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Ninja: automated integrand reduction via Laurent expansion for one-loop amplitudes. (English) Zbl 1360.81021
Summary: We present the public C++ library Ninja, which implements the Integrand Reduction via Laurent Expansion method for the computation of one-loop integrals. The algorithm is suited for applications to complex one-loop processes.

MSC:
81-04 Software, source code, etc. for problems pertaining to quantum theory
81-08 Computational methods for problems pertaining to quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
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[1] Cachazo, F.; Svrcek, P.; Witten, E., MHV vertices and tree amplitudes in gauge theory, J. High Energy Phys., 0409, 006, (2004)
[2] Britto, R.; Cachazo, F.; Feng, B., New recursion relations for tree amplitudes of gluons, Nuclear Phys., B715, 499-522, (2005) · Zbl 1207.81088
[3] Britto, R.; Cachazo, F.; Feng, B.; Witten, E., Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett., 94, 181602, (2005)
[4] Bern, Z.; Dixon, L. J.; Dunbar, D. C.; Kosower, D. A., One loop n point gauge theory amplitudes, unitarity and collinear limits, Nuclear Phys., B425, 217-260, (1994) · Zbl 1049.81644
[5] Britto, R.; Cachazo, F.; Feng, B., Generalized unitarity and one-loop amplitudes in \(N = 4\) super-Yang-Mills, Nuclear Phys., B725, 275-305, (2005) · Zbl 1178.81202
[6] Ossola, G.; Papadopoulos, C. G.; Pittau, R., Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nuclear Phys., B763, 147-169, (2007) · Zbl 1116.81067
[7] Ellis, R. K.; Giele, W.; Kunszt, Z., A numerical unitarity formalism for evaluating one-loop amplitudes, J. High Energy Phys., 0803, 003, (2008)
[8] Mastrolia, P.; Ossola, G., On the integrand-reduction method for two-loop scattering amplitudes, J. High Energy Phys., 1111, 014, (2011) · Zbl 1306.81357
[9] Badger, S.; Frellesvig, H.; Zhang, Y., Hepta-cuts of two-loop scattering amplitudes, J. High Energy Phys., 1204, 055, (2012) · Zbl 1348.81340
[10] Zhang, Y., Integrand-level reduction of loop amplitudes by computational algebraic geometry methods, J. High Energy Phys., 1209, 042, (2012)
[11] Mastrolia, P.; Mirabella, E.; Ossola, G.; Peraro, T., Scattering amplitudes from multivariate polynomial division, Phys. Lett., B718, 173-177, (2012)
[12] Mastrolia, P.; Mirabella, E.; Ossola, G.; Peraro, T., Multiloop integrand reduction for dimensionally regulated amplitudes, Phys. Lett., B727, 532-535, (2013) · Zbl 1331.81218
[13] Ossola, G.; Papadopoulos, C. G.; Pittau, R., Cuttools: a program implementing the OPP reduction method to compute one-loop amplitudes, J. High Energy Phys., 0803, 042, (2008)
[14] Mastrolia, P.; Ossola, G.; Reiter, T.; Tramontano, F., Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level, J. High Energy Phys., 1008, 080, (2010) · Zbl 1290.81151
[15] Hahn, T.; Perez-Victoria, M., Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun., 118, 153-165, (1999)
[16] van Hameren, A.; Papadopoulos, C.; Pittau, R., Automated one-loop calculations: a proof of concept, J. High Energy Phys., 0909, 106, (2009)
[17] Bevilacqua, G.; Czakon, M.; Garzelli, M.; van Hameren, A.; Kardos, A., Helac-nlo, Comput. Phys. Commun., 184, 986-997, (2013)
[18] Berger, C.; Bern, Z.; Dixon, L.; Febres Cordero, F.; Forde, D., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev., D78, 036003, (2008)
[19] Hirschi, V.; Frederix, R.; Frixione, S.; Garzelli, M. V.; Maltoni, F., Automation of one-loop QCD corrections, J. High Energy Phys., 1105, 044, (2011) · Zbl 1296.81138
[20] Cullen, G.; Greiner, N.; Heinrich, G.; Luisoni, G.; Mastrolia, P., Automated one-loop calculations with gosam, Eur. Phys. J., C72, 1889, (2012)
[21] Cascioli, F.; Maierhofer, P.; Pozzorini, S., Scattering amplitudes with open loops, Phys. Rev. Lett., 108, 111601, (2012)
[22] Badger, S.; Biedermann, B.; Uwer, P., Ngluon: a package to calculate one-loop multi-gluon amplitudes, Comput. Phys. Commun., 182, 1674-1692, (2011) · Zbl 1262.81102
[23] Badger, S.; Biedermann, B.; Uwer, P.; Yundin, V., Numerical evaluation of virtual corrections to multi-jet production in massless QCD, Comput. Phys. Commun., 184, 1981-1998, (2013)
[24] Mastrolia, P.; Mirabella, E.; Peraro, T., Integrand reduction of one-loop scattering amplitudes through Laurent series expansion, J. High Energy Phys., 1206, 095, (2012), arXiv:1203.0291. http://dx.doi.org/10.1007/JHEP11(2012)128. http://dx.doi.org/10.1007/JHEP06(2012)095
[25] van Hameren, A., Oneloop: for the evaluation of one-loop scalar functions, Comput. Phys. Commun., 182, 2427-2438, (2011) · Zbl 1262.81253
[26] van Deurzen, H.; Luisoni, G.; Mastrolia, P.; Mirabella, E.; Ossola, G., NLO QCD corrections to Higgs boson production in association with a top quark pair and a jet, Phys. Rev. Lett., 111, 171801, (2013)
[27] H. van Deurzen, G. Luisoni, P. Mastrolia, E. Mirabella, G. Ossola, et al. Multi-leg one-loop massive amplitudes from integrand reduction via Laurent expansion, arXiv:1312.6678.
[28] J. Vermaseren, New features of FORM. arXiv:math-ph/0010025. · Zbl 1309.68231
[29] Kuipers, J.; Ueda, T.; Vermaseren, J.; Vollinga, J., FORM version 4.0, Comput. Phys. Commun., 184, 1453-1467, (2013) · Zbl 1317.68286
[30] J. Kuipers, T. Ueda, J. Vermaseren, Code optimization in FORM. arXiv:1310.7007. · Zbl 1344.65050
[31] Ellis, R. K.; Zanderighi, G., Scalar one-loop integrals for QCD, J. High Energy Phys., 0802, 002, (2008)
[32] Forde, D., Direct extraction of one-loop integral coefficients, Phys.Rev., D75, 125019, (2007)
[33] del Aguila, F.; Pittau, R., Recursive numerical calculus of one-loop tensor integrals, J. High Energy Phys., 0407, 017, (2004)
[34] Mastrolia, P.; Ossola, G.; Papadopoulos, C.; Pittau, R., Optimizing the reduction of one-loop amplitudes, J. High Energy Phys., 0806, 030, (2008)
[35] Badger, S., Direct extraction of one loop rational terms, J. High Energy Phys., 0901, 049, (2009) · Zbl 1243.81219
[36] Kleiss, R.; Stirling, W. J.; Ellis, S., A new Monte Carlo treatment of multiparticle phase space at high-energies, Comput. Phys. Commun., 40, 359, (1986)
[37] Ossola, G.; Papadopoulos, C. G.; Pittau, R., Numerical evaluation of six-photon amplitudes, J. High Energy Phys., 0707, 085, (2007)
[38] Gounaris, G.; Porfyriadis, P.; Renard, F., The gamma gamma \(\rightarrow\) gamma gamma process in the standard and SUSY models at high-energies, Eur. Phys. J., C9, 673-686, (1999)
[39] C. Bernicot, Light-light amplitude from generalized unitarity in massive QED. arXiv:0804.0749.
[40] Cullen, G.; Koch-Janusz, M.; Reiter, T., Spinney: a form library for helicity spinors, Comput. Phys. Commun., 182, 2368-2387, (2011) · Zbl 1263.65002
[41] Mahlon, G., One loop multi—photon helicity amplitudes, Phys. Rev., D49, 2197-2210, (1994)
[42] Nagy, Z.; Soper, D. E., Numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev., D74, 093006, (2006)
[43] Binoth, T.; Heinrich, G.; Gehrmann, T.; Mastrolia, P., Six-photon amplitudes, Phys. Lett., B649, 422-426, (2007)
[44] Gong, W.; Nagy, Z.; Soper, D. E., Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev., D79, 033005, (2009)
[45] Bernicot, C.; Guillet, J.-P., Six-photon amplitudes in scalar QED, J. High Energy Phys., 0801, 059, (2008)
[46] C. Bernicot, The six-photon amplitude. arXiv:0804.1315.
[47] Beenakker, W.; Dittmaier, S.; Kramer, M.; Plumper, B.; Spira, M., Higgs radiation off top quarks at the tevatron and the LHC, Phys. Rev. Lett., 87, 201805, (2001)
[48] Beenakker, W.; Dittmaier, S.; Kramer, M.; Plumper, B.; Spira, M., NLO QCD corrections to t anti-t H production in hadron collisions, Nuclear Phys., B653, 151-203, (2003)
[49] Dawson, S.; Orr, L.; Reina, L.; Wackeroth, D., Associated top quark Higgs boson production at the LHC, Phys. Rev., D67, 071503, (2003)
[50] Dawson, S.; Jackson, C.; Orr, L.; Reina, L.; Wackeroth, D., Associated Higgs production with top quarks at the large hadron collider: NLO QCD corrections, Phys. Rev., D68, 034022, (2003)
[51] Dittmaier, S.; Kramer; Michael; Spira, M., Higgs radiation off bottom quarks at the tevatron and the CERN LHC, Phys. Rev., D70, 074010, (2004)
[52] van Deurzen, H.; Greiner, N.; Luisoni, G.; Mastrolia, P.; Mirabella, E., NLO QCD corrections to the production of Higgs plus two jets at the LHC, Phys.Lett., B721, 74-81, (2013)
[53] Cullen, G.; van Deurzen, H.; Greiner, N.; Luisoni, G.; Mastrolia, P., NLO QCD corrections to Higgs boson production plus three jets in gluon fusion, Phys. Rev. Lett., 111, 131801, (2013)
[54] van Deurzen, H., Associated Higgs production at NLO with gosam, Acta Phys. Polon., B44, 11, 2223-2230, (2013)
[55] Binoth, T.; Guillet, J.-P.; Heinrich, G.; Pilon, E.; Reiter, T., Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs, Comput. Phys. Commun., 180, 2317-2330, (2009) · Zbl 1197.81004
[56] Cullen, G.; Guillet, J. P.; Heinrich, G.; Kleinschmidt, T.; Pilon, E., Golem95C: a library for one-loop integrals with complex masses, Comput. Phys. Commun., 182, 2276-2284, (2011) · Zbl 1223.81172
[57] J.P. Guillet, G. Heinrich, J. von Soden-Fraunhofen, Tools for NLO automation: extension of the golem95C integral library. arXiv:1312.3887. · Zbl 1348.81018
[58] Stuart, R. G., Algebraic reduction of one loop Feynman diagrams to scalar integrals, Comput. Phys. Commun., 48, 367-389, (1988)
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