FIESTA5: numerical high-performance Feynman integral evaluation

Smirnov, A. V.; Shapurov, N. D.; Vysotsky, L. I.

doi:10.48550/arxiv.2110.11660

Cited by 14 publications

(17 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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. It would be interesting to test these computations in the latest version pySecDec 1.5 which contains several important improvements.…”

mentioning

confidence: 99%

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

Lin

Yang

Zhang

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 99%

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

Lin

Yang

Zhang

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…In order to isolate the relevant integration regions in the boundary conditions for the differential equations, we start by re-writing the integrals in a Feynman parametric representation using Symanzik polynomials [113] (with an extra U -like polynomial due to the delta functions in (3)). Using this parameterized form and performing a re-scaling of momenta, we use the asy2.m code included in the FIESTA package to identify the relevant regions of integration [110,111,129]. We find several contributions both from potential and radiation modes, featuring one, two and up to three on-shell fields.…”

mentioning

confidence: 99%

Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion

Dlapa,

Kälin,

Liu

et al. 2021

Preprint

View full text Add to dashboard Cite

We compute the conservative dynamics of non-spinning binaries at fourth Post-Minkowskian order in the large-eccentricity limit, including both potential and radiation-reaction tail effects. This is achieved by obtaining the scattering angle in the worldline effective field theory approach and deriving the bound radial action via analytic continuation. The associated integrals are bootstrapped to all orders in velocities through differential equations, with boundary conditions in the potential and radiation regions. The large angular momentum expansion captures all the local-in-time effects as well as the trademark logarithmic corrections for generic bound orbits. We briefly discuss strategies to extend the full result to the case of small eccentricities, as well as the inclusion of memory terms. Agreement is found in the overlap with the state-of-the-art in Post-Newtonian theory.

show abstract

“…The results for the DB integrals agree with the Ussyukina-Davydychev box functions expansion. We have also performed numerical checks of all our results using FIESTA mathematica package [54,55]. See appendix A for details.…”

Section: N = 5 Point Amplitudementioning

confidence: 99%

“…For the P B[(p 1 l)] integral we found it more convenient to evaluate the coefficients before log 2 , log and the constant term numerically and then fit them with rational numbers and ζ 2 , ζ 3 correspondingly. We 9 utilize the expansion by regions (see, e.g., Ref [67]) and Quasi Monte Carlo integrator [68] implemented in the FIESTA5 package [55]. To circumvent problems with spurious singularities in certain regions, we shift all the propagator by an integer multiple of an additional regularization parameter λ (see Ref.…”

Section: Pentabox and Other Integralsmentioning

confidence: 99%

Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch

Bork,

Muzhichkov,

Sozinov

2022

Preprint

View full text Add to dashboard Cite

We investigate the structure of the five-point W boson scattering amplitude in N = 4 SYM on the Coulomb branch in a small mass limit. We show that up to two loops the IR divergences exponentiate and are controlled by the Γ oct anomalous dimension similar to the four-point amplitude case considered recently in the literature. We also make a conjecture regarding the all-loop structure of the five-point amplitude.

show abstract

FIESTA5: numerical high-performance Feynman integral evaluation

Cited by 14 publications

References 34 publications

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

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

Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion

Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch

Contact Info

Product

Resources

About