Estimate of the branching fraction τ-→ηπ-ντ, the a0-(980), and nonstandard weak interactions

We consider the "second-class current" decay τ-→π- ηντ from several points of view. We first focus on the decay rate as expected within standard weak interaction and QCD due to isospin violation. The decay contributions divide into P- and S-wave parts. The former can be reliably estimated using the ρηπ coupling inferred from the rates and Dalitz-plot distributions of η→3π decays. The somewhat larger S-wave part, which was previously computed using chiral perturbation theory, is estimated from a simple q̄q model. Both estimates of the S-wave part depend on whether the a0(980) scalar particle is a q̄q or some other (4-quark) state. Finally, we discuss genuinely new, non-V-A scalar weak interactions. The τ-→π-ηντ decay provides information on this question, which nicely complements that from precision β decay experiments. In summary, we discuss the possible implications of putative values of the branching fraction B(τ-→π-ηντ). In the case of larger values, in particular, of the S-wave part, not only will detection of the decay be more likely and more reliable, its implications will be more far-reaching and interesting.