In the minimal standard model (MSM) with three generations of quarks and leptons, neutrinos can have tiny charges consistent with electromagnetic gauge invariance. There are three types of nonstandard electric charge given by $Q_{\mathrm{st}}+\epsilon (L_i-L_j)$, where $i,j=e,\mu ,\tau$ ($i\ne j$), $Q_{\mathrm{st}}$ is the standard electric charge, $L_i$ is a family-lepton number, and $\epsilon$ is an arbitrary parameter which is put equal to zero in the usual incarnation of the MSM. These three nonstandard electric charges are of considerable theoretical interest because they are compatible with the MSM Lagrangian and ${\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}}_c\otimes {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\otimes {\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_Y$ gauge anomaly cancellation. The two most conspicuous implications of such nonstandard electric charges are the presence of two generations of massless charged neutrinos and a breakdown in electromagnetic universality for $e$, $\mu$, and $\tau$. We use results from (i) charge conservation in $\beta$ decay, (ii) the physical consequences of charged atoms in various contexts, (iii) the anomalous magnetic moments of charged leptons, (iv) neutrino-electron scattering, (v) energy loss in red giant and white dwarf stars, and (vi) limits on a cosmologically induced thermal photon mass, to place bounds on $\epsilon$. While the constraints derived for $\epsilon$ are rather severe in the $L_e-L_{\mu ,\tau }$ cases ($\left|\epsilon \right|<\mathrm{}{10}^{-17\mathrm{}}-{10}^{-21\mathrm{}}$), the $L_{\mu }-L_{\tau }$ case allows $\left|\epsilon \right|$ to be as large as about ${10}^{-14\mathrm{}}$.

• Received 27 May 1992

DOI:https://doi.org/10.1103/PhysRevD.46.R2764