consider a simple extension of the Standard Model (SM) with a vector-like lepton and a local $$U(1)'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> symmetry, motivated by the recent experimental anomalies in the muon $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> and the W boson mass. The $$U(1)'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> symmetry is spontaneously broken by the VEVs of the dark Higgs scalar and the second Higgs doublet, giving rise to the mixing between the muon and the vector-like lepton. As a result, we obtain the desirable corrections to the muon $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> and the W boson mass simultaneously, dominantly due to the $$Z'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> gauge interactions for the vector-like lepton and the second Higgs doublet, respectively. We also discuss the consistency of the model with the Z boson decay width, the Higgs couplings and the dilepton bounds.