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QCD multiplet bases with arbitrary parton ordering. (English) Zbl 1405.81054
Summary: We develop an algorithm for recursively constructing orthogonal multiplet bases for the color space of QCD, for any order of partons and any \(N_c\). This recipe is then applied for explicitly constructing some of these bases. Using the bases, a corresponding set of Wigner 6\(j\) coefficients are calculated. The Wigner coefficients offer a method of using multiplet bases without resorting to the explicit expressions of the basis vectors, which lead to a significant speed-up compared to other methods of treating full color structure.
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81V05 Strong interaction, including quantum chromodynamics
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[1] Paton, JE; Chan, H-M, Generalized veneziano model with isospin, Nucl. Phys., B 10, 516, (1969)
[2] Berends, FA; Giele, W., The Six Gluon Process as an Example of Weyl-Van Der Waerden Spinor Calculus, Nucl. Phys., B 294, 700, (1987)
[3] Mangano, ML; Parke, SJ; Xu, Z., Duality and Multi-Gluon Scattering, Nucl. Phys., B 298, 653, (1988)
[4] Mangano, ML, The Color Structure of Gluon Emission, Nucl. Phys., B 309, 461, (1988)
[5] Kosower, DA, Color Factorization for Fermionic Amplitudes, Nucl. Phys., B 315, 391, (1989)
[6] Nagy, Z.; Soper, DE, Parton showers with quantum interference, JHEP, 09, 114, (2007)
[7] Sjodahl, M., Color structure for soft gluon resummation: A General recipe, JHEP, 09, 087, (2009)
[8] Alwall, J.; Herquet, M.; Maltoni, F.; Mattelaer, O.; Stelzer, T., MadGraph 5: Going Beyond, JHEP, 06, 128, (2011) · Zbl 1298.81362
[9] Sjodahl, M., ColorFull — a C++ library for calculations in SU(NC) color space, Eur. Phys. J., C 75, 236, (2015)
[10] Plätzer, S.; Sjodahl, M., Subleading N_{c} improved Parton Showers, JHEP, 07, 042, (2012)
[11] G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys.B 72 (1974) 461 [INSPIRE].
[12] A. Kanaki and C.G. Papadopoulos, HELAC-PHEGAS: Automatic computation of helicity amplitudes and cross-sections, hep-ph/0012004 [INSPIRE].
[13] F. Maltoni, K. Paul, T. Stelzer and S. Willenbrock, Color Flow Decomposition of QCD Amplitudes, Phys. Rev.D 67 (2003) 014026 [hep-ph/0209271] [INSPIRE].
[14] A. Kyrieleis and M.H. Seymour, The Colour evolution of the process qqqqg, JHEP01 (2006) 085 [hep-ph/0510089] [INSPIRE].
[15] Yu.L. Dokshitzer and G. Marchesini, Soft gluons at large angles in hadron collisions, JHEP01 (2006) 007 [hep-ph/0509078] [INSPIRE].
[16] Sjodahl, M., Color evolution of 2 → 3 processes, JHEP, 12, 083, (2008)
[17] Beneke, M.; Falgari, P.; Schwinn, C., Soft radiation in heavy-particle pair production: All-order colour structure and two-loop anomalous dimension, Nucl. Phys., B 828, 69, (2010) · Zbl 1203.81165
[18] Keppeler, S.; Sjodahl, M., Orthogonal multiplet bases in SU(NC) color space, JHEP, 09, 124, (2012) · Zbl 1397.81452
[19] Du, Y-J; Sjodahl, M.; Thorén, J., Recursion in multiplet bases for tree-level MHV gluon amplitudes, JHEP, 05, 119, (2015)
[20] Sjodahl, M.; Thorén, J., Decomposing color structure into multiplet bases, JHEP, 09, 055, (2015) · Zbl 1388.81224
[21] Alcock-Zeilinger, J.; Weigert, H., Transition Operators, J. Math. Phys., 58, (2017) · Zbl 1367.81078
[22] P. Cvitanović, Group Theory: Birdtracks, Lie’s and Exceptional Groups, Princeton University Press (2008) [www.birdtracks.eu].
[23] Nagy, Z.; Soper, DE, Parton shower evolution with subleading color, JHEP, 06, 044, (2012)
[24] Nagy, Z.; Soper, DE, Effects of subleading color in a parton shower, JHEP, 07, 119, (2015)
[25] Plätzer, S.; Sjodahl, M.; Thorén, J., Color matrix element corrections for parton showers, JHEP, 11, 009, (2018)
[26] J. Isaacson and S. Prestel, On Stochastically Sampling Color Configurations, arXiv:1806.10102 [INSPIRE].
[27] M. Hamermesh, Group Theory and its Application to Physical Problems, Addison-Wesley (1962). · Zbl 0100.36704
[28] King, RC, Generalized young tableaux and the general linear group, J. Math. Phys., 11, 280, (1970) · Zbl 0199.34604
[29] Keppeler, S.; Sjodahl, M., Hermitian Young Operators, J. Math. Phys., 55, (2014) · Zbl 1292.22008
[30] Alcock-Zeilinger, J.; Weigert, H., Compact Hermitian Young Projection Operators, J. Math. Phys., 58, (2017) · Zbl 1367.81077
[31] A.P. Yutsis, I.B. Levinson and V.V. Vanagas, Theory of angular momentum, Israel Program for Scientific Translations (1962).
[32] Sjodahl, M., ColorMath — A package for color summed calculations in SU(NC), Eur. Phys. J., C 73, 2310, (2013)
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