The partial width is then given by^ r(7]' -rj TTTT) = 3|M| 2 [1 + 0.24a + 0.21a^] = 210keV.(10)We thus find a width enhanced by almost a factor of 70 from the naive current-algebra result.The dominant contribution to the decay rate arises from 6 while the € term yields the correct slope. To summarize our results, the inclusion of 6 and e resonances satisfactorily accounts for the slope parameter and the decay rate for ?]'•* 177777. The reason for no deviation from background in the rjir distribution and the absence of Adler zero are understood from the accidental cancellation of the zero with the 6 pole term. (1975). ^The solution B =-A/m^^ =C/2, D ^E =0 yields the Schwinger model; see J, Schwinger, Phys. Rev, 167^ 1432Rev, 167^ (1968, This model predicts a large slope a w -0.44. With the value of A given in Eq, (3) and with C arbitrary, a large slope is required to increase the theoretical estimate, as discussed in Refs. 3 and 4, ^The effect of scalar mesons 6 and e on the 77' decay was first considered in an effective-Lagragian framework by J. Schechter and Y" Ueda, Phys, Rev, D ^, 2874 (1971), and^, 987 (1973. The main difference between that work and the present approach involves the use of derivative couplings and the numerical estimates of the coupling constants.^An attempt to resolve the 7j'-*r)Tnr puzzle by considering a purely phenomenogical amplitude dominated by the 6 pole was made by C. Singh and J, Pasupathy, Phys. Rev. Lett. 35, 1193Lett. 35, (1975, Their amplitude does not manifestly satisfy the current-algebra constraints, and consequently predicts enhancement in the rj-ir distribution at large invariant mass, a feature totally absent from the data (see Ref. 1), ^H, Osborn and D, J. Wallace, Nucl, Phys. B20, 23 (1970).We present a set of rotationally invariant observables which characterizes the ' * shapes'* of events, and is calculable in quantum-chromod5niamics perturbation theory for final states consisting of quarks and gluons (G), We include the effects of fragmentation to hadrons in comparing the shapes of events from the processes e^e' -*qq^ e^e'-*qqG^ and e^e' -* heavy resonance"* GGG^ and from heavy-quark and lepton production. We indicate how our analysis may be extended to deep-elastic lepton-hadron interactions and hadronhadron collisions involving large transverse momenta.
