Optimal renormalization and the extraction of strange quark mass from semi-leptonic τ\tau-decay

We employ optimal renormalization group analysis to semi-leptonic $\tau$-decay polarization functions and extract the strange quark mass from their moments measured by the ALEPH and OPAL collaborations. The optimal renormalization group makes use of the renormalization group equation of a given perturbation series which then leads to closed form sum of all the renormalization group-accessible logarithms which have reduced scale dependence. Using the latest theoretical inputs we find $m_s(2{\rm GeV}) = 106.70 \pm 9.36~{\rm MeV}$ and $m_s(2{\rm GeV}) = 74.47 \pm 7.77~{\rm MeV}$ for ALEPH and OPAL data respectively.Comment: 3 pages, Contribution to the proceedings of the XXII DAE-BRNS High Energy Physics Symposium, University of Delhi, Dec. 12-16, 201

Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Known perturbative expressions for the decay rates of 115 GeV Higgs particle into either two gluons or a $b\bar{b}$ pair are shown to exhibit renormalization-scale-($\mu$)-dependence that is largely removed via renormalization-group/Pade-approximant estimates of these rates' next order contributions. The extrema in $\mu$ characterizing both rates, as determined from fully-known orders of perturbation theory, are very nearly equal to corresponding $\mu$-insensitive rates obtained via estimation of their next order contributions, consistent with "minimal-sensitivity" expectations.Comment: 12 pages, 3 figures, LaTe

Higgs Decay to Top Quarks at O(\alpha_s^2)

Three-loop corrections to the scalar and pseudo-scalar current correlator are calculated. By applying the large momentum expansion mass terms up to order (m^2/q^2)^4 are evaluated analytically. As an application O(\alpha_s^2) corrections to the decay of a scalar and pseudo-scalar Higgs boson into top quarks are considered. It is shown that for a Higgs mass not far above the $t\bar{t}$ threshold these higher order mass corrections are necessary to get reliable results.Comment: Latex, 20 pages, 14 ps-figures. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment

We present a quenched lattice calculation of the lowest order (alpha^2) hadronic contribution to the anomalous magnetic moment of the muon which arises from the hadronic vacuum polarization. A general method is presented for computing entirely in Euclidean space, obviating the need for the usual dispersive treatment which relies on experimental data for e^+e^- annihilation to hadrons. While the result is not yet of comparable accuracy to those state-of-the-art calculations, systematic improvement of the quenched lattice computation to this level of accuracy is straightforward and well within the reach of present computers. Including the effects of dynamical quarks is conceptually trivial, the computer resources required are not.Comment: 12 pages, including two figures. Added reference and footnote Replaced with published version; minor changes asked for by referees and minor deletions to stay within page limi

The Pseudothreshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

The values at pseudothreshold of two loop sunrise master amplitudes with arbitrary masses are obtained by solving a system of differential equations. The expansion at pseudothreshold of the amplitudes is constructed and some lowest terms are explicitly presented.Comment: 1+22 pages, Latex, no figures, changes in Eq.(41),(44),(47

Semileptonic b --> u decays: lepton invariant mass spectrum

We compute O(alpha_s^2) QCD corrections to the lepton invariant mass spectrum in the decay b --> u l nu_l, relevant for the determination of the CKM matrix element |V_{ub}|. Our method can also be used to evaluate moments of the lepton energy distribution with an O(alpha_s^2) accuracy. The abelian part of our result gives the neutrino invariant mass spectrum in the muon decay and, upon integration, the O(alpha^2) correction to the muon lifetime.Comment: 5 pages, revte

The Threshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained analytically for arbitrary masses.Comment: 1+18 pages, Latex, no figures, as in Journal reference with more changes in Eq.(31),(42),(45

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no 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

QCD sum rules and radial excitaions of light pseudoscalar and scalar mesons

The calculations of masses and decay constants of the radial excitations of light pseudoscalar and scalar mesons within QCD sum rules method are briefly reviewed. The predictions are based on the $1/N_c$-supported model spectra, which consist of infinite number of infinitely narrow resonances, and on the assumption that the ground states of light scalar mesons may be considered as the $\bar{q}q$-bound states. The results of the studies are compared with the existing experimental data and with the predictions of other theoretical approaches.Comment: 10 pages, LaTeX, to be published in Phys.Atom.Nucl. Dedicated to 70th Birthday of Professor Yu.A. Simonov. Additional shortcomings eliminated. Results unchange