Bounds on mixing between light and heavy gauge bosons

Abstract

Upper bounds are derived for the mixing between light and heavy gauge bosons in terms of the closeness of the observed $W$ or $Z$ mass to the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) prediction ${m}_{0}$. The mixing angles between light and heavy bosons with masses ${m}_{1}$ and ${m}_{2}$, respectively, are less than ${[\frac{({{m}_{0}}^{2}\ensuremath{-}{{m}_{1}}^{2})}{({{m}_{2}}^{2}\ensuremath{-}{{m}_{0}}^{2})}]}^{\frac{1}{2}}$. Existing data imply a limit of \ensuremath{\lesssim} 0.04 for the mixing angle between the $W$ and a 1-TeV heavy boson. A similar result holds for the $Z$ if there are no Higgs multiplets with $Ig\frac{1}{2}$ with significant vacuum expectation values.