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Register a new userDetermination of alpha_s from tau decays
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Matthias Jamin
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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 the 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.
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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 reviewed. 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.
Using recent precise hadronic tau-decay data on the V-A spectral function, and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10^r(M_rho) and C_87^r(M_rho). These two low-energy constants appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L_10^r(M_rho) = -(5.22pm 0.06)10^{-3}. Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06pm 0.39)10^{-3} and C_87^r(M_rho) = (4.89pm 0.19)10^{-3}GeV^{-2}. In the SU(2) chiral effective theory, the corresponding low-energy coupling takes the value overline l_5 = 13.30 pm 0.11 at order p^4, and overline l_5 = 12.24 pm 0.21 at order p^6.
We determine the strong coupling constant $alpha_s(M_Z)$ from the static QCD potential by matching a lattice result and a theoretical calculation. We use a new theoretical framework based on operator product expansion (OPE), where renormalons are subtracted from the leading Wilson coefficient. We find that our OPE prediction can explain the lattice data at $Lambda_{rm QCD} r lesssim 0.8$. This allows us to use a larger window in matching, which leads to a more reliable determination. We obtain $alpha_s(M_Z)=0.1179^{+0.0015}_{-0.0014}$.
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.
Hadron colliders offer a unique opportunity to test perturbative QCD because, rather than producing events at a specific beam energy, the dynamics of the hard scattering is probed simultaneously at a wide range of momentum transfers. This makes the determination of $al$ and the parton density functions (PDF) at hadron colliders particularly interesting. In this paper we restrict ourselves to extracting $al$ for a given PDF at a scale which is directly related to the transverse energy produced in the collision. As an example, we focus on the single jet inclusive transverse energy distribution and use the published 88-89 CDF data with an integrated luminosity of 4.2 pb$^{-1}$. The evolution of the coupling constant over a wide range of scales (from 30~GeV to 500~GeV) is clearly shown and is in agreement with the QCD expectation. The data to be obtained in the current Tevatron run (expected to be well in excess 100 pb$^{-1}$ for both the CDF and DO experiments) will significantly decrease the experimental errors.
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