Numerical loop calculations

Precision calculations for multi-parton final states

Higher order calculations in perturbation theory are essential for precision physics. The LHC experiments have data for multi-jet final states (depending on the process roughly up to seven jets) and it is desirable to have NLO predictions for those processes. A numerical apporach is well-suited for multi-parton final states. The motivation for a numerical approach is as follows: The ultimate limitation on the number of final-state partons is the available computing power. A relevant quantity in this context is the scaling behaviour of the required CPU time for the matrix element with the number of final-state particles n. The numerical approach has the best scaling behaviour in CPU time with respect to the number of external particles among all known methods for the computation of NLO corrections (n³-scaling behaviour for the numerical approach as compared to a n⁸- or n⁹-scaling behaviour for unitarity-based methods). Within the numerical approach one uses the subtraction method and contour deformation in order to perform the loop integration numerically.

Talks on this subject:

• Talk given at Loops and Legs, Wörlitz, April 2010, arXiv:1006.4609 [hep-ph].

Selected publications on this subject:

• Satyajit Seth and Stefan Weinzierl, Numerical integration of subtraction terms, Phys.Rev. D93 (2016), 114031, arXiv:1605.06646 [hep-ph].
• S. Becker, D. Götz, Ch. Reuschle, Ch. Schwan and S. Weinzierl, NLO results for five, six and seven jets in electron-positron annihilation, Phys.Rev.Lett. 108 (2012), 032005, arXiv:1111.1733 [hep-ph].
• Sebastian Becker, Christian Reuschle and Stefan Weinzierl, Numerical NLO QCD calculations, JHEP 1012 (2010) 013, arXiv:1010.4187 [hep-ph].
• Mohammad Assadsolimani, Sebastian Becker and Stefan Weinzierl, A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes, Phys.Rev. D81 (2010) 094002, arXiv:0912.1680 [hep-ph].