${\mathrm{E}}_6$ interpretation of an $e^{+}{e}^{-}\gamma \gamma E_T$ event

The lowest-dimensional representation of the group E${}_6$ contains both the standard quarks and leptons and a set of exotic quarks and leptons whose decays can involve a series of chains ending in radiative decay of one light neutrino species into another. An example is given based on the decomposition E${}_6\to$ SU(2)${}_I\times \mathrm{SU}\left(6\right)\mathrm{}$, where SU(2)${}_I$ is an “inert” subgroup whose gauge bosons $W_I^{(\pm )}$ and $Z_I$ are all electromagnetically neutral, while SU(6) contains the conventional SU(5) grand-unified group. The possibility is explored that such a chain is responsible for an event observed by the Collider Detector at Fermilab involving the production in proton-antiproton collisions at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=1.8\mathrm{}$ TeV of an electron-positron pair, two photons, and missing energy ${(e}^{+}{e}^{-}\gamma \gamma E_T)$.