Strong coupling from the revised ALEPH data for hadronicτdecays

Abstract

We apply an analysis method previously developed for the extraction of the strong coupling from the OPAL data to the recently revised ALEPH data for nonstrange hadronic τ decays. Our analysis yields the values α s (m 2 τ ) = 0.296±0.010 using fixed-order perturbation theory, and α s (m 2 τ ) = 0.310±0.014 using contourimproved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find α s (m 2 τ ) = 0.303 ± 0.009, respectively, α s (m 2 τ ) = 0.319 ± 0.012. We present a critique of the analysis method employed previously, for example in analyses by the ALEPH and OPAL collaborations, and compare it with our own approach. Our conclusion is that non-perturbative effects limit the accuracy with which the strong coupling, an inherently perturbative quantity, can be extracted at energies as low as the τ mass. Our results further indicate that systematic errors on the determination of the strong coupling from analyses of hadronic τ -decay data have been underestimated in much of the existing literature.

Low-energy constants and condensates from ALEPH hadronicτdecay data

“…[22], and it was shown in Refs. [4,5] that this model can be used to successfully parametrize the resonance structure in the data for s ∼ > 1. In what follows we will denote by Π A , Π …”

“…(2.4), using the values of the DV parameters obtained from the fits to these same data, described in Ref. [4]. In addition, one needs the experimental values of m π , f π , 4 m K and f K .…”

“…That implies that even if these OPE contributions are not very well known, and one has therefore to include very conservative estimates of their errors in the total error budget, the impact on our final errors is minor. 4 Our normalization is such that f π = 92.21 (14) MeV. 5 See, in particular, Sec.…”

“…Above the τ mass one needs a theoretical representation, and we will use the one obtained in Ref. [4].…”

“…1 In Ref. [4] we analyzed these data in order to extract the strong coupling at the τ mass, α s (m 2 τ ), as well as OPE condensates, following the strategy previously developed in Refs. [5,6].…”