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. Guillet, J.Ph.; Heinrich, G.; von Soden-Fraunhofen, J.F.: Tools for NLO automation: Extension of the golem95C integral library (2014)
  2. Donati, Alice M.; Pittau, Roberto: Gauge invariance at work in FDR: $H\to \gamma\gamma$ (2013)
  3. Søgaard, Mads: Global residues and two-loop hepta-cuts (2013)
  4. Søgaard, Mads; Zhang, Yang: Multivariate residues and maximal unitarity (2013)
  5. Anastasiou, Charalampos; Herzog, Franz; Lazopoulos, Achilleas: The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD (2012)
  6. Bailey, D.H.; Barrio, R.; Borwein, J.M.: High-precision computation: mathematical physics and dynamics (2012)
  7. Britto, Ruth; Mirabella, Edoardo: External leg corrections in the unitarity method (2012)
  8. Ita, Harald; Ozeren, Kemal: Colour decompositions of multi-quark one-loop QCD amplitudes (2012)
  9. Pittau, R.: Primary Feynman rules to calculate the $\epsilon$-dimensional integrand of any 1-loop amplitude (2012)
  10. Yuasa, F.; de Doncker, E.; Hamaguchi, N.; Ishikawa, T.; Kato, K.; Kurihara, Y.; Fujimoto, J.; Shimizu, Y.: Numerical computation of two-loop box diagrams with masses (2012)
  11. Alioli, Simone; Nason, Paolo; Oleari, Carlo; Re, Emanuele: Vector boson plus one jet production in POWHEG (2011)
  12. Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F.; Caron-Huot, S.; Trnka, J.: The all-loop integrand for scattering amplitudes in planar $\cal N = 4$ SYM (2011)
  13. Badger, S.; Biedermann, B.; Uwer, P.: NGluon: A package to calculate one-loop multi-gluon amplitudes (2011)
  14. Bern, Zvi; Carrasco, John Joseph; Dixon, Lance J.; Johansson, Henrik; Roiban, Radu: Amplitudes and ultraviolet behavior of $\cal N=8$ supergravity (2011)
  15. Bjerrum-Bohr, N.E.J.; Damgaard, P.H.; Johansson, H.; Søndergaard, T.: Monodromy-like relations for finite loop amplitudes (2011)
  16. Boughezal, Radja; Ridder, Aude Gehrmann-De; Ritzmann, Mathias: Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours (2011)
  17. Britto, Ruth; Mirabella, Edoardo: Single cut integration (2011)
  18. Bullimore, Mathew: Inverse soft factors and Grassmannian residues (2011)
  19. Campanario, Francisco: Towards $pp \to VVjj$ at NLO QCD: bosonic contributions to triple vector boson production plus jet (2011)
  20. Dixon, Lance J.: Scattering amplitudes: the most perfect microscopic structures in the universe (2011)

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