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Orthogonal multiplet bases in SU\((N_c)\) color space. (English) Zbl 1397.81452
Summary: We develop a general recipe for constructing orthogonal bases for the calculation of color structures appearing in QCD for any number of partons and arbitrary \(N_c\). The bases are constructed using hermitian gluon projectors onto irreducible subspaces invariant under \(\text{SU}(N_c)\). Thus, each basis vector is associated with an irreducible representation of \(\text{SU}(N_c)\). The resulting multiplet bases are not only orthogonal, but also minimal for finite \(N_c\). As a consequence, for calculations involving many colored particles, the number of basis vectors is reduced significantly compared to standard approaches employing over-complete bases. We exemplify the method by constructing multiplet bases for all processes involving a total of 6 external colored partons.

MSC:
81V25 Other elementary particle theory in quantum theory
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ALPGEN; OEIS
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[1] Zeppenfeld, D., Diagonalization of color factors, Int. J. Mod. Phys., A 3, 2175, (1988)
[2] Duca, V.; Dixon, LJ; Maltoni, F., New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys., B 571, 51, (2000)
[3] Dokshitzer, Y.; Marchesini, G., Soft gluons at large angles in hadron collisions, JHEP, 01, 007, (2006)
[4] Kyrieleis, A.; Seymour, M., The colour evolution of the process qq → qqg, JHEP, 01, 085, (2006)
[5] Sjodahl, M., Color evolution of 2 → 3 processes, JHEP, 12, 083, (2008)
[6] Paton, JE; Chan, H-M, Generalized veneziano model with isospin, Nucl. Phys., B 10, 516, (1969)
[7] Dittner, P., Invariant tensors in SU(3). II, Commun. Math. Phys., 27, 44, (1972) · Zbl 0241.22032
[8] Cvitanović, P., Group theory for Feynman diagrams in non-abelian gauge theories, Phys. Rev., D 14, 1536, (1976)
[9] Cvitanović, P.; Lauwers, P.; Scharbach, P., Gauge invariance structure of quantum chromodynamics, Nucl. Phys., B 186, 165, (1981)
[10] Mangano, ML; Parke, SJ; Xu, Z., Duality and multi-gluon scattering, Nucl. Phys., B 298, 653, (1988)
[11] Mangano, ML, The color structure of gluon emission, Nucl. Phys., B 309, 461, (1988)
[12] Nagy, Z.; Soper, DE, Parton showers with quantum interference, JHEP, 09, 114, (2007)
[13] Platzer, S.; Sjodahl, M., Subleading N_{c} improved parton showers, JHEP, 07, 042, (2012)
[14] Sjodahl, M., Color structure for soft gluon resummation - a general recipe, JHEP, 09, 087, (2009)
[15] Caravaglios, F.; Mangano, ML; Moretti, M.; Pittau, R., A new approach to multijet calculations in hadron collisions, Nucl. Phys., B 539, 215, (1999)
[16] Maltoni, F.; Paul, K.; Stelzer, T.; Willenbrock, S., Color flow decomposition of QCD amplitudes, Phys. Rev., D 67, 014026, (2003)
[17] Papadopoulos, CG; Worek, M., Multi-parton cross sections at hadron colliders, Eur. Phys. J., C 50, 843, (2007)
[18] Duhr, C.; Hoeche, S.; Maltoni, F., Color-dressed recursive relations for multi-parton amplitudes, JHEP, 08, 062, (2006)
[19] Giele, W.; Kunszt, Z.; Winter, J., Efficient color-dressed calculation of virtual corrections, Nucl. Phys., B 840, 214, (2010) · Zbl 1206.81124
[20] Hameren, A.; Papadopoulos, C.; Pittau, R., Automated one-loop calculations: a proof of concept, JHEP, 09, 106, (2009)
[21] Sotiropoulos, MG; Sterman, GF, Color exchange in near forward hard elastic scattering, Nucl. Phys., B 419, 59, (1994)
[22] Kidonakis, N.; Oderda, G.; Sterman, GF, Evolution of color exchange in QCD hard scattering, Nucl. Phys., B 531, 365, (1998)
[23] 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
[24] P. Cvitanović, Group Theory: Birdtracks, Lies, and Exceptional Groups. Princeton University Press (2008) http://www.birdtracks.eu/.
[25] W. Lang, private communication; see also The On-Line Encyclopedia of Integer Sequences (2010) http://oeis.org/A000255.
[26] Parke, SJ; Taylor, T., An amplitude for n gluon scattering, Phys. Rev. Lett., 56, 2459, (1986)
[27] Kleiss, R.; Kuijf, H., Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys., B 312, 616, (1989)
[28] Berends, FA; Giele, W., Recursive calculations for processes with n gluons, Nucl. Phys., B 306, 759, (1988)
[29] Cachazo, F.; Svrček, P.; Witten, E., MHV vertices and tree amplitudes in gauge theory, JHEP, 09, 006, (2004)
[30] Britto, R.; Cachazo, F.; Feng, B., New recursion relations for tree amplitudes of gluons, Nucl. Phys., B 715, 499, (2005) · Zbl 1207.81088
[31] Bern, Z.; Carrasco, J.; Johansson, H., New relations for gauge-theory amplitudes, Phys. Rev., D 78, 085011, (2008)
[32] Bjerrum-Bohr, N.; Damgaard, PH; Feng, B.; Sondergaard, T., Gravity and Yang-Mills amplitude relations, Phys. Rev., D 82, 107702, (2010)
[33] Bjerrum-Bohr, N.; Damgaard, PH; Feng, B.; Sondergaard, T., New identities among gauge theory amplitudes, Phys. Lett., B 691, 268, (2010)
[34] M. Hamermesh, Group Theory and its Application to Physical Problems. Addison-Wesley (1962). · Zbl 0100.36704
[35] MacFarlane, A.; Sudbery, A.; Weisz, P., On Gell-mann’s λ-matrices, d- and f-tensors, octets and parametrizations of SU(3), Commun. Math. Phys., 11, 77, (1968)
[36] P. Cvitanović, Group TheoryClassics Illustratedpart I. Nordita, Copenhagen (1984).
[37] Oderda, G., Dijet rapidity gaps in photoproduction from perturbative QCD, Phys. Rev., D 61, 014004, (2000)
[38] D.E. Littlewood, The Theory of Group Characters, Oxford University Press, 2nd ed. (1950). · Zbl 0038.16504
[39] S. Keppeler and M. Sjodahl, in preparation.
[40] Dittner, P., Invariant tensors in SU(3), Commun. Math. Phys., 22, 238, (1971) · Zbl 0241.22031
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