Hadronic production of a Higgs boson in association with two jets at ...

5.1. Introduction 134Figure 5.1: Sample diagrams contributing to the primitive amplitudes, from leftto right we have; the left piece A L 4 (φ, 1¯q , 2 q , 3 g , 4 g ), the subleading right pieceA R 4 (φ, 1¯q, 2 q , 3 g , 4 g ), terms which contain a closed fermion loop (the N f piece),A f 4 (φ, 1¯q, 2 q , 3 g , 4 g ) and the subleading left piece A L 4 (φ, 1¯q, 2 g , 3 q , 4 g ). The φ fieldcan attach to any gluon line in the diagram.5.1.2 Known analytic results for Hqqjj amplitudesIn this section we review results from the literature and collect formulae, for both treeand one-loop results, that will be useful in constructing the Higgs NMHV amplitude.Tree level resultsThe results for the tree graphs that are primarily of interest here, i.e. φ¯qqgg amplitudeswith gluons of the same helicity, are:−iA (0)4 (φ, 1 −¯q , 2 + q , 3 − g , 4 − g ) = − 〈3 |p φ| 2] 2 〈4 1〉[2 4] s 124[ 1s 12+ 1s 41]− 〈4 |p φ| 2] 2 〈1 3〉 〈1 |p φ | 2] 2+[2 3] s 12 s 123 〈1 2〉[2 4][2 3][3 4] , (5.6)−iA (0)4 (φ, 1−¯q , 2+ q , 3+ g , 4+ g ) = 0 , (5.7)and for the subleading colour piece,−iA (0)4 (φ, 1 −¯q , 2 − g , 3 + q , 4 − g ) = − 〈4 |p φ| 3] 2[1 2][2 3] s 123− 〈2 |p φ| 3] 2[3 4][4 1] s 341, (5.8)−iA (0)4 (φ, 1 −¯q , 2 + g , 3 + q , 4 + g ) = 0 . (5.9)A summary of our spinor notation is given in Appendix A. Compact analytic expressionsfor all helicity amplitudes are presented in references [109,208].