On evaluation of two-loop self-energy diagram with three propogator

Small momentum expansion of the "sunset" diagram with three different masses is obtained. Coefficients at powers of $p^2$ are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of "sunset" diagram in terms of different sets of variables are given.Comment: 9 pages, LaTEX, MSU-PHYS-HEP-Lu3/9

Causal construction of the massless vertex diagram

The massless one-loop vertex diagram is constructed by exploiting the causal structure of the diagram in configuration space, which can be translated directly into dispersive relations in momentum space.Comment: 14 pages, LATEX with style file, corresponds to published versio

Analytical evaluation of certain on-shell two-loop three-point diagrams

An analytical approach is applied to the calculation of some dimensionally-regulated two-loop vertex diagrams with essential on-shell singularities. Such diagrams are important for the evaluation of QED corrections to the muon decay, QCD corrections to top quark decays t->W^{+}b, t->H^{+}b, etc.Comment: 2 pages, LaTeX, contribution to proceedings of ACAT2002 (Moscow, June 2002

Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.Comment: 8 pages, late

One-loop results for the quark-gluon vertex in arbitrary dimension

Results on the one-loop quark-gluon vertex with massive quarks are reviewed, in an arbitrary covariant gauge and in arbitrary space-time dimension. We show how it is possible to get on-shell results from the general off-shell expressions. The corresponding Ward-Slavnov-Taylor identity is discussed.Comment: 6 pages, LaTeX, including 1 figure, uses epsfig, requires espcrc2.sty, contribution to the Zeuthen Workshop "Loops and Legs in Gauge Theories" (Bastei, Germany, April 2000

An easy way to solve two-loop vertex integrals

Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle, contrary to the usual parametric ones. The result of the integral worked out in $D<0$ must be analytically continued again --- of course --- to real physical world, $D>0$, and this step presents no difficulties. We consider four two-loop three-point vertex diagrams with arbitrary exponents of propagators and dimension. These original results give the correct well-known particular cases where the exponents of propagators are equal to unity.Comment: 13 pages, LaTeX, 4 figures, misprints correcte

Two-loop sunset diagrams with three massive lines

In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit representations for the master integrals and an analytic result through O(epsilon) in d=4-2epsilon space-time dimensions for the case of equal masses, m = M.Comment: 11 page

Some remarks on the epsilon-expansion of dimensionally regulated Feynman diagrams

Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine integrals related to the polylogarithms. It is shown how the analytic continuation of these functions can be constructed in terms of the generalized Nielsen polylogarithms.Comment: 6 pages, requires espcrc2.sty, contribution to the Zeuthen Workshop "Loops and Legs in Gauge Theories" (Bastei, Germany, April 2000

One-loop results for three-gluon vertex in arbitrary gauge and dimension

We review the calculation of one-loop contributions to the three-gluon vertex, for arbitrary (off-shell) external momenta, in arbitrary covariant gauge and in arbitrary space-time dimension. We discuss how one can get the results for all on-shell limits of interest directly from the general off-shell expression.Comment: 6 pages, LaTex, uses espcrc2 style (version 2.5, included; hep-ph version, 2.6, contains a bug). Invited report at the Workshop ``QCD and QED in Higher Order", Rheinsberg, April 1996, to appear in Proceeding

Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the HTL approximation

We evaluate the fermion-photon vertex in QED at the one loop level in Hard Thermal Loop approximation and write it in covariant form. The complete vertex can be expanded in terms of 32 basis vectors. As is well known, the fermion-photon vertex and the fermion propagator are related through a Ward-Takahashi Identity (WTI). This relation splits the vertex into two parts: longitudinal (Gamma_L) and transverse (Gamma_T). Gamma_L is fixed by the WTI. The description of the longitudinal part consumes 8 of the basis vectors. The remaining piece Gamma_T is then written in terms of 24 spin amplitudes. Extending the work of Ball and Chiu and Kizilersu et. al., we propose a set of basis vectors T^mu_i(P_1,P_2) at finite temperature such that each of these is transverse to the photon four-momentum and also satisfies T^mu_i(P,P)=0, in accordance with the Ward Identity, with their corresponding coefficients being free of kinematic singularities. This basis reduces to the form proposed by Kizilersu et. al. at zero temperature. We also evaluate explicitly the coefficient of each of these vectors at the above-mentioned level of approximation.Comment: 13 pages, uses RevTe