The last of the seven-parton tree amplitudes

We compute the four-quark plus three-gluon and six-quark plus one-gluon tree level amplitudes using on-shell recursion relations. They are needed for the calculation of the 5-jet cross-section at the Born level, and constitute an essential ingredient for next-to-leading order 4-jet and next-to-next-to-leading order 3-jet production at hadronic colliders. Very compact expressions for all possible helicity configurations are provided, allowing direct implementation in computer codes. With the results presented in this paper, the full set of seven-parton tree amplitudes becomes available