Melosh symmetries of vector-meson decays and a criterion for rapid convergence of semilocal averages

The rapid t = 0 convergence of the classic superconvergence relation rhoπ → rhoπ and its SU(6) generalizations VM → VM (V = vector nonet, M = pseudoscalar or vector nonet) is reexamined. It is suggested that the rapid convergence is due to a zero of the amplitude in t (crossed-channel energy) rather than the rapid falloff of the amplitude with s (''superconvergence'' in s), as is usually assumed. In a separate investigation involving only symmetry arguments, we find that the Melosh-transform parameterization for decays to VV states involves only two undetermined scalar couplings, rather than the four (six) required in related processes involving vector particles, B* → Bγ (B* → BV) decays, where B is a decuplet or octuplet baryon. A critical discussion is given of the Gilman-Kugler-Meshkov and related prescriptions used to correct SU(6) -symmetric couplings for the effects of mass splitting