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Hadronic $tau$ decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic $tau$ decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong coupling constant, quark and gluon condensates. Using the ALEPH spectral functions and branching ratios, complemented by some other available measurements, and a revisited analysis of the theoretical framework, the value $asm = 0.345 pm 0.004_{rm exp} pm 0.009_{rm th}$ is obtained. Taken together with the determination of asZ from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of $alpha_s^{-1}(s)$ is found to agree with QCD at a precision of 4%. The value of asZ obtained from $tau$ decays is $asZ = 0.1215 pm 0.0004_{rm exp} pm 0.0010_{rm th} pm 0.0005_{rm evol} = 0.1215 pm 0.0012$.
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An update of the ALEPH non-strange spectral functions from hadronic $tau$ decays is presented. Compared to the 2005 ALEPH publication, the main improvement is related to the use of a new method to unfold the measured mass spectra from detector effects. This procedure also corrects a previous problem in the correlations between the unfolded mass bins. Results from QCD studies and for the evaluation of the hadronic vacuum polarisation contribution to the anomalous muon magnetic moment are derived using the new spectral functions. They are found in agreement with published results based on the previous set of spectral functions.
We present a new analysis of $alpha_s$ from hadronic $tau$ decays based on the recently revised ALEPH data. The analysis is based on a strategy which we previously applied to the OPAL data. We critically compare our strategy to the one traditionally used and comment on the main differences. Our analysis yields the values $alpha_s(m_tau^2)=0.296pm 0.010$ using fixed-order perturbation theory, and $alpha_s(m_tau^2)=0.310pm 0.014$ using contour-improved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find $alpha_s(m_tau^2)=0.303pm 0.009$, respectively, $alpha_s(m_tau^2)=0.319pm 0.012$, as the most reliable results for $alpha_s$ from $tau$ decays currently available.
We summarize a comparison of the two strategies which are currently available in the literature for determining the value of $alpha_s(m_tau)$. We will refer to these as the truncated Operator Product Expansion model and the Duality Violation model. After describing the main features of both approaches, we explain why the former fails to pass crucial tests. The latter, on the other hand, passes all the tests known up to date and, therefore, should be currently considered the only reliable method.
The Quantum Chromodynamics (QCD) coupling, $alpha_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by $hatalpha_s$, whose running is explicitly renormalization scheme invariant. The scheme dependence of the new coupling $hatalpha_s$ is parameterized by a single parameter $C$, related to transformations of the QCD scale $Lambda$. It is demonstrated that appropriate choices of $C$ can lead to substantial improvements in the perturbative prediction of physical observables. As phenomenological applications, we study $e^+e^-$ scattering and decays of the $tau$ lepton into hadrons, both being governed by the QCD Adler function.
Evidence is presented for the necessity of including duality violations in a consistent description of spectral function moments employed in the precision determination of $alpha_s$ from $tau$ decay. A physically motivated ansatz for duality violations in the spectral functions enables us to perform fits to spectral moments employing both pinched and unpinched weights. We describe our analysis strategy and provide some preliminary findings. Final numerical results await completion of an ongoing re-determination of the ALEPH covariance matrices incorporating correlations due to the unfolding procedure which are absent from the currently post
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