Intermediate Bosons and the Electromagnetic Field

Abstract

Possible symmetries between the (hypothetical) charged intermediate-boson field ${{W}_{\ensuremath{\nu}}}^{\ifmmode\pm\else\textpm\fi{}}$ and the derivative of the electromagnetic field $\frac{\ensuremath{\partial}{F}_{\ensuremath{\mu}\ensuremath{\nu}}}{\ensuremath{\partial}{x}_{\ensuremath{\nu}}}$ are investigated. We assume that (a) the total electromagnetic current operator ${{\mathcal{I}}_{\ensuremath{\nu}}}^{\ensuremath{\gamma}}={{e}_{0}}^{\ensuremath{-}1}(\frac{\ensuremath{\partial}{F}_{\ensuremath{\mu}\ensuremath{\nu}}}{\ensuremath{\partial}{x}_{\ensuremath{\nu}}})$ is proportional to a neutral member ${{W}_{\ensuremath{\nu}}}^{0}$ of the intermediate-boson fields, (b) all hadron mass differences between different members of the same isospin multiplet consist of finite $O({e}^{2})$ terms but no $O({f}^{2})$ terms, and (c) all known leptonic, semileptonic, and $\ensuremath{\Delta}S\ensuremath{\ne}0$ nonleptonic weak processes are transmitted by a single ${{W}_{\ensuremath{\nu}}}^{\ifmmode\pm\else\textpm\fi{}}$ field, where $f$, $e$, and ${e}_{0}$ are, respectively, the semiweak coupling constant, the renormalized charge, and the unrenormalized charge. The simplest model compatible with (a), (b), and (c) is found to be one consisting of six intermediate bosons, which may be regarded as forming an $S{U}_{3}$ triplet and its Hermitian conjugate. Assumption (a) also implies finite radiative corrections for other processes such as weak decays, charge renormalization, etc. The unrenormalized charge ${e}_{0}$ is shown to be finite, bounded by the inequality $1\ensuremath{\leqq}(\frac{{e}_{0}}{e})\ensuremath{\leqq}\sqrt{2}$. A lower limit of ${f}^{2}$ is established. Neglecting higher-order corrections, one finds this lower limit of ${f}^{2}$ to be $\frac{4}{3}{e}^{2}{sec}^{2}\ensuremath{\theta}$ and, in this limit, ${e}_{0}=\sqrt{2}e$ and $\frac{{m}_{W}}{{m}_{N}}\ensuremath{\cong}{\ensuremath{\alpha}}^{\ensuremath{-}1}$, where $\ensuremath{\alpha}$ is the fine structure constant, ${m}_{W}$ and ${m}_{N}$ are, respectively, the ${W}^{\ifmmode\pm\else\textpm\fi{}}$ mass and the nucleon mass, and $\ensuremath{\theta}$ is the Cabibbo angle. The same model can also lead, in a reasonably natural way, to $\mathrm{CP}$ nonconservation.