Problems with extracting ms from flavor breaking in hadronic τ decays

Abstract

A numerical error is pointed out in the existing expression for the O(αs²) longitudinal component of the squared-mass (D=2) contribution to the hadronic τ decay rate. The corrected version is found to be such that, to O(αs²), each term in the resulting series is larger than the previous one, hence ruling out the direct use of flavor breaking in hadronic τ decays as a means of extracting the strange quark mass. An alternate approach, in which one uses the model spectral functions previously developed for the strangeness-changing scalar channel (and employed in alternate sum rule analyses of ms) as input to the τ decay analysis, is shown to provide mutual consistency checks for the two different methods. The results for ms implied by τ decay data and the existing model spectral function are also presented.