Geometric approach to asymptotic expansion of Feynman integrals

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.Comment: 6 pages, 2 figure

How to choose master integrals

The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear combination of so-called master integrals. To do this, public (AIR, FIRE, REDUZE, LiteRed, KIRA) and private codes based on solving integration by parts relations are used. However, the choice of the master integrals provided by these codes is not always optimal. We present an algorithm to improve a given basis of the master integrals, as well as its computer implementation; see also a competitive varian

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

On one master integral for three-loop on-shell HQET propagator diagrams with mass

An exact expression for the master integral I_2 arising in three-loop on-shell HQET propagator diagrams with mass is derived and its analytical expansion in the dimensional regularization parameter epsilon is given.Comment: 6 pages, 1 figure; v3: completely re-written, 2 new authors, many new results, additional reference

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

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

On the Resolution of Singularities of Multiple Mellin-Barnes Integrals

One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.mComment: LaTeX, 10 page

Some methods to evaluate complicated Feynman integrals

I discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method.Comment: 2 pages, 1 figure, latex. Talk presented at the 8th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2002), Moscow, Russia, June 200

Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals

We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in \ep expansion for each master integral

New variables of separation for particular case of the Kowalevski top

We discuss the polynomial bi-Hamiltonian structures for the Kowalevski top in special case of zero square integral. An explicit procedure to find variables of separation and separation relations is considered in detail.Comment: 11 pages, LaTeX with Ams font