July 1997 PAR-LPTHE 97/32 AN ELECTROWEAK SU(2)L × U(1) GAUGE THEORY OF J = 0 MESONS.

Universités Pierre et Marie Curie (Paris 6) et Denis Diderot (Paris 7); Unité associée au CNRS URA 280. Extended version of the talk " Custodial symmetry in a SU (2) L × U (1) gauge theory of J = 0 mesons " given at the 2 Abstract: I display all J = 0 scalar and pseudoscalar representations of the standard SU (2) L × U (1) group of electroweak interactions which transform like sets of fermion-antifermion composite fields. They can fit into quadruplets of definite CP quantum numbers. SU (2) L × U (1) is embedded in a natural way, compatible with the Glashow-Salam-Weinberg model for quarks, into the chiral group U (N) L ×U (N) R , N being the (even) number of " flavours ". It involves a unitary N/2×N/2 " mixing matrix " for fermions which are however only considered here as mathematical objects in the fundamental representation of U (N). The electroweak gauge Lagrangian for the J = 0 particles exhibits a chiral SU (2) L × SU (2) R symmetry at the limit when the hypercharge coupling g ′ goes to zero. It is spontaneously broken down to its diagonal SU (2) V subgroup, which includes the electromagnetic U (1), spanning a bridge to an explanation of electric charge quantization. Chiral are electroweak spontaneous breaking are identical. The consequences for the nature of the Goldstone bosons are examined. 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. SU (2) L × U (1) allows one mass scale per quadruplet; as each decomposes into one triplet and one singlet of SU (2) V , the custodial symmetry doubles the amount of masses allowed for the 2N 2 mesons, from N 2 /2 to N 2. They bear no special connection with the nature of their " fermionic content " and share 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 just appears to be the consequence of 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 …