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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| Abstract | 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. |
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| AbstractList | JHEP 0912:124,2012 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. 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. |
| Author | Keppeler, Stefan Sjodahl, Malin |
| Author_xml | – sequence: 1 givenname: Stefan surname: Keppeler fullname: Keppeler, Stefan – sequence: 2 givenname: Malin surname: Sjodahl fullname: Sjodahl, Malin |
| BackLink | https://doi.org/10.48550/arXiv.1207.0609$$DView paper in arXiv https://doi.org/10.1007/JHEP09(2012)124$$DView published paper (Access to full text may be restricted) |
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| DOI | 10.48550/arxiv.1207.0609 |
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| Title | Orthogonal multiplet bases in SU(Nc) color space |
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