4 research outputs found
QCD tests in tau decays with optimized perturbation expansion
The next-to-next-to-leading order perturbative QCD corrections to R_tau and
the higher moments of the invariant mass distribution in the hadronic tau
decays are considered. The renormalization scheme dependence of these
corrections is discussed. The optimized predictions are obtained, using the
principle of minimal sensitivity as a guide to select the preferred
renormalization scheme. A simplified fit is performed, using R_tau and
R^12_tau, to see how the use of the optimized expansion may affect the
determination of the alpha_s and the dimension six condensates from the
experimental data.Comment: 6 pages in LateX, 4 PostScript figures embedded in text, uses
espcrc2.sty (included), to appear in the Proceedings of the Fourth
International Workshop on Tau Lepton Physics, 16-19 September 1996, Estes
Park, Colorado, U.S.
Resummation of Nonalternating Divergent Perturbative Expansions
A method for the resummation of nonalternating divergent perturbation series
is described. The procedure constitutes a generalization of the Borel-Pad\'{e}
method. Of crucial importance is a special integration contour in the complex
plane. Nonperturbative imaginary contributions can be inferred from the purely
real perturbative coefficients. A connection is drawn from the quantum field
theoretic problem of resummation to divergent perturbative expansions in other
areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman
criterion added; version to appear in Phys. Rev.
Renormalization scheme dependence and the problem of determination of alpha_s and the condensates from the semileptonic tau decays
The QCD corrections to the moments of the invariant mass distribution in the
semileptonic decays are considered. The effect of the renormalization
scheme dependence on the fitted values of alpha_s(m^2_tau) and the condensates
is discussed, using a simplified approach where the nonperturbative
contributions are approximated by the dimension six condensates. The fits in
the vector and the axial-vector channel are investigated in the next-to-leading
and the next-to-next-to-leading order. The next-to-next-to-leading order
results are found to be relatively stable with respect to change of the
renormalization scheme. A change from the MS-bar scheme to the minimal
sensitivity scheme results in the reduction of the extracted value of
alpha_s(m^2_tau) by 0.01.Comment: Some typographical errors have been corrected, including two small
misprints in table 1 and table 2 and one in Eq.15. 20 pages Latex, 5 figure
Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
We consider the resummation of the perturbation series describing the energy
displacement of a hydrogenic bound state in an electric field (known as the
Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal
power series in the electric field strength. The perturbation series exhibits a
rich singularity structure in the Borel plane. Resummation methods are
presented which appear to lead to consistent results even in problematic cases
where isolated singularities or branch cuts are present on the positive and
negative real axis in the Borel plane. Two resummation prescriptions are
compared: (i) a variant of the Borel-Pade resummation method, with an
additional improvement due to utilization of the leading renormalon poles (for
a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317,
p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with
an analytic continuation by conformal mapping, and Pade approximations in the
conformal variable. The singularity structure in the case of the LoSurdo-Stark
effect in the complex Borel plane is shown to be similar to (divergent)
perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results
enhanced; one section and one appendix added and some minor changes and
additions; to appear in phys. rev.