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Register a new userDuality violations in tau hadronic spectral moments
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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
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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.
The vector and axial-vector ALEPH hadronic spectral functions from $tau$-decay are used to probe potential quark-hadron duality violations (DV). This is done in the framework of finite energy QCD sum rules (FESR). A pinched integration kernel is introduced in the FESR in order to (a) quench potential duality violations on the real axis in the complex squared energy $s$-plane, and (b) effectively extend the analysis well beyond the kinematical $tau$-decay end-point where there is no longer data, i.e. in the range $s = 3 - 10 ,{mbox{GeV}}^2$. In the vector channel this procedure is supplemented with actual data from $e^+ e^-$-annihilation into hadrons, above the tau-decay kinematical end-point, with results fully supporting this extension. Very good agreement is obtained between data and two specific pinched FESR. Results from this analysis are confronted with those from a specific model of DV. As the sum rules are well satisfied in both cases within experimental errors, we conclude that possible DV must be buried under the experimental uncertainties. In other words, there seems to be no need for explicit models of DV in this case. Pinched kernels work as well, but with far less free parameters.
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.
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.
We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality violating contributions. Starting with the assumption that for QCD at $N_c=infty$ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite $N_c$.
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