Efficient numerical evaluation of Feynman integrals

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Zhao Li, Jian Wang, Qi-Shu Yan and Xiaoran Zhao. Efficient numerical evaluation of Feynman integrals[J]. Chinese Physics C, 2016, 40(3): 033103. doi: 10.1088/1674-1137/40/3/033103
Zhao Li, Jian Wang, Qi-Shu Yan and Xiaoran Zhao. Efficient numerical evaluation of Feynman integrals[J]. Chinese Physics C, 2016, 40(3): 033103.  doi: 10.1088/1674-1137/40/3/033103 shu
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Received: 2015-08-13
Revised: 2015-10-23
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    Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

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Efficient numerical evaluation of Feynman integrals

    Corresponding author: Zhao Li,
    Corresponding author: Jian Wang,
    Corresponding author: Qi-Shu Yan,
    Corresponding author: Xiaoran Zhao,
  • 1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
  • 2. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 3.  PRISMA Cluster of Excellence &
  • 4. School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 5. Center for High-Energy Physics, Peking University, Beijing 100871, China
  • 6. School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:  Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

Abstract: Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. 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 the physical kinematic region can be evaluated in less than half a minute with O(10-3) accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.

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