Numerical multi-loop calculations: tools and applications

We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like multi-loop integrals.

[1]  A. V. Smirnov,et al.  FIESTA 3: Cluster-parallelizable multiloop numerical calculations in physical regions , 2013, Comput. Phys. Commun..

[2]  Gudrun Heinrich,et al.  Massive non-planar two-loop four-point integrals with SecDec 2.1 , 2013, Comput. Phys. Commun..

[3]  T. Zirke,et al.  Calculation of Multi-Loop Integrals with SecDec-3.0 , 2016, 1601.03982.

[4]  T. Riemann,et al.  Numerical evaluation of tensor Feynman integrals in Euclidean kinematics , 2010, 1010.1667.

[5]  Gudrun Heinrich,et al.  Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0 , 2012, Comput. Phys. Commun..

[6]  G. Bell,et al.  Analytic regularization in Soft-Collinear Effective Theory , 2011, 1112.3907.

[7]  T. Binoth,et al.  An automatized algorithm to compute infrared divergent multi-loop integrals , 2000 .

[8]  C. Studerus,et al.  Reduze - Feynman integral reduction in C++ , 2009, Comput. Phys. Commun..

[9]  Gudrun Heinrich,et al.  SecDec: A general program for sector decomposition , 2010, Comput. Phys. Commun..

[10]  A. V. Smirnov,et al.  Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA) , 2008, Comput. Phys. Commun..

[11]  Christian Bogner,et al.  Operating system: Unix , 1983 .

[12]  Gudrun Heinrich,et al.  SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop , 2015, Comput. Phys. Commun..

[13]  S. Stieberger,et al.  Differential equations, associators, and recurrences for amplitudes , 2015, 1507.01582.

[14]  Gudrun Heinrich,et al.  Sector Decomposition , 2008, 0803.4177.

[15]  Takahiro Ueda,et al.  A geometric method of sector decomposition , 2009, Comput. Phys. Commun..

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

[17]  P. Nogueira.  Automatic Feynman graph generation , 1993 .