Application of the DRA method to the calculation of the four-loop QED-type tadpoles

We apply the DRA method to the calculation of the four-loop `QED-type' tadpoles. For arbitrary space-time dimensionality D the results have the form of multiple convergent sums. We use these results to obtain the epsilon-expansion of the integrals around D=3 and D=4.Comment: References added, some typos corrected. Results unchange

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the extraction of ultraviolet and infrared divergencies. The coefficients of these singularities and the non-singular part can be integrated numerically. However, the numerical integration often does not converge for diagrams with massive propagators and physical branch cuts. In this work, several steps are proposed which substantially improve the behavior of the numerical integrals. The efficacy of the method is demonstrated by calculating several two-loop examples, some of which have not been known before.Comment: 13 pp. LaTe

On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes

We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms of master integrals can be realized through polynomial fitting of the integrand, without any apriori knowledge of the integral basis. We discuss how the polynomial shapes of the residues determine the basis of master integrals appearing in the final result. We present a four-dimensional constructive algorithm that we apply to planar and non-planar contributions to the 4- and 5-point MHV amplitudes in N=4 SYM. The technique hereby discussed extends the well-established analogous method holding for one-loop amplitudes, and can be considered a preliminary study towards the systematic reduction at the integrand-level of two-loop amplitudes in any gauge theory, suitable for their automated semianalytic evaluation.Comment: 26 pages, 11 figure

Second order QCD corrections to inclusive semileptonic b \to Xc l \bar \nu_l decays with massless and massive lepton

We extend previous computations of the second order QCD corrections to semileptonic b \to c inclusive transitions, to the case where the charged lepton in the final state is massive. This allows accurate description of b \to c \tau \bar \nu_\tau decays. We review techniques used in the computation of O(\alpha_s^2) corrections to inclusive semileptonic b \to c transitions and present extensive numerical studies of O(\alpha_s^2) QCD corrections to b \to c l \bar \nu_l decays, for l =e, \tau.Comment: 30 pages, 4 figures, 5 table

IBP methods at finite temperature

We demonstrate the applicability of integration-by-parts (IBP) identities in finite-temperature field theory. As a concrete example, we perform 3-loop computations for the thermodynamic pressure of QCD in general covariant gauges, and confirm earlier Feynman-gauge results.Comment: 16 pages, 4 Axodraw figure