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

4.4. Higgs plus four gluon amplitudes 128while the rational part is given by [206],{[ (R 4 (H, 1 − , 2 + , 3 − , 4 + ) = − 1 − N )(f [24] 4 s23 s 34− 3 s )]23s 34N c 12[12][23][34][41] s 24 s 124 s 2 24[] }+ (1 ↔ 2), (3 ↔ 4)〈ij〉↔[ij]{ } { }+ (1 ↔ 3) + (2 ↔ 4)+{}(1 ↔ 3), (2 ↔ 4) .(4.45)4.4.4 The NMHV amplitude A (1)4 (H, 1+ , 2 − , 3 − , 4 − )By combining the results for the NMHV φ amplitudes given in sections 4.2 and 4.3and the rational φ † amplitude of [106] according to eq. (A.2.21), we obtain theHiggs NMHV-amplitude, which is symmetric under the exchange (2 ↔ 4). Thefinite cut-constructible contribution is,{F 4 (H, 1 + , 2 − , 3 − , 4 − s 3 234) = −4〈1|p H |2]〈1|p H |4][23][34] W (1)()〈2|p H |1] 3−2s 134 〈2|p H |3][34][41] + 〈34〉 3 m 4 HW (2)2s 134 〈1|p H |2]〈3|p H |2]〈41〉+ 1 ()〈3|p H |1] 44s 124 〈3|p H |2]〈3|p H |4][21][41] + 〈24〉 4 m 4 HW (3)〈12〉〈14〉〈2|p H |3]〈4|p H |3](∑ m 4 φ−〈K♭ 1 2〉3 〈34〉 3 )γ(γ + m 2 γ=γ ± (p H ,p 1 +p 2 ) φ )〈K♭ 1 1〉〈K♭ 1 3〉〈K♭ 1 4〉〈12〉 F 3m3 (m2 H , s 12, s 34 )(+ 1 − N ) (f 〈3|pH |1] 24N c s 124 [24] 2 F1m 4F (s 12, s 14 ; s 124 )− 4〈24〉〈3|p H|1] 2ˆL 1 (s 124 , s 12 ) + 4〈23〉〈4|p )H|1] 2ˆL 1 (s 123 , s 12 )s 124 [42]s 123 [32](− 1 − N )(f [12][41]〈3|pH |2]〈3|p H |4]F 1mN c 2s 124 [24] 4 4F (s 12 , s 14 ; s 124 )+ 2s 124〈24〉〈34〉 2 [41] 23[42]+ 〈34〉[41] (3s 124〈34〉[41] + 〈24〉〈3|p H |1][42])+ˆL 3 (s 124 , s 12 )3[42] 2 ˆL2 (s 124 , s 12 ))ˆL 1 (s 124 , s 12 )(2s124 〈34〉 2 [41] 2− 〈24〉〈3|p H|1] 2〈24〉[42] 3 3s 124 [42]+ 〈3|p H|1](4s 124 〈34〉[41] + 〈3|p H |1](2s 14 + s 24 ))s 124 〈24〉[42] 3 ˆL0 (s 124 , s 12 )− 2s 123〈23〉〈34〉 2 [31] 23[32]ˆL 3 (s 123 , s 12 ) + 〈23〉〈34〉[31]〈4|p H|1]3[32]ˆL 2 (s 123 , s 12 )