Euclidean asymptotic expansions of Green functions of quantum fields (II) Combinatorics of the asymptotic operation

The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The asymptotic operation for integrals is defined and a simple combinatorial techniques is developed to study its exponentiation. The asymptotic operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance operator-product expansions, the decoupling theorem etc.; e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R-operation is constructed. The results are valid for arbitrary QFT models.Comment: one .sty + one .tex (LaTeX 2.09) + one .ps (GSview) = 46 pp. Many fewer misprints than the journal versio

Asymptotic structure of perturbative series for τ\tau lepton decay observables: ms2m_s^2 corrections

In a previous paper we performed an analysis of asymptotic structure of perturbation theory series for semileptonic $\tau$-lepton decays in massless limit. We extend our analysis to the Cabibbo suppressed $\Delta S=1$ decay modes of the $\tau$ lepton. In particular we address the problem of $m_s^2$ corrections to theoretical formulas. The properties of the asymptotic behavior of the finite order perturbation theory series for the coefficient functions of the $m_s^2$ corrections are studied.Comment: 25 page

Determination of the strange quark mass from Cabibbo-suppressed tau decays with resummed perturbation theory in an effective scheme

We present an analysis of the m_s^2-corrections to Cabibbo-suppressed tau lepton decays employing contour improved resummation within an effective scheme which is an essential new feature as compared to previous analyses. The whole perturbative QCD dynamics of the tau-system is described by the beta-function of the effective coupling constant and by two gamma-functions for the effective mass parameters of the strange quark in different spin channels. We analyze the stability of our results with regard to high-order terms in the perturbative expansion of the renormalization group functions. A numerical value for the strange quark mass in the MS scheme is extracted m_s(M_\tau)=130\pm 27_{exp}\pm 9_{th} MeV. After running to the scale 1 GeV this translates into m_s(1 GeV)=176 \pm 37_{exp}\pm 13_{th} MeV.Comment: 32 pages, latex, 4 postscript figures, revised version to appear in European Physical Journal C, discussion of the choice of the moments added, some errors correcte

Asymptotic structure of perturbative series for tau lepton observables

We analyze tau lepton decay observables, namely moments of the hadronic spectral density in the finite energy interval (0,M_\tau), within finite order perturbation theory including \alpha_s^4 corrections. The start of asymptotic growth of perturbation theory series is found at this order in a scheme invariant manner. We establish the ultimate accuracy of finite order perturbation theory predictions and discuss the construction of optimal observables.Comment: 21 page