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Register a new user$alpha_{s}$ from the (revised) ALEPH data for $tau$ decay
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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.
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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.
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-perturbative 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 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 $asZ = 0.1215 pm 0.0004_{rm exp} pm 0.0010_{rm th} pm 0.0005_{rm evol} = 0.1215 pm 0.0012$.
A recent analysis of data on the two photon production of the $eta_c$ and its decay to $K(Kpi)$ has determined the $Kpi$ $S$-wave amplitude in a model-independent way assuming primarily that the additional kaon is a spectator in this decay. The purpose of this paper is to fit these results, together with classic $Kpi$ production data from LASS, within a formalism that implements unitarity for the di-meson interaction. This fixes the $I=1/2$ $Kpito Kpi$ $S$-wave amplitude up to 2.4 GeV. This resolves the Barrelet ambiguity in the original LASS analysis, and constrains the amount of inelasticity in $Kpi$ scattering, highlighting that this becomes significant beyond 1.8 GeV. This result needs to be checked by experimental information on the many inelastic channels, in particular $Keta^prime$ and $Kpipipi$. Our analysis provides a single representation for the $Kpi$ $S$-wave from threshold, controlled by Chiral Perturbation Theory, through the broad $kappa$, $K_0^*(1430)$ and $K_0^*(1950)$ resonances. There is no arbitrary sum of Breit-Wigner forms and random backgrounds for real $Kpi$ masses. Rather the form provides a representation that can be translated to other processes with $Kpi$ interactions with their own coupling functions, while automatically maintaining consistency with the chiral dynamics near threshold, with the LASS data and the new results on $eta_c$ decay.
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.
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