All Tree-level Amplitudes in Massless QCD
We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N = 4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N = 4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N = 4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark-pairs.
- Research Organization:
- SLAC National Accelerator Laboratory (SLAC)
- Sponsoring Organization:
- US DOE Office of Science (DOE SC)
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 992874
- Report Number(s):
- SLAC-PUB-14278; arXiv:1010.3991
- Journal Information:
- JHEP 1101:035,2011, Journal Name: JHEP 1101:035,2011
- Country of Publication:
- United States
- Language:
- English
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