Longitudinal contributions to hadronic tau decay - art. no. 093014

A number of recent determinations of m(S) using hadronic tau decay data inv olve inclusive analyses based on the so-called (k,0) spectral weights. We s how here that the OPE representations of the longitudinal contributions app earing in these analyses, which are already known to be poorly converging, have in addition an unphysical k dependence that produces a significant unp hysical decrease in m(S) with increasing k. We also show how, using additio nal sum rule constraints, the decay constants of the excited resonances in the strange scalar and pseudoscalar channels may be determined, allowing on e to evaluate the longitudinal spectral contributions to the (k,0) sum rule s. Taking into account the very accurately known pi and K pole contribution s, we find that longitudinal contributions can be determined with an accura cy at the few percent level, and hence reliably subtracted, leaving an anal ysis for m(S) involving the sum of longitudinal and transverse contribution s, for which the OPE representation is much better converged.