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تسجيل مستخدم جديد$alpha_s$ in 2016 from the (revised) ALEPH data for $tau$ decay
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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.
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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 discuss sum-rule determinations of $alpha_s$ from non-strange hadronic $tau$-decay data. We investigate, in particular, the reliability of the assumptions underlying the truncated OPE strategy, which specifies a certain treatment of non-perturbati
ve contributions, and which was employed in Refs. [1-3]. Here, we test this strategy by applying the strategy to the $R$-ratio obtained from $e^+e^-$ data, which extend beyond the $tau$ mass, and, based on the outcome of these tests, we demonstrate the failure of this strategy.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 $alpha_s$, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.
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 quant
ities 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 $asZ = 0.1215 pm 0.0004_{rm exp} pm 0.0010_{rm th} pm 0.0005_{rm evol} = 0.1215 pm 0.0012$.
Hadronic tau decays offer the possibility of determining the strong coupling alpha_s at relatively low energy. Precisely for this reason, however, good control over the perturbative QCD corrections, the non-perturbative condensate contributions in th
e framework of the operator product expansion (OPE), as well as the corrections going beyond the OPE, the duality violations (DVs), is required. On the perturbative QCD side, the contour-improved versus fixed-order resummation of the series is still an issue, and will be discussed. Regarding the analysis, self-consistent fits to the data including all theory parameters have to be performed, and this is also explained in some detail. The fit quantities are moment integrals of the tau spectral function data in a certain energy window and care should be taken to have acceptable perturbative behaviour of those moments as well as control over higher-dimensional operator corrections in the OPE.
The evolution of the determination of the strong coupling constant $alpha_s$ from the leptonic branching ratios, the lifetime, and the invariant mass distributions of the hadronic final state of the $tau$ lepton over the last two decades is briefly r
eviewed. The improvements in the latest ALEPH update are described in some detail. Currently this is one of the most precise $alpha_s$ determinations. Together with the other determination at the $Z$ boson mass pole, they constitutes the most accurate test of the asymptotic freedom in QCD.
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