<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>D</mml:mi></mml:msub></mml:math> lepton portals for the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-boson mass, and dark matter
Seong-Sik Kim, Hyun Min Lee, Adriana G. Menkara, Kimiko Yamashita
Abstract
We propose a novel model for lepton flavor and dark matter based on the $SU(2{)}_{D}$ gauge symmetry and vectorlike leptons in its fundamental representations. We introduce a dark $SU(2{)}_{D}$ Higgs doublet and a Higgs bidoublet for the mass mixing between the vectorlike lepton and the lepton. As a result, the seesaw lepton masses are generated and there are sizable one-loop contributions to the muon $g\ensuremath{-}2$ via the $SU(2{)}_{D}$ gauge bosons and the relatively heavy vectorlike lepton, as indicated in Fermilab E989. The tree-level mass mixing between the $Z$ boson and the isospin-neutral gauge boson of $SU(2{)}_{D}$ in our model accounts for the shift in the $W$ boson mass, being consistent with Tevatron CDFII. Finally, we show that the isospin charged gauge boson of $SU(2{)}_{D}$ becomes a plausible candidate for dark matter with a small mass splitting tied up to the modified $W$ boson mass, and there is a viable parameter space where the favored corrections to the muon $g\ensuremath{-}2$ and the $W$ boson mass and the dark matter constraints are simultaneously fulfilled.