Abstract
We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Berger, Z. Bern, L.J. Dixon, F. Febres Cordero, D. Forde, et al., Precise predictions for W + 3 jet production at hadron colliders, Phys. Rev. Lett. 102 (2009) 222001 [arXiv:0902.2760] [INSPIRE].
K. Melnikov and G. Zanderighi, W+3 jet production at the LHC as a signal or background, Phys. Rev. D 81 (2010) 074025 [arXiv:0910.3671] [INSPIRE].
G. Bevilacqua, M. Czakon, C. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO wishlist: \( pp\to t\overline{t}b\overline{b} \), JHEP 09 (2009) 109 [arXiv:0907.4723] [INSPIRE].
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. Full hadronic results, JHEP 03 (2010) 021 [arXiv:1001.4006] [INSPIRE].
P. Bolzoni, F. Maltoni, S.-O. Moch and M. Zaro, Higgs production via vector-boson fusion at NNLO in QCD, Phys. Rev. Lett. 105 (2010) 011801 [arXiv:1003.4451] [INSPIRE].
S. Catani, G. Ferrera and M. Grazzini, W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD, JHEP 05 (2010) 006 [arXiv:1002.3115] [INSPIRE].
S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
C. Anastasiou, G. Dissertori and F. Stockli, NNLO QCD predictions for the H → WW → lνlν signal at the LHC, JHEP 09 (2007) 018 [arXiv:0707.2373] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys. B 724 (2005) 197 [hep-ph/0501130] [INSPIRE].
K. Melnikov and F. Petriello, Electroweak gauge boson production at hadron colliders through \( o\left( {\alpha_s^2} \right) \), Phys. Rev. D 74 (2006) 114017 [hep-ph/0609070] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett. 108 (2012) 072001 [arXiv:1110.2375] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Infrared structure of e + e − → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, NNLO corrections to event shapes in e + e − annihilation, JHEP 12 (2007) 094 [arXiv:0711.4711] [INSPIRE].
S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett. 101 (2008) 162001 [arXiv:0807.3241] [INSPIRE].
P. Baernreuther, M. Czakon and A. Mitov, Percent level precision physics at the Tevatron: first genuine NNLO QCD corrections to \( q\overline{q}\to t\overline{t}+x \), Phys. Rev. Lett. 109 (2012) 132001 [arXiv:1204.5201] [INSPIRE].
SM and NLO Multileg Working Group collaboration, J. Andersen et al., The SM and NLO multileg working group: summary report, arXiv:1003.1241 [INSPIRE].
A. Denner, S. Dittmaier, T. Kasprzik and A. Muck, Electroweak corrections to W + jet hadroproduction including leptonic W-boson decays, JHEP 08 (2009) 075 [arXiv:0906.1656] [INSPIRE].
J.H. Kuhn, A. Kulesza, S. Pozzorini and M. Schulze, Electroweak corrections to hadronic production of W bosons at large transverse momenta, Nucl. Phys. B 797 (2008) 27 [arXiv:0708.0476] [INSPIRE].
S. Catani, T. Gleisberg, F. Krauss, G. Rodrigo and J.-C. Winter, From loops to trees by-passing Feynman’s theorem, JHEP 09 (2008) 065 [arXiv:0804.3170] [INSPIRE].
S. Caron-Huot, Loops and trees, JHEP 05 (2011) 080 [arXiv:1007.3224] [INSPIRE].
J. Gluza, K. Kajda and D.A. Kosower, Towards a basis for planar two-loop integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472] [INSPIRE].
I. Bierenbaum, S. Catani, P. Draggiotis and G. Rodrigo, A tree-loop duality relation at two loops and beyond, JHEP 10 (2010) 073 [arXiv:1007.0194] [INSPIRE].
I. Bierenbaum, Towards a loop-tree duality at two loops and beyond, Nucl. Phys. Proc. Suppl. 205-206 (2010) 164 [arXiv:1007.0213] [INSPIRE].
R. Feynman, Quantum theory of gravitation, Acta Phys. Polon. 24 (1963) 697 [INSPIRE].
R.P. Feynman, Closed loop and tree diagrams, in Magic without magic, J.R. Klauder ed., Freeman, San Francisco U.S.A. (1972) 355 [in Selected papers of Richard Feynman, L.M. Brown ed., World Scientific, Singapore (2000) 867].
A. Smirnov, Algorithm FIRE — Feynman integral reduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
V.A. Smirnov, Feynman integral calculus, Springer-Verlag, Berlin Germany (2006).
A. von Manteuffel and C. Studerus, Reduze 2 - Distributed Feynman integral reduction, arXiv:1201.4330 [INSPIRE].
C. Bauer, A. Frink, R. Kreckel Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comp. 33 (2002) 1 [http://www.ginac.de] [cs/0004015].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1211.5048
Rights and permissions
About this article
Cite this article
Bierenbaum, I., Buchta, S., Draggiotis, P. et al. Tree-loop duality relation beyond single poles. J. High Energ. Phys. 2013, 25 (2013). https://doi.org/10.1007/JHEP03(2013)025
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2013)025