An electroweak SU(2)left x U(1) gauge theory of J=0 mesons

Abstract

I build a SU(2)left x U(1) electroweak gauge theory of J=0 mesons, which transform like sets of fermion-antifermion composite fields. SU(2)left x U(1) is embedded in a natural way, compatible with the Glashow-Salam-Weinberg model for quarks, into the chiral group U(N)left x U(N)right, N being the (even) number of ``flavours''. The Lagrangian exhibits a chiral SU(2)left x SU(2)right symmetry at the limit when the hypercharge coupling g' goes to zero. It is spontaneously broken down to its diagonal SU(2)v subgroup; as the latter includes the U(1) group of electromagnetism, this provides an explanation for the quantization of the electric charge. Comparison with recent works by Cho et al. unraveling dyon-like solution is an electroweak model with the same structure suggests that electric-magnetic duality may be realized here, with the occurrence of a strongly interacting sector. Chiral are electroweak spontaneous breaking are identical. Consequences for the nature of the Goldstone bosons are examined. The mass spectrum is analysed. It bears no special connection with the nature of the ``fermionic content'' of the mesons and shares with the leptonic sector the same arbitrariness. No information on the mass of the Higgs boson can be expected without additional input. New results about CP violation are obtained: ``indirect'' CP violation appears to results from P violation (unitarity compels the electroweak mass eigenstates to be C eigenstates), and the role of the Kobayashi-Maskawa mixing matrix for fermions fades away: mesonic mass eigenstates can still be CP eigenstates despite the presence of a complex phase. I briefly show how the customary results for the leptonic decays of pseudoscalar mesons are recovered. The extension to leptons is discussed.