Unified Lepton-Hadron Symmetry and a Gauge Theory of the Basic Interactions

Abstract

An attempt is made to unify the fundamental hadrons and leptons into a common irreducible representation $F$ of the same symmetry group $G$ and to generate a gauge theory of strong, electromagnetic, and weak interactions. Based on certain constraints from the hadronic side, it is proposed that the group $G$ is SU(4\ensuremath{'}) \ifmmode\times\else\texttimes\fi{} SU(4\ensuremath{''}), which contains a Han-Nambu-type SU(3\ensuremath{'}) \ifmmode\times\else\texttimes\fi{} SU(3\ensuremath{''}) group for the hadronic symmetry, and that the representation $F$ is (4,4*). There exist four possible choices for the lepton number $L$ and accordingly four possible assignments of the hadrons and leptons within the (4,4*). Two of these require nine Han-Nambu-type quarks, three "charmed" quarks, and the observed quartet of leptons. The other two also require the nine Han-Nambu quarks, plus heavy leptons in addition to observed leptons and only one or no "charmed" quark. One of the above four assignments is found to be suitable to generate a gauge theory of the weak, electromagnetic, and SU(3\ensuremath{''}) gluonlike strong interactions from a selection of the gauges permitted by the model. The resulting gauge symmetry is $\mathrm{SU}{({2}^{\ensuremath{'}})}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{({3}^{\ensuremath{'}\ensuremath{'}})}_{L+R}$. The scheme of all three interactions is found to be free from Adler-Bell-Jackiw anomalies. The normal strong interactions arise effectively as a consequence of the strong gauges $\mathrm{SU}{({3}^{\ensuremath{'}\ensuremath{'}})}_{L+R}$. Masses for the gauge bosons and fermions are generated suitably by a set of 14 complex Higgs fields. The neutral neutrino and $\ensuremath{\Delta}S=0$ hadron currents have essentially the same strength in the present model as in other $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ theories. The mixing of strong- and weak-gauge bosons (a necessary feature of the model) leads to parity-violating nonleptonic amplitudes, which may be observable depending upon the strength of SU(3\ensuremath{''}) symmetry breaking. The familiar hadron symmetries such as SU(3\ensuremath{'}) and chiral $\mathrm{SU}{({3}^{\ensuremath{'}})}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{({3}^{\ensuremath{'}})}_{R}$ are broken only by quark mass terms and by the electromagnetic and weak interactions, not by the strong interactions. The difficulties associated with generating gauge interactions in the remaining three assignments are discussed in Appendix A. Certain remarks are made on the question of proton and quark stability in these three schemes.