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Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalization-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the $tau$ hadronic width, the contour-improved and the renormalization-group summed non-power expansions in the ${overline{rm MS}}$ scheme lead to the prediction $alpha_s(M_tau^2)= 0.3192~^{+ 0.0167}_{-0.0126}$, which translates to $alpha_s(M_Z^2)= 0.1184~^{+0.0020}_{-0.0016}$.
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 r
The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling $alpha_s$ and other QCD parameters from the hadronic decays of the $tau$ lepton. Motivated by the recent analyses of a large class of moments in
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, $a
The standard approach to determine the parameters of a resonance is based on the study of the volume dependence of the energy spectrum. In this work we study a non-linear sigma model coupled to a scalar field in which a resonance emerges. Using an an
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 f