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

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

Ultrasoft contribution to quarkonium production and annihilation

We compute the third-order correction to electromagnetic S-wave quarkonium production and annihilation rates due to the emission and absorption of an ultrasoft gluon. Our result completes the analysis of the non-relativistic quarkonium bound-state dynamics in the next-to-next-to-next-to-leading order. The impact of the ultrasoft correction on the Upsilon(1S) leptonic width and the top quark-antiquark threshold production cross section is estimated.Comment: 10 page

Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of $t\bar{t}$, $b\bar{b}$ and $c\bar{c}$ systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict $\Gamma(\eta_b(1S) \to \gamma\gamma)=0.659\pm 0.089 ({\rm th.}) {}^{+0.019}_{-0.018} (\delta \alpha_{\rm s})\pm 0.015 ({\rm exp.}) {\rm keV}$. Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain novel corrections to the ratio of the ortho- and parapositronium decay rates: the corrections of order $\alpha^4\ln^2\alpha$ and $\alpha^5\ln^3\alpha$.Comment: Appendices A.4, A.5 and B correcte

Bottom quark mass from Upsilon sum rules to O (alpha(3)(s))

We use the O(α3s) approximation of the heavy-quark vacuum polarization function in the threshold region to determine the bottom quark mass from nonrelativistic Υ sum rules. We find very good stability and convergence of the perturbative series for the bottom quark mass in MS¯¯¯¯¯ renormalization scheme. Our final result is m¯¯¯b(m¯¯¯b)=4.169±0.008th±0.002αs±0.002exp

M(Bc∗)−M(Bc)M(B^*_c)-M(B_c) Splitting from Nonrelativistic Renormalization Group

We compute the hyperfine splitting in a heavy quarkonium composed of different flavors in next-to-leading logarithmic approximation using the nonrelativistic renormalization group. We predict the mass difference of the vector and pseudoscalar charm-bottom mesons to be $M(B^*_c)-M(B_c)=46 \pm 15 {(\rm th)} {}^{+13}_{-11} (\delta\alpha_s)$ MeV.Comment: Eq.(22) and Appendix corrected, numerical results slightly changed. arXiv admin note: text overlap with arXiv:hep-ph/031208

Coulomb resummation for bbˉb \bar b system near threshold and precision determination of \al_s and mbm_b.

We analyze sum rules for the $\Upsilon$ system with resummation of threshold effects on the basis of the nonrelativistic Coulomb approximation. We find for the pole mass of the bottom quark $m_b=4.75\pm 0.04 GeV$ and for the strong coupling constant \al_s(M_Z)=0.118\pm 0.006. The origin of the contradiction between two recent estimates obtained within the same formal framework is clarified.Comment: 22 pages Latex, some misprints in the Appendix are correcte

Numerical analysis of renormalon technique in quantum mechanics

We discuss the ways of extracting a low energy scale of an underlying theory using high energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power corrections accounting for asymptotically small terms and an alternative approach exploiting a modified running coupling constant of the model and nonperturbative continuation of evolution equations into an infrared region. Numerical estimates show that the latter is more efficient in approximating low-energy data of the model.Comment: 14 pages, Latex, the text is corrected according to the Phys.Lett.B referee comment

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