Derivation of Functional Equations for Feynman Integrals from Algebraic Relations

New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of functional equations Feynman integrals in general kinematics can be expressed in terms of simpler integrals.Comment: 20 pages, 4 jpeg figure

Application and explicit solution of recurrence relations with respect to space-time dimension

A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop integrals with arbitrary momenta and masses is presented. The result is written as multiple hypergeometric series depending on ratios of Gram determinants. For the 3-point function a new expression in terms of the Appell hypergeometric function F_1 is presented.Comment: 9 pages, 1 figure, LaTe

Methods for deriving functional equations for Feynman integrals

We present short review of two methods for obtaining functional equations for Feynman integrals. Application of these methods for finding functional equations for one- and two- loop integrals is described in detail. It is shown that with the aid of functional equations Feynman integrals in general kinematics can be expressed in terms of simpler integrals. Similarities between functional equations for Feynman integrals and addition theorem for Abel integrals are shortly discussed.Comment: 11 pages, 2 figures, PdfLate

AN ALGORITHM FOR SMALL MOMENTUM EXPANSION OF FEYNMAN DIAGRAMS

An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several coefficients of the Taylor series expansion for the two-loop propagator and two-loop non-planar vertex diagrams are calculated. The results of the numerical evaluation of these diagrams using conformal mapping and Pade approximants are given.Comment: 7 page, Talk presented at the AI-HENP 95 workshop, Pisa, April 1995 (Some minor misprints are corrected

Massless on-shell box integral with arbitrary powers of propagators

The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension $d$ is shown to reduce to a sum over three generalised hypergeometric functions. This result follows from the solution to the third order differential equation of hypergeometric type. To derive the differential equation, the Gr\"obner basis technique for integrals with noninteger powers of propagators was used. A complete set of recurrence relations from the Gr\"obner basis is presented. The first several terms in the $\varepsilon =(4-d)/2$ expansion of the result are given.Comment: 9 pages, 1figur

Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme

We compute the conversion factors needed to obtain the MS-bar and RGI up, down, and strange-quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM_gamma_mu renormalization schemes. This is important for obtaining the MS-bar masses with the best possible precision from numerical lattice-QCD simulations, because the customary RI(')/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scale dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM_gamma_mu scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.Comment: Added results for the RI/SMOM_gamma_mu scheme and anomalous dimensions; typos fixed (results unchanged); added reference

Three-loop calculations in non-Abelian gauge theories

A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations have been published by the present authors (with A.Yu., Zharkov and L.V., Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, has also been published in 1980 as the JINR Communication E2-80-483.Comment: 21 pages, uses axodraw.st

Long-Range Coulomb Forces in DIS: Missed Radiative Corrections?

The Born approximation, one photon exchange, used for DIS is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Z\alpha is not a small parameter. So far these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case the cross section is modified also. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than 'swept under the carpet'. The importance of these radiative corrections is questioned in present paper. We show that in the simplest case of a constant hadronic current the Coulomb corrections provide a phase to the Born amplitude, therefore the cross section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving exact lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Z\alpha, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation.Comment: 24 pages including 4 figures. Fig.4 is modified and stylistic corrections are made. The final version to appear in Eur.Phys.J.

Analytic epsilon-Expansion of the Scalar One-loop Bhabha Box Function

We derive the first three terms of the epsilon-expansion of the scalar one-loop Bhabha box function from a representation in terms of three generalized hypergeometric functions, which is valid in arbitrary dimensions.Comment: 12 pages, latex, uses appolb.cls; presented by J.F. at 27th International Conference of Theoretical Physics: Matter to the Deepest: Recent Developments in Physics of Fundamental Interactions (Ustron 03), Ustron, Poland, 15-21 Sep 200

A Quasiclassical Approximation in the Theory of the Landau-Pomeranchuk Effect

Using the improved value of the screening angular parameter in the quasiclassical approximation of the Moliere multiple scattering theory we show that the best agreement between the Migdal theory of the LPM-effect and experiment is achieved if the multiple scattering of electrons by target atoms is described using the quasiclassical approximation instead of the traditionally used Born one.Comment: 9 pages, no figures, LaTEX; v2: PDFLaTeX, 7 pages, an updated versio