ABSTRACT: This paper describes applications of extrapolation for the computation of
coefficients in an expansion of infrared divergent integrals. An extrapolation
procedure is performed with respect to a parameter introduced by dimensional
regularization. While this treats typical IR singularities at the boundaries of
the integration domain, special care needs to be taken in cases where the
integrand is singular in the interior of the domain as well as on the
boundaries. A double extrapolation is devised for a class of massless vertex
integrals. Quadruple precision results are presented, demonstrating high
accuracy. The computations are supported by the use of general adaptive
integration programs from the QUADPACK package, in iterated integrations with
highly singular integrand functions.
Computational Science and Its Applications - ICCSA 2010, International Conference, Fukuoka, Japan, March 23-26, 2010, Proceedings, Part II; 01/2010
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human 2009, Seoul, Korea, 24-26 November 2009; 01/2009
Computational Science - ICCS 2005, 5th International Conference, Atlanta, GA, USA, May 22-25, 2005, Proceedings, Part I; 01/2005
ABSTRACT: We present a class of methods for the evaluation of loop integrals based on extrapolation. The method is based on generating a sequence of approximations which converge to the loop integral value as a parameter ε introduced in the integrand tends to zero. We examine the applicability of linear and non-linear extrapolation processes. Test results are given for one-loop three-point vertex and four-point functions and for a two-loop vertex diagram. 2004 Elsevier B.V. All rights reserved.
Computer Physics Communications 01/2004; 159:145-156. · 3.27 Impact Factor
ABSTRACT: Overview. ♦ The two-loop crossed vertex diagram gives rise to a six-dimensional integral, where the outer integration is over the simplex z 1 +z 2 +z 3 = 1 and the inner integration over the hyper-rectangle [−1, +1] 3 . The factor 1/D 2 3 in the integrand has a non-integrable singularity interior to the integration domain and a singularity on the boundary. ♦ The integral can be evaluated by iterated numerical integration.
ABSTRACT: The 0(α) radiative corrections to e^ + e^ - -> bar tt are
calculated in the standard SU(2)×U(1) theory keeping the top quark
mass. The contribution of the hard photon emission is included with
suitable experimental cuts. We found that the 1-loop vertex diagrams for
the top quark give rise to a fairly large correction in the order of 5%
to the differential cross-section. Effects of the Higgs boson exchange
are also discussed.
Modern Physics Letters A 3:581-587. · 1.08 Impact Factor