alpha_s from tau decays revisited

Being a determination at low energies, the analysis of hadronic tau decay data provides a rather precise determination of the strong coupling alpha_s after evolving the result to M_Z. At such a level of precision, even small non-perturbative effects become relevant for the central value and error. While those effects had been taken into account in the framework of the operator product expansion, contributions going beyond it, so-called duality violations, have previously been neglected. The following investigation fills this gap through a finite-energy sum rule analysis of tau decay spectra from the OPAL experiment, including duality violations and performing a consistent fit of all appearing QCD parameters. The resulting values for alpha_s(M_tau) are 0.307(19) in fixed-order perturbation theory and 0.322(26) in contour-improved perturbation theory, which translates to the n_f=5 values 0.1169(25) and 0.1187(32) at M_Z, respectively.Comment: 4 pages, 3 figures. Prepared for the Proceedings of the International Workshop on e+e- collisions from Phi to Psi (PHIPSI11), Sep. 19-22, 2011, BINP, Novosibirsk, Russi

Scalar resonances: scattering and production amplitudes

Scattering and production amplitudes involving scalar resonances are known, according to Watson's theorem, to share the same phase $\delta(s)$. We show that, at low energies, the production amplitude is fully determined by the combination of $\delta(s)$ with another phase $\omega(s)$, which describes intermediate two-meson propagation and is theoretically unambiguous. Our main result is a simple and almost model independent expression, which generalizes the usual $K$-matrix unitarization procedure and is suited to be used in analyses of production data involving scalar resonances.Comment: 10 pages, 4 figures. Minor changes, references added, version to appear in Phys. Rev.

Duality Violation and the K --> pi pi Electroweak Penguin Operator Matrix Elements from Hadronic Tau Decays

We discuss a preliminary study of the impact of duality violations on extractions from tau decay data of the D=6 VEVs which determine chiral limit Standard Model K-->pi pi matrix elements of the electroweak penguin operators.Comment: 4 pages, 5 figures, prepared for the Proceedings of the 11th Particle and Nuclear Intersections Conference (PANIC 2011), Boston, USA, July 24-29, 201

Issues in determining alpha_s from hadronic tau decay and electroproduction data

We discuss some key issues associated with duality-violating and non-perturbative OPE contributions to the theoretical representations of light quark current-current two-point functions and relevant to precision determinations of alpha_s from hadronic tau decay and electroproduction cross-section data. We demonstrate that analyses with an explicit representation of duality-violating effects are required to bring theoretical errors in such extractions under control, motivating the accompanying paper in these proceedings, which presents the results of such an analysis.Comment: 5 pages, 4 figures. Prepared for the Proceedings of the International Workshop on e+e- collisions from Phi to Psi (PHIPSI11), Sep. 19-22, 2011, BINP, Novosibirsk, Russi

A contour integral approach to the computation of invariant pairs

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner [3] and by Beyn and Thümmler [6]. Invariant pairs extend the notion of eigenvalue–eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. We compute formulations for the condition numbers and the backward error for invariant pairs and solvents. We then adapt the Sakurai–Sugiura moment method [1] to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues. Numerical refinement via a variant of Newton's method is also studied. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials

Isotope partitioning between cow milk and farm water: A tool for verification of milk provenance

Rationale: The oxygen and hydrogen isotope compositions of the water component of the milk from nine Italian dairy farms were studied together with the farm water for one year. The aim was to verify the importance of farm water and seasonal temperature variation on milk isotope values and propose mathematical relations as new tools to identify the milk origin. Methods: Milk was centrifuged to separate the solids and then distilled under vacuum to separate water. δ(18O/16O) and δ(2H/1H) analyses of the water molecules were carried out using a water equilibrator online with a mass spectrometer. For oxygen and hydrogen isotope determination, water was equilibrated with pure CO2 for 7.5 h and with pure H2 for 5 h, respectively. The isotope ratio value is indicated with δ (expressed on the VSMOW/SLAP scale) as defined by IUPAC. Results: The average annual isotope value of milk at the different cattle sheds is mostly related to the farm water suggesting that the drinking water is the most important factor influencing the isotopic values of the milk water. The milk/water fractionation factor correlates with the milking time and, thus, the seasonal temperature is best described by a 4th order polynomial regression line. A two-level check model was used to verify the milking provenance. Conclusions: This study shows that it is essential to analyze both milk and farm water to indicate provenance. A two-step verification tool, based on the difference between the measured and calculated δ(18O/16O)M values, and the difference between the calculated and estimated milk-water fractionation factors, allowed the source determination of milk. Both conditions must be met if the milk is considered to be from the Parmigiano-Reggiano production region. Although this approach was developed for this region, it can easily be tested and adapted to other dairy production areas

D^+ \to K^- \p^+ \p^+ : the low-energy sector

An effective $SU(3)\times SU(3)$ chiral lagrangian, which includes scalar resonances, is used to describe the process D^+ \rar K^- \p^+ \p^+ at low-energies. Our main result is a set of five $S$-wave amplitudes, suited to be used in analyses of production data.Comment: Talk given at SCADRON 70 - Workshop on Scalar Mesons and Related Topics - Lisbon - February 200