Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case

Self Cite

We present the first numerical results for the two-loop helicity amplitudes for the scattering of four partons and a W -boson in QCD. We use a finite field sampling method to reduce directly from Feynman diagrams to the coefficients of a set of master integrals after applying integration-by-parts identities. Since the basis of master integrals is not yet fully known analytically, we identify a set of master integrals with a simple divergence structure using local numerator insertions. This allows for accurate numerical evaluation of the amplitude using sector decomposition methods.

Section: Discussionmentioning

confidence: 99%

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons

Hartanto

Badger

Brønnum-Hansen

et al. 2019

Self Cite

“…Our six-particle results represent a natural step forward in complexity, following recent developments at two loops for five particles [60][61][62][63][64][67][68][69][70][71][72]. It furthermore opens up avenues for exploring a potential extension of dual conformal symmetry beyond the planar limit [44,55,56,[73][74][75] as well as an extension of the empirical second entry conditions for five-particle amplitudes [76].…”

Section: 2)mentioning

confidence: 66%

Prescriptive unitarity for non-planar six-particle amplitudes at two loops

Bourjaily

Herrmann

Langer

et al. 2019

We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all softcollinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as ancillary files to this work's submission to the arXiv. arXiv:1909.09131v1 [hep-th]

“…With the success of Large Hadron Collider (LHC) Run II and the upcoming LHC run III, high precision background computation, especially next-to-next-to-leading-order (NNLO) scattering computation, is crucial for the interpretation of experimental results. In recent years, great progress has been made in multi-loop scattering amplitude calculations, for instance, in the case of 2 → 3 processes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The progress is due to modern developments of scattering amplitudes, like the integrand construction method [16,17], canonical integrals [18,19], numeric unitarity [20,21], bootstrap methods [22][23][24][25][26][27][28][29], reconstruction using finite fields [30][31][32][33] and new ideas in the integration-by-parts (IBP) reduction.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, it is possible to numerically generate and reduce the IBP relations, and, while skipping the IBP coefficient reconstruction, directly carry out an amplitude reconstruction. (For examples, see [9,10,13,50]). In this paper, we in particular present our own implementation of a semi-numeric rational interpolation method, see Appendix A for more details.…”

Section: Introductionmentioning

confidence: 99%

Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

Bendle

Boehm

Decker

et al. 2020

We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the computer algebra system Singular with the workflow management system GPI-Space, which are being developed at the TU Kaiserslautern and the Fraunhofer Institute for Industrial Mathematics (ITWM), respectively. In our approach, the IBP relations are first trimmed by modern tools from computational algebraic geometry and then solved by sparse linear algebra and our new interpolation method. Modelled in terms of Petri nets, these steps are efficiently automatized and automatically parallelized by GPI-Space. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point nonplanar double-pentagon integrals. We also use GPI-Space to convert the basis of IBP reductions, and discuss the possible simplification of IBP coefficients in a uniformly transcendental basis.