Longitudinal contributions to hadronic τ decay

Abstract

A number of recent determinations of ms using hadronic τ decay data involve inclusive analyses based on the so-called (k,0) spectral weights. We show here that the OPE representations of the longitudinal contributions appearing in these analyses, which are already known to be poorly converging, have in addition an unphysical k dependence that produces a significant unphysical decrease in ms with increasing k. We also show how, using additional sum rule constraints, the decay constants of the excited resonances in the strange scalar and pseudoscalar channels may be determined, allowing one to evaluate the longitudinal spectral contributions to the (k,0) sum rules. Taking into account the very accurately known π and K pole contributions, we find that longitudinal contributions can be determined with an accuracy at the few percent level, and hence reliably subtracted, leaving an analysis for ms involving the sum of longitudinal and transverse contributions, for which the OPE representation is much better converged.