Abstract
We discuss sum-rule determinations of \alpha_sαs from non-strange hadronic \tauτ-decay data. We investigate, in particular, the reliability of the assumptions underlying the “truncated OPE strategy,” which specifies a certain treatment of non-perturbative contributions, and which was employed in Refs. . Here, we test this strategy by applying the strategy to the RR-ratio obtained from e^+e^-e+e− data, which extend beyond the \tauτ mass, and demonstrate that the assumptions underlying this strategy are not, in general, valid. We then present a brief overview of new results on the form of duality-violating non-perturbative contributions, which are conspicuously present in the experimentally determined spectral functions. As we show, with the current precision claimed for the extraction of \alpha_sαs, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.
Highlights
As is well known, the determination of αs from finite-energy sum-rule (FESR) analyses of hadronic τ-decay data provides one of the most precise determinations of αs
We have argued that the mass of the τ lepton is not high enough to be able to dismiss the duality violations (DVs) term (5) in the FESR (3) and that, because of that, one has to use a parametrization of the DV term which is physically sound, such as that given in Eq (6)
Attempts to work only at s0 = m2τ, assuming integrated DVs are negligible at this s0 for doubly and triply pinched weights, run into the problem that the number of Operator Product Expansion (OPE) parameters to be fit exceeds the number of spectral integrals available as input, unless, as in the truncated OPE strategy, one neglects sufficiently many higher-D OPE contributions present in the analysis
Summary
The determination of αs from finite-energy sum-rule (FESR) analyses of hadronic τ-decay data provides one of the most precise determinations of αs. Since the weights involved in these tests are doubly and/or triply pinched, and expected to have suppressed integrated DV contributions, especially above s0 = m2τ, the poor OPE-spectral integral matches imply a breakdown of the assumption that the OPE can be truncated as it would were the OPE a rapidly converging expansion up to at least D = 16 The consequences of this observation for τ-based analyses are (i) that the truncations in dimension of the OPE employed in the truncated OPE strategy are completely unsafe and (ii) that, in order to have fewer OPE parameters than spectral integrals required to fit them, one must consider spectral integrals involving whatever set of weights one is employing at s0 different from m2τ, which, for analyses of τ-decay data, means s0 < m2τ. Since quite sizeable DV oscillations about perturbation theory are observed in the spectral functions in this region, even when one considers the ud V +A sum, it becomes important to use some representation of DV contributions to estimate the impact of possible residual DV effects, even in FESRs involving doubly and triply pinched weights
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