Orthogonal multiplet bases in SU(Nc) color space

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 Nc. The bases are constructed using hermitian gluon projectors onto irreducible subspaces invariant under SU(Nc). Thus, each basis vector is...

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Bibliographic Details
Published inarXiv.org
Main Authors Keppeler, Stefan, Sjodahl, Malin
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.10.2012
Subjects
Color
Mathematical analysis
Mathematics - Mathematical Physics
Partons
Physics - High Energy Physics - Phenomenology
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Projectors
Subspaces
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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 Nc. The bases are constructed using hermitian gluon projectors onto irreducible subspaces invariant under SU(Nc). Thus, each basis vector is associated with an irreducible representation of SU(Nc). The resulting multiplet bases are not only orthogonal, but also minimal for finite Nc. As a consequence, for calculations involving many colored particles, the number of basis vectors is reduced significantly compared to standard approaches employing overcomplete bases. We exemplify the method by constructing multiplet bases for all processes involving a total of 6 external colored partons.
Bibliography:LU-TP 12-27
ISSN:2331-8422
DOI:10.48550/arxiv.1207.0609