2030454 SzGeCERN 20220810144210.0 oai:cds.cern.ch:2030454 cerncds:FULLTEXT cerncds:CERN:FULLTEXT cerncds:CERN DOI 10.1007/JHEP01(2016)170 arXiv oai:arXiv.org:1507.00332 Inspire 1380614 arXiv arXiv:1507.00332 hep-ph CERN-PH-TH-2015-149 UUITP-13-15 NORDITA-2015-79 EDINBURGH-2015-11 eng CERN Library TH-2015-149 CERN-PH-TH-2015-149 UUITP-13-15 NORDITA-2015-79 EDINBURGH 2015-11 Johansson, Henrik CERN Uppsala U. Nordita Royal Inst. Tech., Stockholm Stockholm U. Theory Division - Physics Department - CERN - CH-1211 - Geneva 23 - Switzerland Department of Physics and Astronomy - Uppsala U. - Box 516 - SE-75120 - Uppsala - Sweden Nordita - KTH Royal Institute of Technology and Stockholm U. - Roslagstullsbacken 23 - SE-10691 - Stockholm - Sweden Color-Kinematics Duality for QCD Amplitudes 2016-01-27 01 Jul 2015 CERN Geneva 38 p Comments: 33 pages + refs, 7 figures, 4 tables arXiv 33 pages + refs, 7 figures, 4 tables; v3 minor corrections, journal version We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD. Springer We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n − 2k) gluons, are taken in the (n − 2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n − 3)!(2k − 2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD. arXiv We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD. arXiv http://arxiv.org/licenses/nonexclusive-distrib/1.0/ arXiv nonexclusive-distrib. 1.0 CC-BY-4.0 preprint CC-BY-4.0 publication SCOAP3 CERN 2015 preprint The Author(s) 2016 publication OA CERN-TH LANL EDS arXiv Particle Physics - Phenomenology arXiv Particle Physics - Theory ARTICLE CERN LANL EDS hep-ph LANL EDS hep-th Ochirov, Alexander U. Edinburgh, Higgs Ctr. Theor. Phys. Higgs Centre for Theoretical Physics - School of Physics U. and Astronomy - The Edinburgh - Edinburgh - EH9 3JZ - Scotland - U.K. PH-TH JHEP 01 2016 170 JHEP 1601 (2016) 170 http://arxiv.org/pdf/1507.00332.pdf Preprint 490605 http://cds.cern.ch/record/2030454/files/arXiv:1507.00332.pdf 1112101 1823 http://cds.cern.ch/record/2030454/files/pics_Multiperipheral.png 00002 \small Multi-peripheral cubic diagram for the color factors in formulas~\eqref{QuarkLineDecomposition} and~\eqref{DDM}. All permuted legs are gluons, while the horizontal line can be either a quark or a gluon line. 1112099 2113 http://cds.cern.ch/record/2030454/files/pics_ColorVertices.png 00000 \small Color vertices with planar ordering consistent with the color-stripped Feynman rules. 1112105 3861 http://cds.cern.ch/record/2030454/files/pics_A5.png 00004 \small Feynman diagrams for the four-quark one-gluon amplitude ${\cal A}^{\text{tree}}_{5,2}(\u{1},\o{2},\u{3},\o{4},5)$. 1112100 4233 http://cds.cern.ch/record/2030454/files/pics_Xi.png 00005 \small Diagrammatic form of the operator $\Xi^a_l$. It is drawn as a single diagram with hollow quark-gluon vertices, this represents summation over the possible locations where the gluon line can attach. 1112102 4406 http://cds.cern.ch/record/2030454/files/pics_ColorFactorExample.png 00006 \small Diagrammatic representation for the color coefficient of the planar amplitude $A(\u{1},\o{2},13,\u{3},\u{5},\o{6},\o{4}, \u{7},\u{9},14,\u{11},\o{12},\o{10},\o{8})$, obtained by using the notation of \fig{fig:Xi}. Note that the diagram has the same structure as the word $\{2\:13 \{ 3 \{5\:6\} 4 \} \{ 7 \{ 9\:14 \{11\:12\} 10 \} 8 \} 1\}$. 1112104 5972 http://cds.cern.ch/record/2030454/files/pics_JacobiTreeF.png 00001 \small Color-algebra relations in the adjoint~(a) and fundamental representation~(b). The color-kinematics duality requires that the kinematic numerators satisfy the corresponding kinematic-algebra relations, which can be represented by the same graphs. 1112103 7615 http://cds.cern.ch/record/2030454/files/pics_A6.png 00003 \small Feynman diagrams for the six-quark amplitude ${\cal A}^{\text{tree}}_{6,3}(\u{1},\o{2},\u{3},\o{4},\u{5},\o{6})$. 1112098 1178076 968284 http://cds.cern.ch/record/2030454/files/JHEP0128201629170.pdf Springer Open Access article 1178076 1925547 http://cds.cern.ch/record/2030454/files/JHEP0128201629170.pdf?subformat=pdfa pdfa Springer Open Access article 2336246 968284 http://cds.cern.ch/record/2030454/files/scoap.pdf Article from SCOAP3 n 201526 13 ARTICLE CERN