BlackHat

Automated implementation of on-shell methods for one-loop amplitudes. We present the first results from BlackHat, an automated C++ program for calculating one-loop amplitudes. The program implements the unitarity method and on-shell recursion to construct amplitudes. As input to the calculation, it uses compact analytic formulæ for tree amplitudes for four-dimensional helicity states. The program performs all related computations numerically. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, introducing a discrete Fourier projection as a means of improving efficiency and numerical stability. We illustrate the numerical stability of our approach by computing and analyzing six-, seven-, and eight-gluon amplitudes in QCD and comparing against previously obtained analytic results.


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  1. Abreu, S.; Dormans, J.; Febres Cordero, F.; Ita, H.; Page, B.; Sotnikov, V.: Analytic form of the planar two-loop five-parton scattering amplitudes in QCD (2019)
  2. Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu; Peraro, Tiziano: Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case (2019)
  3. Bourjaily, Jacob L.; Dulat, Falko; Panzer, Erik: Manifestly dual-conformal loop integration (2019)
  4. De Laurentis, Giuseppe; Maître, Daniel: Extracting analytical one-loop amplitudes from numerical evaluations (2019)
  5. Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav: Prescriptive unitarity (2017)
  6. Frellesvig, Hjalte; Papadopoulos, Costas G.: Cuts of Feynman integrals in Baikov representation (2017)
  7. Bjerrum-Bohr, N. E. J.; Donoghue, John F.; Holstein, Barry R.; Planté, Ludovic; Vanhove, Pierre: Light-like scattering in quantum gravity (2016)
  8. Conkey, Peter; Dubovsky, Sergei: Four loop scattering in the Nambu-Goto theory (2016)
  9. Hahn, Thomas: Computer algebra in high-energy physics (invited talk) (2016)
  10. Hirschi, Valentin; Peraro, Tiziano: Tensor integrand reduction via Laurent expansion (2016)
  11. Johansson, Henrik; Ochirov, Alexander: Color-kinematics duality for QCD amplitudes (2016)
  12. Peraro, Tiziano: Scattering amplitudes over finite fields and multivariate functional reconstruction (2016)
  13. Bailey, David H.; Borwein, Jonathan M.: High-precision arithmetic in mathematical physics (2015)
  14. Bury, M.; van Hameren, A.: Numerical evaluation of multi-gluon amplitudes for high energy factorization (2015)
  15. Gerwick, Erik; Schumann, Steffen; Höche, Stefan; Marzani, Simone: Soft evolution of multi-jet final states (2015)
  16. Alwall, J.; Frederix, R.; Frixione, S.; Hirschi, V.; Maltoni, F.; Mattelaer, O.; Shao, H.-S.; Stelzer, T.; Torrielli, P.; Zaro, M.: The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations (2014)
  17. Guillet, J. Ph.; Heinrich, G.; von Soden-Fraunhofen, J. F.: Tools for NLO automation: Extension of the golem95C integral library (2014)
  18. Peraro, Tiziano: Ninja: automated integrand reduction via Laurent expansion for one-loop amplitudes (2014)
  19. Batista, Carlos; Carneiro da Cunha, Bruno: Spinors and the Weyl tensor classification in six dimensions (2013)
  20. Donati, Alice M.; Pittau, Roberto: Gauge invariance at work in FDR: (H\to\gamma\gamma) (2013)

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