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Register a new userChiral low-energy constants L_10 and C_87 from hadronic tau decays
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Mart\\'in Gonz\\'alez-Alonso
Publication date
2008
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English
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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 and C_87. At order p^4 we obtain L_10^r(M_rho)=-(5.22+-0.06)10^-3, whereas at order p^6 we get L_10^r(M_rho)=-(4.06+-0.39)10^-3 and C_87^r(M_rho) = (4.89+-0.19)10^-3 GeV^-2.
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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.
Recent experimental data on tau decays are used to reconstruct the difference in hadronic spectral densities with vector and axial-vector quantum numbers. The saturation of Das-Mathur-Okubo and Weinberg sum rules is studied. Two methods of improving convergence and decreasing errors are applied, and good agreement with the predictions of current algebra and chiral perturbation theory is observed. The resulting value of the pion polarisability is (2.64 +/- 0.36) 10^-4 fm^3.
Tau decays into hadrons foresee the study of the hadronization of vector and axial-vector QCD currents, yielding relevant information on the dynamics of the resonances entering into the processes. We analyse tau -> (3 pion) nu_tau decays within the framework of the Resonance Chiral Theory, comparing this theoretical scheme with the experimental data, namely ALEPH spectral function and branching ratio. Hence we get values for the mass and on-shell width of the a_1(1260) resonance, and provide the structure functions that have been measured by OPAL and CLEO-II.
Perturbative QCD corrections to hadronic $tau$ decays and $e^+e^-$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong coupling, $alpha_s$, from these processes suffer from an ambiguity related to the treatment of unknown higher orders in the perturbative series. In this work, we exploit the method of Pade approximants and its convergence theorems to extract information about higher-order corrections to the Adler function in a systematic way. First, the method is tested in the large-$beta_0$ limit of QCD, where the perturbative series is known to all orders. We devise strategies to accelerate the convergence of the method employing renormalization scheme variations and the so-called D-log Pade approximants. The success of these strategies can be understood in terms of the analytic structure of the series in the Borel plane. We then apply the method to full QCD and obtain reliable model-independent predictions for the higher-order coefficients of the Adler function. For the six-, seven-, and eight-loop coefficients we find $c_{5,1} = 277pm 51$, $c_{6,1}=3460pm 690$, and $c_{7,1}=(2.02pm0.72)times 10^4$, respectively, with errors to be understood as lower and upper bounds. Our model-independent reconstruction of the perturbative QCD corrections to the $tau$ hadronic width strongly favours the use of fixed-order perturbation theory (FOPT) for the renormalization-scale setting.
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.
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