Composite quarks and leptons from restricted anomaly matching

Abstract

A composite model based on the unique and simple solution $\mathrm{SU}{(3)}_{\mathrm{HC}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(6)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(6)}_{R}$ (HC denotes hypercolor) of a restricted 't Hooft anomaly-matching program is systematically analyzed. Particular emphasis is placed on implementing the idea that not only fermions but also Higgs scalars should be composite. The composite fermions remaining massless on the level of the physically appealing gauged subgroup $\mathrm{SU}{(3)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{B\ensuremath{-}L}$ of $\mathrm{SU}{(6)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(6)}_{R}$ are identified as conventional quarks and leptons as well as color-sextet quarks and color-singlet pointlike baryons. The other composite fermions can be shown to become massive in a most economical fashion by participating in dynamical Higgs condensates which effect the required spontaneous symmetry breaking. It is speculated how a second step of dynamical symmetry breaking down to $\mathrm{SU}{(3)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{\mathrm{EM}}$ could be achieved with only massless quarks and leptons surviving. A second embedding of $\mathrm{SU}{(3)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ into $\mathrm{SU}{(6)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(6)}_{R}$ is shown to lead to Harari and Seiberg's rishons with a $\mathrm{U}{(1)}_{B\ensuremath{-}L}$ charge only. Our whole analysis illustrates a general procedure proposed for relating a given solution of 't Hooft's program to physical reality at present energies.