Structure of the vertex

The large data sample expected permits a detailed investigation of the structure of the vertex. The Michel parameter has been measured with a precision of 7%using the decay and 8%using the decay [71]. This is in sharp contrast to the precision of 0.3%in decay[42]. Current measurements of this quantity are limited by statistics. A large sample of events can be selected using a tag where the momentum of the lepton must be as low as practical for particle identification. We expect to achieve a precision comparable to that obtained in the decay. Unlike the decay, however, the two leptonic decay modes of the permit a test of lepton universality.

The measurement of the parameter consistent with 0.75 could still allow some admixture of , scalar, vector, or tensor interactions. The most general Hamiltonian for the four-fermion point interaction has ten complex coupling constants, corresponding to 19 independent parameters and an arbitrary phase. In contrast to the lepton where only the parameter has been measured, the weak couplings of the have been completely determined. It is not necessary to measure all 19 observables in order to determine the interaction. Fetscher, Gerber, and Johnson[72] have shown only five measurements are needed to describe the interaction:

• lifetime
• decay asymmetry parameters and
• polarization parameter
• inverse decay cross section for with of known helicity.

The lifetime measurement will be discussed in the next section. The decay asymmetry parameters and of the daughter lepton with respect to the spin direction of the parent lepton can be measured using the fact that the spin of the two produced in annihilation are strongly correlated[60]. The spin of the can be determined from the two-body decay modes. For example, if we assume a pure interaction in the decay , the is emitted preferentially parallel to the spin of the . The spin of the can be selected by requiring the momentum of the to be in the region corresponding to the being produced forward or backward in the center-of-mass of the . The polarization parameter measurement requires the analysis of the polarization of the daughter lepton which is not yet practical at any collider. The cross section for scattering is even less likely to be measured in the near future since direct scattering is yet to be observed. Fetscher[73] finds that , , , and even , the ``low energy parameter,'' can be measured to a statistical precision of a few percent with the data sample expected from CLEO III.