Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
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5.1. Introduction 134Figure 5.1: Sample diagrams contribut<strong>in</strong>g 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 sublead<strong>in</strong>g right pieceA R 4 (φ, 1¯q, 2 q , 3 g , 4 g ), terms which conta<strong>in</strong> a closed fermion loop (the N f piece),A f 4 (φ, 1¯q, 2 q , 3 g , 4 g ) and the sublead<strong>in</strong>g left piece A L 4 (φ, 1¯q, 2 g , 3 q , 4 g ). The φ fieldcan <strong>at</strong>tach to any gluon l<strong>in</strong>e <strong>in</strong> the diagram.5.1.2 Known analytic results for Hqqjj amplitudesIn this section we review results from the liter<strong>at</strong>ure and collect formulae, for both treeand one-loop results, th<strong>at</strong> will be useful <strong>in</strong> construct<strong>in</strong>g the <strong>Higgs</strong> NMHV amplitude.Tree level resultsThe results for the tree graphs th<strong>at</strong> are primarily <strong>of</strong> <strong>in</strong>terest here, i.e. φ¯qqgg amplitudes<strong>with</strong> gluons <strong>of</strong> 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 sublead<strong>in</strong>g 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 <strong>of</strong> our sp<strong>in</strong>or not<strong>at</strong>ion is given <strong>in</strong> Appendix A. Compact analytic expressionsfor all helicity amplitudes are presented <strong>in</strong> references [109,208].