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

A.4. φ plus parton amplitudes 175A.4 φ plus parton amplitudesFor the MHV configurations the φ plus parton amplitudes have the same structureas the pure QCD ones (although momentum is now no longer conserved amongstthe partons only).A (0)n (φ, 1+ , . . .,i − , . . .,j − , . . .,n + ) =〈ij〉 4∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.4.31)A (0)n (φ, 1− q , 2+ , . . .,j − , . . .,n + q ) = 〈1j〉 3 〈nj〉∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.4.32)A (0)n (φ, 1+ q , . . .,i−, . . Q .j+ Q , . . .,n− q ) = − 〈1i〉〈in〉 2 〈nj〉∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.4.33)A (0)n (φ, 1− q , . . .,i− Q , . . .j+ Q , . . .,n+ q ) =The all plus and single minus φ amplitudes also vanish,〈1i〉 3 〈jn〉∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.4.34)A (0)n (φ, 1± , 2 + , . . .,n + ) = 0A (0)n (φ, 1− q , 2+ , . . .,n + q ) = 0(A.4.35)(A.4.36)The φ all-minus amplitude does not vanish however,A (0)n (φ, 1− , . . ., n − ) =We will also need the following φ-NMHV amplitudes,A (0)n (φ, 1+ , 2 − , 3 − , 4 − ) =−(−1) n m 4 φ∏ n−1α=1 [α(α + 1)][n1] (A.4.37)m 4 φ 〈24〉4s 124 〈12〉〈14〉〈2|p φ |3]〈4|p φ |3] + 〈4|p φ |1] 3s 123 〈4|p φ |3][12][23] − 〈2|p φ |1] 3s 134 〈2|p φ |3][14][34] .and the φqq-NMHV amplitude,(A.4.38)A (0)n (φ, 1+ q , 2− , 3 − , 4 −¯q ) =〈24〉 3 m 4 φs 124 〈14〉〈2|p φ |3]〈4|p φ |3] − 〈4|p φ |1] 2〈4|p φ |3][12][23] + 〈2|p φ|1] 2 〈2|p φ |4]s 134 〈2|p φ |3][14][34] .(A.4.39)Finally for the subleading colour amplitudes we will need the following amplitude,A (0)4 (φ, 1− q , 2− , 3 + q , 4− ) = − 〈4|p φ|3] 2[12][23]s 123+ {2 ↔ 4}(A.4.40)