SU(5) × U(1) phenomenology: Theorems on neutral-current analysis

We embed the SU(5) unified theory of Georgi and Glashow in a U(5) theory. This may result from the breaking of an $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$, $N>\mathrm{}5\mathrm{}$, theory or of a GL(5,$c$) theory. At low energy this leads to an SU(2) × U(1) × U(1) electroweak theory. We show that, with a suitable choice of Higgs representations, the predictions of this theory for neutral-current experiments are characterized by three parameters. For appropriate values of these parameters, the predictions are practically indistinguishable from the standard SU(2) × U(1) theory. Certain theorems on the analysis of neutral-current interactions are proved. (Section V is independent for readers who are interested only in the theorems.) More accurate neutral-current measurement might answer the question of whether SU(5) × U(1) is relevant. Possible verification of the present electroweak theory can result from (roughly) an order suppression relative to the standard prediction on the asymmetries in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ and discovery of two $Z$ bosons around 90-100 GeV. $\mathrm{GL}\mathrm{}(n,c)\mathrm{}$ gauge theories are formulated in the Appendix.