Employing our previous framework to treat non-perturbative effects selfconsistently, including duality violations, we update the determination of the strong coupling, α s , using a modified version of the 1998 OPAL data, updated to reflect current values of exclusive mode hadronic τ decay branching fractions. To account for non-perturbative effects, non-linear, multi-parameter fits are necessary. We have, therefore, investigated the posterior probability distribution of the model parameters underlying our fits in more detail. We find that OPAL data alone provide only weak constraints on some of the parameters needed to model duality violations, especially in the case of fits involving axial vector channel data, making additional prior assumptions on the expected size of these parameters necessary at present. We provide evidence that this situation could be greatly improved if hadronic spectral functions based on the high-statistics BaBar and Belle data were to be made available.2

We apply an analysis method previously developed for the extraction of the strong coupling from the OPAL data to the recently revised ALEPH data for nonstrange hadronic τ decays. Our analysis yields the values α s (m 2 τ ) = 0.296±0.010 using fixed-order perturbation theory, and α s (m 2 τ ) = 0.310±0.014 using contourimproved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find α s (m 2 τ ) = 0.303 ± 0.009, respectively, α s (m 2 τ ) = 0.319 ± 0.012. We present a critique of the analysis method employed previously, for example in analyses by the ALEPH and OPAL collaborations, and compare it with our own approach. Our conclusion is that non-perturbative effects limit the accuracy with which the strong coupling, an inherently perturbative quantity, can be extracted at energies as low as the τ mass. Our results further indicate that systematic errors on the determination of the strong coupling from analyses of hadronic τ -decay data have been underestimated in much of the existing literature.

We present a new framework for the extraction of the strong coupling from hadronic τ decays through finite-energy sum rules. Our focus is on the small, but still significant non-perturbative effects that, in principle, affect both the central value and the systematic error. We employ a quantitative model in order to accommodate violations of quark-hadron duality, and enforce a consistent treatment of the higher-dimensional contributions of the Operator Product Expansion to our sum rules. Using 1998 OPAL data for the non-strange isovector vector and axial-vector spectral functions, we find the n f = 3 values α s (m 2 τ) = 0.307 ±0.019 in fixed-order perturbation theory, and 0.322±0.026 in contour-improved perturbation theory. For comparison, the original OPAL analysis of the same data led to the values 0.324 ± 0.014 (fixed-order) and 0.348 ± 0.021 (contour-improved).

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In this article we present a calculation of the bbbb tetraquark ground-state energy using a diffusion Monte Carlo method to solve the non-relativistic many-body system. The static potential for the four quark system is chosen to align with the flux-tube picture of QCD. Using this approach, we find that the 0 ++ state has a mass of 18.69±0.03 GeV, which is around 100 MeV below twice the η b mass. This bound state can behave as a four-lepton resonance via its decay to Υ(1S)Υ(1S) * → ℓ + ℓ − ℓ + ℓ − .