arXiv subjects
Publications and source records attributed to A. A. Pivovarov.
Results of evaluating the leading order $α_s$ corrections to the correlator of tensor currents in pure gluodynamics are presented. These corrections to the parton result for the correlator are not large numerically that allows one to use perturbation theory for the analysis of the resonance spectrum within the sum rules method.
The total cross section of the top quark-antiquark pair production near threshold in $γγ$ 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.
We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.
We present a consistent analysis of $Υ$ sum rules and $B$-meson semileptonic width in the next-to-next-to-leading order in the strong coupling constant. The analysis is based on the analytical result for the heavy quark vector current correlator near threshold in the second order in perturbative and relativistic expansion around the nonrelativistic Coulomb approximation.
The most recent recalculation of the two-loop correction to the static quark-antiquark potential gave the numerical value different from the previously known one. We comment on the effect this change produces on the numerical estimates of the bottom quark pole mass $m_b$, the strong coupling constant $\al_s$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ obtained in our papers [1,2].
We present a discussion on how to define the running electromagnetic coupling constant at $M_Z$ or some other intermediate scale as e.g. $m_Υ$. We argue that a natural definition consistent with general requirements of the renormalization group should be based on Euclidean values of the momentum of the photon propagator as the appropriate scale. We demonstrate in an explicit example of evaluating the running coupling constant at the scale of the $Υ$ resonance mass that the usual definition of the hadronic contribution with a principal value prescription is inconsistent. In the determination of the value of $α$ at $M_Z$ the numerical difference due to using a Euclidean definition rather than the principal value one is comparable in size to the errors caused by existing experimental and QCD inputs to the evaluation of $α(M_Z)$.
We present the next-to-next-to-leading order relation between the moments of the $Υ$ 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.
In this work radiative corrections in the total hadronic decay rate of the tau-lepton and some moments of its differential distributions are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections in the strange mass to the decay rate ratio R_tau to the order O(α_s^3 m^2) and find that they contribute appreciably to the Cabibbo suppressed decay modes of the tau-lepton. Using the results of a recent experimental analysis, we obtain m_s(1 GeV) = 200 \pm 40_exp \pm 30_th MeV.
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 $Υ$ system. The next-to-next-to-leading corrections are found to be of order of next-to-leading ones.
We analyze sum rules for the $Υ$ 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.
Local duality estimates for the $ρ$-meson leptonic width and the spectrum of radial excitations are updated. New perturbative corrections are included in the analysis that gives good agreement with experimental data on low energy resonances.
Long distance contribution to the $K^0-\bar K^0$ mixing is taken into account consistently and the corrections to the naive duality result represented by the famous box diagram are found to be small. Estimates are given in the leading order of the chiral perturbation theory.
A pattern of partial resummation of perturbation theory series inspired by analytical continuation is discussed for some physical observables.
We check quantitatively the validity of some popular phenomenological approaches of QCD in simple models. Dispersion sum rules are considered within the ladder approximation of a field-theoretic model with OPE given by ordinary loop diagrams which are computable for any number of loops. A correlator of two currents within the model complies with all requirements of standard QCD sum rules approach for fitting low-lying resonances such as fast convergence and good stability while the exact spectrum contains no resonance. Optimized PT as it is inspired by the principle of minimal sensitivity is analyzed within a quantum mechanical model and is shown to work well as compared to pure asymptotic expansion in the coupling constant or Padé approximation. Renormalon technique is tested within another quantum mechanical model and is found to fail to detect its low-energy structure.
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.
We extract the strong coupling constant $α_s(m_τ^2)$ from the semileptonic $τ$ decay width taking into account resummation effects from the running of the strong coupling constant. In the $\overline{\rm MS}$ scheme the result reads $α_s=0.375\pm 0.007$ to third order and $α_s=0.378\pm 0.007$ to fourth order in the $β$-function, respectively, where we use the recently computed four-loop coefficient $β_3$. These values for the coupling constant have to be compared with the value $α_s=0.354\pm 0.005$ derived from a third order analysis of $τ$ decays. We determine the exact value of the convergence radius of the perturbation series by analyzing the singularity structure of the complex coupling constant plane.
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 $τ$ 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 $β$-function expansion. The analysis involves the unknown five-loop coefficient $k_3$ for which we give some new estimates.
We exploit the fact that within massless perturbative QCD the same Green's function determines the hadronic contribution to the $τ$ decay width and the moments of the $e^+e^-$ cross section. This allows one to obtain relations between physical observables in the two processes up to an unprecedented high order of perturbative QCD. A precision measurement of the $τ$ decay width allows one then to predict the first few moments of the spectral density in $e^+e^-$ annihilations integrated up to $s\sim m_τ^2$ with high accuracy. The proposed tests are in reach of present experimental capabilities.