Is it possible to explain the muon and electron <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> in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>Z</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> model?
A. E. Cárcamo Hernández, Stephen F. King, H. Lee, Samuel J. Rowley
Abstract
In order to address this question, we consider a simple renormalizable and gauge invariant model in which the ${Z}^{\ensuremath{'}}$ only has couplings to the electron and muon and their associated neutrinos, arising from mixing with a heavy vectorlike fourth family of leptons. Within this model we discuss the contributions to the electron and muon anomalous magnetic moments from ${Z}^{\ensuremath{'}}$ exchange, subject to the constraints from $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and neutrino trident production. Using analytic and numerical arguments, we find that such a ${Z}^{\ensuremath{'}}$ model can account for either the electron or the muon $g\ensuremath{-}2$ anomalies, but not both, while remaining consistent with the experimental constraints from $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and neutrino trident production.