Efficient Numerical Evaluation of Feynman Integral

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 $\mathcal{O}(10^{-3})$ 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.

8 pages, 5 figures, published in Chinese Physics C

References in corpus (12)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Big-Bang Nucleosynthesis
• Higgs boson gluon-fusion production in N3LO QCD
• Higgs boson production in association with a jet at next-to-next-to-leading order
• Precise QCD predictions for the production of Higgs+jet final states
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• Sector decomposition via computational geometry

Cited by in corpus (28)

• Higgs boson pair production in gluon fusion at NLO with full top-quark mass dependence
• Full top quark mass dependence in Higgs boson pair production at NLO
• Higgs boson pair production at NNLO with top quark mass effects
• Collider Physics at the Precision Frontier
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• NLO QCD corrections to Higgs boson plus jet production with full top-quark mass dependence
• Higgs boson pair production via gluon fusion at N${}^3$LO in QCD
• The gluon-fusion production of Higgs boson pair: N${}^3$LO QCD corrections and top-quark mass effects
• Numerical Scattering Amplitudes with pySecDec
• Mixed QCD-EW corrections for Higgs boson production at $e^{+}{e}^{-}$ colliders
• $ZH$ production in gluon fusion: two-loop amplitudes with full top quark mass dependence
• Two-loop helicity amplitudes for $gg\to ZZ$ with full top-quark mass effects
• N${}^3$LO+N${}^3$LL QCD improved Higgs pair cross sections
• ZH production in gluon fusion at NLO in QCD
• Full-color three-loop three-point form factors in N=4 SYM
• Evaluating multi-loop Feynman integrals numerically through differential equations
• Comparing Machine Learning and Interpolation Methods for Loop-Level Calculations
• Fiducial cross sections for the four-lepton decay mode in Higgs-plus-jet production up to NNLO QCD
• HepLib: A C++ Library for High Energy Physics
• Discovery potential of Higgs boson pair production through 4$\ell$+$E/$ final states at a 100 TeV collider
• Specific three-loop contributions to $b\to s\gamma$ associated with the current-current operators
• Next-to-Leading Order Corrections to Higgs Boson Pair Production in Gluon Fusion
• Top-quark mass effects in H+jet and H+2 jets production
• Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields
• Numerical evaluation of multi-loop integrals
• A general approach to quantum integration of cross sections in high-energy physics
• Top quark mass effects in HJ production at NLO
• Laplace method for the simplest diagrams of elastic scattering of scalar particles