On a subtle point of sum rules calculations: toy model

We consider a two-point correlator in massless $\phi^3$ model within the ladder approximation . The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rules technique with a simple "resonance + continuum" model of the spectrum allows to predict parameters of the "resonance" very accurately in the sense that all necessary criteria of stability are perfectly satisfied.Comment: LaTeX fil

Next-to-next-to-leading order vacuum polarization function of heavy quark near threshold and sum rules for bbˉb \bar b system

A correlator of the vector current of a heavy quark is computed analytically near threshold in the next-to-next-to-leading order in perturbative and relativistic expansion that includes \al_s^2, \al_sv and $v^2$ corrections in the coupling constant and velocity of the heavy quark to the nonrelativistic Coulomb approximation. Based on this result, the numerical values of the $b$-quark pole mass and the strong coupling constant are determined from the analysis of sum rules for the $\Upsilon$ system. The next-to-next-to-leading corrections are found to be of order of next-to-leading ones.Comment: 12 pages Latex, misprints in the formulae for the nonrelativistic Green function are correcte

Next-to-next-to-leading order relation between R(e+e−→bbˉ)R(e^+e^-\to b\bar b) and Γsl(b→clνl)\Gamma_{\rm sl}(b\to cl\nu_l) and precise determination of ∣Vcb∣|V_{cb}|

We present the next-to-next-to-leading order relation between the moments of the $\Upsilon$ system spectral density and the inclusive $B$-meson semileptonic width. The perturbative series for the width as an explicit function of the moments is well convergent in three consequent orders in the strong coupling constant that provides solid and accurate theoretical estimate. As a result, the uncertainty of the value of $|V_{cb}|$ Cabibbo-Kobayashi-Maskawa matrix element is reduced.Comment: journal version, references update

Analytical continuation and resummed perturbation theory

A pattern of partial resummation of perturbation theory series inspired by analytical continuation is discussed for some physical observables.Comment: 9 pages, 2 tables, Late

A new technique for computing the spectral density of sunset-type diagrams: integral transformation in configuration space

We present a new method to investigate a class of diagrams which generalizes the sunset topology to any number of massive internal lines. Our attention is focused on the computation of the spectral density of these diagrams which is related to many-body phase space in $D$ dimensional space-time. The spectral density is determined by the inverse $K$-transform of the product of propagators in configuration space. The inverse $K$-transform reduces to the inverse Laplace transform in any odd number of space-time dimensions for which we present an explicit analytical result.Comment: 13 pages in LaTeX, one PostScript figure included in the tex

Perturbative relations between e+e−e^+e^- annihilation and τ\tau decay observables including resummation effects

By exploiting the analyticity properties of the two-point current-current correlator we obtain numerical predictions for the $e^+e^-$ moments in terms of the $\tau$ decay rate. We perform a partial resummation of the pertinent perturbative series expansion by solving the renormalization group equation for Adler's function. Our predictions are renormalization scheme independent but depend on the order of the perturbative $\beta$-function expansion. The analysis involves the unknown five-loop coefficient $k_3$ for which we give some new estimates.Comment: 10 pages, LaTeX, 2 postscript figure

Strong coupling constant from τ\tau decay within renormalization scheme invariant treatment

We extract a numerical value for the strong coupling constant \alpha_s from the \tau-lepton decay rate into nonstrange particles. A new feature of our procedure is the explicit use of renormalization scheme invariance in analytical form in order to perform the actual analysis in a particular renormalization scheme. For the reference coupling constant in the \MSsch-scheme we obtain \alpha_s(M_\tau)= 0.3184 \pm 0.0060_{exp} which corresponds to \al_s(M_Z)= 0.1184 \pm 0.0007_{exp} \pm 0.0006_{hq mass}. This new numerical value is smaller than the standard value from $\tau$-data quoted in the literature and is closer to \al_s(M_Z)-values obtained from high energy experiments.Comment: 8 page

QSSR estimate of the BBB_B parameter at next-to-leading order

We compute the leading $\alpha_s$ corrections to the two-point correlator of the $O_{\Delta B=2}$ operator which controls the $B^0 \bar B^0$ mixing. Using this result within the QCD spectral sum rules approach and some phenomenologically reasonable assumptions in the parametrization of the spectral function, we conclude that the vacuum saturation values $B_B\simeq B_{B^*}\simeq 1$ are satisfied within 15\%.Comment: 8 pages, LaTeX, CERN-TH.7140/94, PM 93/16, and KEK Preprint 93-184, two figures appended as a PS fil

Top quark threshold production in γγ\gamma\gamma collision in the next-to-leading order

The total cross section of the top quark-antiquark pair production near threshold in $\gamma\gamma$ collision is computed analytically up to the next-to-leading order in perturbative and nonrelativistic expansion for general photon helicity. The approximation includes the first order corrections in the strong coupling constant and the heavy quark velocity to the nonrelativistic Coulomb approximation.Comment: 27 pages Latex, misprints correcte

Theoretical uncertainties for weak decays: higher dimension operators

A brief review of recent results on computing contributions of higher dimension operators to weak effective $\Delta S=1,2$ hamiltonians for light quarks is presented.Comment: 14 pages, Late