Expansion by regions with pySecDec

Heinrich, G.; Jahn, S.; Jones, Stephen; Kerner, M.; Langer, F.; Magerya, Vitaly; Poldaru, A.; Schlenk, J.; Villa, Emilio

doi:10.1016/j.cpc.2021.108267

Cited by 40 publications

(29 citation statements)

References 39 publications

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“…To evaluate the master integrals, we applied sector decomposition as implemented in the program pySecDec [48,49], using a quasi-Monte Carlo algorithm [49,50] for the numerical integration. In particular, we made use of one of the new features of pySecDec [51] to integrate a weighted sum of integrals such that the number of sampling points used for each integral is dynamically set, according to its contribution to the total uncertainty of the amplitude.…”

Section: Virtual Two-loop Contributionsmentioning

confidence: 99%

ZH production in gluon fusion at NLO in QCD

Chen,

Davies,

Heinrich

et al. 2022

Preprint

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We present fully differential next-to-leading order results for Higgs production in association with a Z boson in gluon fusion. Our two-loop virtual contributions are evaluated numerically using sector decomposition, including full top-quark mass effects, and supplemented at high p T by an analytic high-energy expansion to order (m 4 Z , m 4 H , m 32 t ). Using the expanded results we also present a study of the top-quark mass scheme uncertainty at large p T .

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Section: Virtual Two-loop Contributionsmentioning

confidence: 99%

ZH production in gluon fusion at NLO in QCD

Chen,

Davies,

Heinrich

et al. 2022

Preprint

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“…Recently, pySecDec develops some interesting new functions[128] like expansion by regions and automatic summation in the version 1.5, which was not applied in our calculation. Also, the new FIESTA5 has been published in[129] 22.…”

mentioning

confidence: 99%

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Lin

Yang

Zhang

2022

J. High Energ. Phys.

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We present the detailed computation of full-color three-loop three-point form factors of both the stress-tensor supermultiplet and a length-three BPS operator in 𝒩 = 4 SYM. The integrands are constructed based on the color-kinematics (CK) duality and generalized unitarity method. An interesting observation is that the CK-dual integrands contain a large number of free parameters. We discuss the origin of these free parameters in detail and check that they cancel in the simplified integrands. We further perform the numerical evaluation of the integrals at a special kinematics point using public packages FIESTA and pySecDec based on the sector-decomposition approach. We find that the numerical computation can be significantly simplified by expressing the integrals in terms of uniformly transcendental basis, although the final three-loop computations still require large computational resources. Having the full-color numerical results, we verify that the non-planar infrared divergences reproduce the non-dipole structures, which firstly appear at three loops. As for the finite remainder functions, we check that the numerical planar remainder for the stress-tensor supermultiplet is consistent with the known result of the bootstrap computation. We also obtain for the first time the numerical results of the three-loop non-planar remainder for the stress-tensor supermultiplet as well as the three-loop remainder for the length-three operator.

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“…A possible way to control this behavior has been proposed in Ref. [47]. Together with the absolute integration error, the improvement factors also start to fluctuate strongly for large energies.…”

Section: Performancementioning

confidence: 99%

“…They can be dealt with by a deformation of the integration contour into the complex plane [39][40][41][42]. An automated procedure to do so has been implemented for the first time in SECDEC [43] and has been refined in SECDEC-3 [44] and pySECDEC [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Targeting multi-loop integrals with neural networks

et al. 2022

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Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the chosen contour. We present methods to optimize this contour using a combination of optimized, global complex shifts and a normalizing flow. They can lead to a significant gain in precision.

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Expansion by regions with pySecDec

Cited by 40 publications

References 39 publications

ZH production in gluon fusion at NLO in QCD

ZH production in gluon fusion at NLO in QCD

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Targeting multi-loop integrals with neural networks

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