28/07/2011

Tree-level amplitudes in massless QCD

Bachelor thesis at Humboldt University of Berlin, supervised by Jan Plefka

We present a fast implementation for calculating tree-level color-ordered amplitudes in massless QCD up to NNMHV level involving up to three quark-lines. Because of certain symmetries at tree-level this covers all existing color-ordered QCD amplitudes with maximal N = 9 external particles involving maximal six quarks. The implementation is based on the work of L. Dixon, J. Henn, J. Plefka and T. Schuster (arXiv:1010.3991) who derived compact analytical expressions for all tree-level amplitudes in massless QCD. We compare the performance of our implementation with the Berends-Giele off-shell recursion. Berends-Giele’s asymptotic behavior is quartic, the number of external particles, and therefore our implementation covers exactly those formulae with the same and better behavior concerning the number of terms – these are those with up to four negative helicity particles (NNMHV). Even though such benchmarking is highly dependent on the specific implementation, we find significant differences in terms of speed and asymptotic behavior between the two approaches – concretely MHV and NMHV implementation are faster with up to a factor of nine for n = 10 and better for larger n, while the NNMHV implementation scales with the same order shows slight advantages for n < 8.

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