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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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Evidence is presented for the necessity of including duality violations in a consistent description of spectral function moments employed in the precision determination of $alpha_s$ from $tau$ decay. A physically motivated ansatz for duality violations in the spectral functions enables us to perform fits to spectral moments employing both pinched and unpinched weights. We describe our analysis strategy and provide some preliminary findings. Final numerical results await completion of an ongoing re-determination of the ALEPH covariance matrices incorporating correlations due to the unfolding procedure which are absent from the currently post
An exhaustive number of QCD finite energy sum rules for $tau$-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension $d=2$ condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions $d=6$ and $d=8$, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic $tau$-decay in the kinematic region above $ssimeq2.2$ GeV$^{2}$ for these kernels.
Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the $sigma$ and $eta-eta$ mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant $Lambda$ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.
Recent sum rule determinations of |V_us|, employing flavor-breaking combinations of hadronic tau decay data, are significantly lower than either expectations based on 3-family unitarity or determinations from K_ell3 and Gamma[K_mu2]/Gamma[pi_mu2]. We use lattice data to investigate the accuracy/reliability of the OPE representation of the flavor-breaking correlator combination entering the tau decay analyses. The behavior of an alternate correlator combination, constructed to reduce problems associated with the slow convergence of the D = 2 OPE series, and entering an alternate sum rule requiring both electroproduction cross-section and hadronic tau decay data, is also investigated. Preliminary updates of both analyses, with the lessons learned from the lattice data in mind, are also presented.
The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_mu$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_mu|_{uds} =686 pm 26$, and in the heavy-quark sector $a^{HAD}_mu|_{c} =14.4 pm 0.1$, and $a^{HAD}_mu|_{b} =0.29 pm 0.01$, resulting in $a^{HAD}_mu = 701 pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this approach the most accurate and trustworthy determination of the leading order $a^{HAD}_mu$.
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