Quark-loop anomalies and the SU(4) mixing angles

Abstract

Three mixing angles are used to describe the mixing of the three isoscalar mesons assigned to the $15\ensuremath{\bigoplus}1$ representation of SU(4). The formalism is applied to the pseudoscalar ($P$), vector ($V$), and tensor ($T$) multiplets, the mixing angles being determined for both linear and quadratic mass formulas. The mixing angles can also be independently determined from decay rates. To reduce the number of parameters involved, the effective $\mathrm{PVV}$, $\mathrm{PV}\ensuremath{\gamma}$, and $P\ensuremath{\gamma}\ensuremath{\gamma}$ interactions are derived from the $\mathrm{VPP}$ interaction using anomalies in the partial conservation of the axial-vector current. The $\mathrm{VVV}$ vertex is also incorporated without introducing an additional parameter since a U(4) Yang-Mills effective Lagrangian is used. The mixing angles so determined in the case of the vectors and the pseudoscalars are used to reduce from five to two the number of parameters in the mass matrix. By fitting the remaining parameters to the observed masses it is found that the quadratic mass formula is strongly favored in both cases.