Efficient Numerical Evaluation of Feynman Integral

Zhao Li, Jian Wang, Qi-Shu Yan, Xiaoran Zhao
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, P.R. China
arXiv:1508.02512 [hep-ph], (11 Aug 2015)

   title={Efficient Numerical Evaluation of Feynman Integral},

   author={Li, Zhao and Wang, Jian and Yan, Qi-Shu and Zhao, Xiaoran},






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Feynman loop integral is the key ingredient of high order radiation effect, which is responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing quasi-Monte Carlo method associated with the technique of CUDA/GPU. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in physical kinematic region can be evaluated in less than half minute with $mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for the precise investigation on the high order effect in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with finite top quark mass.
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