$E_6$ Models in Light of Precision $M_W$ Measurements

We propose a solution to the recent $W$ mass measurement by embedding the Standard Model within $E_6$ models. The presence of a new $U(1)$ group shifts the $W$ boson mass at the tree level and introduces a new gauge boson $Z^{\mathrm{\prime }}$ which has been searched for at collider experiments. In this article, we identity the parameter space that explains the new $W$ mass measurement and is consistent with current experimental $Z^{\mathrm{\prime }}$ searches. As $U(1)$ extensions can be accommodated in supersymmetric models, we also consider the supersymmetric scenario of $E_6$ models, and show that a 125 GeV Higgs may be easily achieved in such settings.