Mixing between ordinary and exotic fermions

The results of a comprehensive analysis of the limits on mixings between ordinary fermions and possible heavy fermions with exotic SU(2)×U(1) assignments (e.g., left-handed singlets and/or right-handed doublets) are presented. A general formalism for describing such mixings is given. It is shown that a variety of constraints, including the relation between the W and Z masses and the Fermi constant, charged-current universality, limits on induced right-handed charged currents, and flavor-diagonal neutral currents suffice to limit all directions in parameter space that are not excluded by the absence of flavor-changing neutral currents. Limits on $s^2$, the square of the mixing between ordinary and exotic fermions, are quite stringent for the ${\nu }_{\mu L}$, ${\mu }_L^{\mathrm{-}}$, $u_L$, and $d_L$ ($s^2$≤0.002–0.005) if only one particle is allowed to mix at a time, but are weaker by an order of magnitude if fine-tuned cancellations between different mixings are allowed. Similar statements apply to quark mixings with heavy sequential doublets. Limits on $s^2$ for the other light fermions (${\nu }_{\mathrm{eL}}$, ${\mathit{e}}_{\mathit{L}}^{\mathrm{-}}$,${\mathit{e}}_{\mathit{R}}^{\mathrm{-}}$,${\mathrm{\mu }}_{\mathit{R}}^{\mathrm{-}}$, ${\mathit{u}}_{\mathit{R}}$,${\mathit{d}}_{\mathit{R}}$) are in the range 0.02–0.06, while those for the s, c, b, ${\nu }_{\tau }$, and ${\tau }^{\mathrm{-}}$ are considerably weaker. Slightly stronger limits are found in specific models (e.g., ${\mathrm{E}}_6$). Implications for the masses of the heavy exotic fermions are discussed.