Built on

S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD , JHEP 05
Original
1904
Earlier work this paper cites.
C. Duhr, H. Johansson, G. Kälin, G. Mogull and B. Verbeek, The Full-Color Two-Loop Four-Gluon Amplitude in 𝒩 = 2 \mathcal{N}=2 Super-QCD , 1904.05299
Original
1904
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. M. Henn, T. Peraro et al., Analytic form of the full two-loop five-gluon all-plus helicity amplitude , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
R. Kleiss and H. Kuijf, Multi - Gluon Cross-sections and Five Jet Production at Hadron Colliders , Nucl.Phys. B312
1989
Earlier work this paper cites.
Z. Bern and D. A. Kosower, Color decomposition of one loop amplitudes in gauge theories , Nucl.Phys. B362
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits , Nucl. Phys. B425
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes , Nucl.Phys. B435
1995
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, One loop corrections to two quark three gluon amplitudes , Nucl. Phys. B437
1995
Earlier work this paper cites.
L. J. Dixon, Calculating scattering amplitudes efficiently , in QCD and beyond. Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics, TASI-95, Boulder, USA, June 4-30, 1995 , pp. 539–584, 1996, hep-ph/9601359 , http://www-public.slac.stanford.edu/sciDoc/docMeta.aspx?slacPubNumber=SLAC-PUB-7106
1996
Earlier work this paper cites.
V. Del Duca, L. J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level , Nucl.Phys. B571
2000
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills , Nucl.Phys. B725
2005
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl. Phys. B763
2007
Earlier work this paper cites.
Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes , Phys.Rev. D78
Original
2008
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory , Phys.Rev.Lett. 105
Original
2010
Earlier work this paper cites.
P. Mastrolia and G. Ossola, On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes , JHEP 1111
Original
2011
Earlier work this paper cites.
H. Ita and K. Ozeren, Colour Decompositions of Multi-quark One-loop QCD Amplitudes , JHEP 1202
Original
2012
Earlier work this paper cites.
Y. Zhang, Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods , JHEP 1209
Original
2012
Earlier work this paper cites.
P. Mastrolia, E. Mirabella, G. Ossola and T. Peraro, Scattering Amplitudes from Multivariate Polynomial Division , Phys.Lett. B718
Original
2012
Earlier work this paper cites.

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2019

Multi-Quark Colour Decompositions from Unitarity

Ochirov, Alexander, Page, Ben

Understand

Any loop QCD amplitude at full colour is constructed from kinematic and gauge-group building blocks.

In a unitarity-based on-shell framework, both objects can be reconstructed from their respective counterparts in tree-level amplitudes.
This procedure is at its most powerful when aligned with flexible colour decompositions of tree-level QCD amplitudes.
In this note we derive such decompositions for amplitudes with an arbitrary number of quarks and gluons from the same principle that is used to bootstrap kinematics - unitarity factorisation.

Built on

S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD , JHEP 05
Original
1904
Earlier work this paper cites.
C. Duhr, H. Johansson, G. Kälin, G. Mogull and B. Verbeek, The Full-Color Two-Loop Four-Gluon Amplitude in 𝒩 = 2 \mathcal{N}=2 Super-QCD , 1904.05299
Original
1904
Earlier work this paper cites.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. M. Henn, T. Peraro et al., Analytic form of the full two-loop five-gluon all-plus helicity amplitude , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
R. Kleiss and H. Kuijf, Multi - Gluon Cross-sections and Five Jet Production at Hadron Colliders , Nucl.Phys. B312
1989
Earlier work this paper cites.
Z. Bern and D. A. Kosower, Color decomposition of one loop amplitudes in gauge theories , Nucl.Phys. B362
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits , Nucl. Phys. B425
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes , Nucl.Phys. B435
1995
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, One loop corrections to two quark three gluon amplitudes , Nucl. Phys. B437
1995
Earlier work this paper cites.
L. J. Dixon, Calculating scattering amplitudes efficiently , in QCD and beyond. Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics, TASI-95, Boulder, USA, June 4-30, 1995 , pp. 539–584, 1996, hep-ph/9601359 , http://www-public.slac.stanford.edu/sciDoc/docMeta.aspx?slacPubNumber=SLAC-PUB-7106
1996
Earlier work this paper cites.
V. Del Duca, L. J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level , Nucl.Phys. B571
2000
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills , Nucl.Phys. B725
2005
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl. Phys. B763
2007
Earlier work this paper cites.
Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes , Phys.Rev. D78
Original
2008
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory , Phys.Rev.Lett. 105
Original
2010
Earlier work this paper cites.
P. Mastrolia and G. Ossola, On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes , JHEP 1111
Original
2011
Earlier work this paper cites.
H. Ita and K. Ozeren, Colour Decompositions of Multi-quark One-loop QCD Amplitudes , JHEP 1202
Original
2012
Earlier work this paper cites.
Y. Zhang, Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods , JHEP 1209
Original
2012
Earlier work this paper cites.
P. Mastrolia, E. Mirabella, G. Ossola and T. Peraro, Scattering Amplitudes from Multivariate Polynomial Division , Phys.Lett. B718
Original
2012
Earlier work this paper cites.