Decoupling of heavy quarks in HQET

Decoupling of c-quark loops in b-quark HQET is considered. The decoupling coefficients for the HQET heavy-quark field and the heavy-light quark current are calculated with the three-loop accuracy. The last result can be used to improve the accuracy of extracting f_B from HQET lattice simulations (without c-quark loops). The decoupling coefficient for the flavour-nonsinglet QCD current with n antisymmetrized gamma-matrices is also obtained at three loops; the result for the tensor current (n=2) is new.Comment: JHEP3 documentclass; the results in a computer-readable form can be found at http://www-ttp.physik.uni-karlsruhe.de/Progdata/ttp06/ttp06-25/ V2: a few typos corrected, a few minor text improvements, a few references added; V3: several typos in formulas fixe

An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations

This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals and has proven itself efficient in several complicated cases.Comment: LaTeX, 9 page

Calculation of Feynman diagrams with zero mass threshold from their small momentum expansion

A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large compared to all momenta squared). Using dimensional regularization, a finite result is obtained in terms of powers of logarithms (describing the zero-threshold singularity) times power series in the momentum squared. Surprisingly, these latter ones represent functions, which not only have the expected physical `second threshold' but have a branchcut singularity as well below threshold at a mirror position. These can be understood as pseudothresholds corresponding to solutions of the Landau equations. In the spacelike region the imaginary parts from the various contributions cancel. For the two-loop examples with one mass $M$, in the timelike region for $q^2 \approx M^2$ we obtain approximations of high precision. This will be of relevance in particular for the calculation of the decay $Z \to b\bar{b}$ in the $m_b=0$ approximation.Comment: 17 pages with figures and tables, PostScript file gzip'ed and uuencode

The Photophysical Properties Investigation of Hybrid Associates of Methylene Blue Molecules with Colloidal CdS Quantum Dots and CdS / Cd(OH)2 "Core-Shell" Systems

The spectral properties of associates of methylene blue molecules with colloidal CdS quantum dots and CdS / Cd(OH)2 «core-shell» systems were investigated. It is shown that according to env ironment methylene blue changes its photophysical properties during association. These properties are due to changes of MB structure as a result of oxidation-reduction reactions. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3527

The Picosecond Kinetic of Luminescence in Hydrophilic Colloidal CdS Quantum Dots

The picosecond kinetic of luminescence in conglomerations of hydrophilic colloidal CdS quantum dots with an average diameter of 2.5 nm in gelatin was investigated. It was observed in the recombination luminescence band with a maximum at 580 nm. A complicated character of depending in the time interval from 300 ps to 1800 ns was found. Obtained dependences were interpreted in terms of radiative recombination at the donor-acceptor pairs (different sizes), complicated non-radiative transitions involving localized charge carriers on deeper levels. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3527

Numerical evaluation of loop integrals

We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to extract the divergent parts in the epsilon->0 limit. We then perform an epsilon-expansion and evaluate the integral coefficients of the expansion numerically. The method yields stable results in physical kinematic regions avoiding intricate analytic continuations. It can also be applied to evaluate both scalar and tensor integrals without employing reduction methods. We demonstrate our method with specific examples of infrared divergent integrals with many kinematic scales, such as two-loop and three-loop box integrals and tensor integrals of rank six for the one-loop hexagon topology

Spectral Manifestation of Hybrid Association of Zn0.7Sd0.3S Colloidal Quantum Dots with J-Aggregates of Thiacarbocyanine Dye

Spectral properties of mixtures of Zn0.7Sd0.3S colloidal quantum dots with mean diameter value of 3.5 nm with the molecules of 3,3'-di(γ-sulfopropil)-9-ethyl-4,5,4',5'-dibenzo-thiacarbocyanine betaine pyridine salt (DEC), prepared in gelatin were investigated. The obtained data indicated that the formation of well-luminescent trans-J-aggregates and spectral tuning in the position of the absorption band of DEC and the luminescence band of quantum dots, providing requirements for resonant energy transfer in the hybrid associate are the determinant factors in the increase of the luminescent emission of DEC molecules, interacting with Zn0.7Cd0.3S colloidal quantum dots. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3532

On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.Comment: 3 pages, 1 figure, results unchanged, discussion improved, to appear in European Physical Journal

"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.Comment: 13 pages; uses axodraw.st

Two-Loop Gluon-Condensate Contributions To Heavy-Quark Current Correlators: Exact Results And Approximations

The coefficient functions of the gluon condensate $$, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of $z=q^2/4m^2$. In the limiting cases $z\to0$, $z\to1$, and $z\to-\infty$, comparisons are made with previous partial results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A {\em single} moment, combined with only the {\em leading} threshold and asymptotic behaviours, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields $\approx0.021$ GeV$^4$.Comment: 9 page