SU(2)×U(1) vectorlike model: New leptons, quarks, and the axion question

We present a detailed study of an SU(2)×U(1) gauge theory of the weak and electromagnetic interactions in which parity is broken spontaneously. A global, chiral U(1) symmetry is incorporated in order to avoid a zeroth-order neutrino mass. We investigate an eight-quark scheme and two different lepton assignments, each of which produces almost pure vector coupling of the electron to the weak neutral current. One lepton assignment leads to a calculable neutrino mass, while the other one leads to calculable electron and neutrino masses. There are heavy leptons in the models whose masses are mildly constrained by the bound on the electron-neutrino mass. The neutrino-mass limit and the interpretation of the $\Upsilon$ as a bound state of a heavy right-handed quark require that the expectation value of a "left" Higgs doublet be small compared to that of a "right" Higgs doublet. Because of the global U(1) symmetry, if one or more extra Higgs particles and/or quark singlets are added then an axion can be present. The conditions under which an axion appears are sketched, and its couplings and mass are less restricted than those discussed by other authors. Alternatively, a soft breaking of the U(1) symmetry can be introduced to avoid a Goldstone boson and to insure that both Higgs doublets have nonzero vacuum expectation values. Suppression of strong $\mathrm{CP}$ violation can be naturally achieved in this case, and the axion is not present. Both the axion and the soft-breaking possibilities are discussed.