Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically

Abstract

We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an appropriate contour deformation. We have validated our technique comparing with recent analytic results for the gg → h two-loop amplitudes with heavy quarks and scalar quarks.

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts

“…Second, in this review we did not talk about attempts to design a framework where one-loop computations can be performed by pure numerical methods [33,34,35,36,37,38,39,40,44,41,42,43,44,139]. It will be interesting to see how numerical methods will develop in the future, given the robust seminumerical nature of the OPP approach and recent attempts to automate it [17,124].…”

“…As a final remark we note that other approaches to one-loop calculations beyond traditional Passarino-Veltman reduction and generalized unitarity have have been studied in the literature [33,34,35,36,37,38,39,40,41,42,43,44], but we will not discuss them in this review.…”

Efficiency improvements for the numerical computation of NLO corrections

“…The calculation has been performed with a method, which uses numerical Monte Carlo integration for the computation of the one-loop amplitude. To render this part finite, the subtraction method [2][3][4][5] and a contour deformation [2,3,[6][7][8][9][10][11] have been used. Also, it has been the first time ever that the numerical method has been applied to a cutting-edge process.…”

“…The basic principles how the virtual corrections are calculated within the numerical method have already been discussed in the literature [2][3][4][5][6][7][8][9][10][11]. What is missing in the literature is information on how this can be done efficiently.…”

Developments in QCD

“…Furthermore, numerical [47,48] and semi-numerical [49] techniques for loop integrals have progressed to the level where much work taken care of for the user through programs like Blackhat [50], Cuttools [51], or Rocket [52].…”