zbMATH — the first resource for mathematics

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.

81V25 Other elementary particle theory in quantum theory
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.