Numerical computation of two-loop box diagrams with masses

[1]  J. Fujimoto,et al.  GRACE at ONE-LOOP: Automatic calculation of 1-loop diagrams in the electroweak theory with gauge parameter independence checks , 2003, hep-ph/0308080.

[2]  J. Vermaseren,et al.  New algorithms for one-loop integrals , 1990 .

[3]  Yoshimitsu Shimizu,et al.  Numerical Approach to One-Loop Integrals , 1992 .

[4]  N. Greiner,et al.  Automated one-loop calculations with GoSam , 2011, 1111.2034.

[5]  Y. Kurihara,et al.  Numerical approach to multi-loop integrals , 2012, 1201.6127.

[6]  F. Yuasa,et al.  Toward Automatic Regularization for Feynman Loop Integrals in Perturbative Quantum Field Theory , 2012 .

[7]  Fukuko Yuasa,et al.  Regularization of IR divergent loop integrals , 2012 .

[8]  Fukuko Yuasa.  Precise Numerical Results of IR-vertex and box integration with Extrapolation Method , 2009 .

[9]  S. Weinzierl,et al.  Multiparton NLO corrections by numerical methods , 2011, 1112.3521.

[10]  Robert Piessens,et al.  Quadpack: A Subroutine Package for Automatic Integration , 2011 .

[11]  Paul Roman,et al.  The Analytic S-Matrix , 1967 .

[12]  G. Passarino,et al.  Algebraic-numerical evaluation of Feynman diagrams: two-loop self-energies , 2001, hep-ph/0112004.

[13]  D. Soper,et al.  Numerical integration of one-loop Feynman diagrams for N-photon amplitudes , 2006, hep-ph/0610028.

[14]  G. Ossola,et al.  Tensorial reconstruction at the integrand level , 2010, 1008.2441.

[15]  Shujun Li,et al.  On Iterated Numerical Integration , 2005, International Conference on Computational Science.

[16]  J. Fujimoto,et al.  Numerical Evaluation of Feynman Integrals by a Direct Computation Method , 2008 .

[17]  P. Wynn,et al.  On a Device for Computing the e m (S n ) Transformation , 1956 .

[18]  Rikkert Frederix,et al.  Automation of one-loop QCD computations , 2011, 1103.0621.

[19]  S. Kawabata,et al.  A new version of the multi-dimensional integration and event generation package BASES/SPRING , 1995 .

[20]  Gudrun Heinrich,et al.  Golem95C: A library for one-loop integrals with complex masses , 2011, Comput. Phys. Commun..

[21]  Nakanish.  Graph Theory and Feynman Integrals , 1971 .

[22]  S. Laporta,et al.  difference equations , 2001 .

[23]  Yoshimitsu Shimizu,et al.  Radiative Corrections to e+e− Reactions in Electroweak Theory , 1990 .

[24]  N. Greiner,et al.  GoSam: A program for automated one-loop calculations , 2011, 1111.6534.

[25]  G. Tiktopoulos.  HIGH-ENERGY BEHAVIOR OF FEYNMAN AMPLITUDES , 1963 .

[26]  B. Burrows,et al.  Lower bounds for quartic anharmonic and double‐well potentials , 1993 .

[27]  S. Bauberger,et al.  Simple one-dimensional integral representations for two-loop self-energies: the master diagram , 1995 .

[28]  C. Anastasiou,et al.  Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically , 2007, hep-ph/0703282.

[29]  Toyohisa Kaneko,et al.  Numerical contour integration for loop integrals , 2006, Comput. Phys. Commun..

[30]  E. Doncker,et al.  Loop integration results using numerical extrapolation for a non-scalar integral , 2004, hep-ph/0405098.

[31]  Nobuyuki Hamaguchi,et al.  Numerical precision control and GRACE , 2006 .

[32]  Shujun Li,et al.  Regularization and Extrapolation Methods for Infrared Divergent Loop Integrals , 2005, International Conference on Computational Science.

[33]  D. Maitre,et al.  An Automated Implementation of On-shell Methods for One-Loop Amplitudes , 2008, 0803.4180.

[34]  F. Yuasa,et al.  Parallel computation of Feynman loop integrals , 2012 .

[35]  Elise de Doncker,et al.  Computation of loop integrals using extrapolation , 2004 .

[36]  T. Gleisberg,et al.  Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders , 2009, 0907.1984.

[37]  Junpei Fujimoto,et al.  New implementation of the sector decomposition on FORM , 2009, 0902.2656.

[38]  T. Hahn,et al.  Automatic loop calculations with FeynArts, FormCalc, and LoopTools , 2000 .

[39]  D. Kreimer,et al.  The master two-loop two-point function. The general case , 1991 .

[40]  G. Zanderighi,et al.  On the numerical evaluation of one-loop amplitudes: the gluonic case , 2008, 0805.2152.

[41]  D. Shanks.  Non‐linear Transformations of Divergent and Slowly Convergent Sequences , 1955 .

[42]  Elise de Doncker,et al.  Transformation, Reduction and Extrapolation Techniques for Feynman Loop Integrals , 2010, ICCSA.

[43]  T. Binoth,et al.  golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs , 2008, Comput. Phys. Commun..

[44]  Elise de Doncker,et al.  Quadpack computation of Feynman loop integrals , 2012, J. Comput. Sci..

[45]  G. Passarino,et al.  Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations , 2003, hep-ph/0311186.

[46]  Elise de Doncker,et al.  On a Numerical Evaluation of Loop Integrals , 2003 .

[47]  R. Pittau,et al.  Automated one-loop calculations: a proof of concept , 2009, 0903.4665.

[48]  T. Sasaki,et al.  How to Calculate One-Loop Diagrams , 1989 .

[49]  J. FUJIMOTO,et al.  NUMERICAL APPROACH TO TWO-LOOP THREE POINT FUNCTIONS WITH MASSES , 1995 .

[50]  P. Wynn,et al.  On the Convergence and Stability of the Epsilon Algorithm , 1966 .