Abstract
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the αα s corrections to Drell-Yan lepton production with up to one massive vector boson in physical kinematics. As a reference, we evaluate these planar and non-planar integrals by the method of differential equations through to weight five. Choosing a basis of finite integrals for the numerical evaluation with SecDec 3 leads to tremendous performance improvements and renders the otherwise problematic seven-line topologies numerically accessible. As another example, basis integrals for massless QCD three loop form factors are evaluated with FIESTA 4. Here, employing a basis of finite integrals results in an overall speedup of more than an order of magnitude.
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von Manteuffel, A., Schabinger, R.M. Numerical multi-loop calculations via finite integrals and one-mass EW-QCD Drell-Yan master integrals. J. High Energ. Phys. 2017, 129 (2017). https://doi.org/10.1007/JHEP04(2017)129
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DOI: https://doi.org/10.1007/JHEP04(2017)129