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

A.3. Pure QCD amplitudes 174Furthermore parity relates φ and φ † amplitudes,(∗A n (m) (φ† , g λ 11 , . . .,gλn n ) = A n (m) (φ, g−λ 11 , . . ., gn )) −λn . (A.2.23)Hence we will only list φ-amplitudes, knowing that all others can be obtained usingeqs. (A.2.21)–(A.2.23).In this section we list the primitive amplitude which can be used to generate thefull coloured amplitudes using the equations given in section A.1.2A.3 Pure QCD amplitudesThe all multiplicity pure gluon MHV is given byA (0)n (1+ , . . .,i − , . . .,j − , . . ., n + ) =〈ij〉 4∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.3.24)The all multiplicity gluon plus quark pair MHV has the following form,A (0)n (1− q , 2+ , . . ., j − , . . .,n + q ) =〈1j〉 3 〈nj〉∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.3.25)The following two quark pair amplitudes are also needed at various stagesA (0)n (1+ q , . . .,i−, . . Q .j+ Q , . . .,n− q ) = − 〈1i〉〈in〉 2 〈nj〉∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.3.26)A (0)n (1 − q , . . .,i − , . . Q .j+ Q , . . .,n+ q ) = 〈1i〉 3 〈jn〉∏ n−1α=1 〈α(α + 1)〉〈n1〉 (A.3.27)Although having no overall (non box or triangle) contribution to the double cuts ofany Higgs plus gluon amplitude we need to use the 6-point NMHV amplitude whenconstructing the s 1234 cut of the φ-NHMV amplitude.(A (0)6 (1− , 2 − , 3 − , 4 + , 5 + , 6 + 1 〈1|P 23 |4] 3) =〈5|P 34 |2] [23][34]〈56〉〈61〉s 234)〈3|P 45 |6] 3+[61][12]〈34〉〈45〉s 345We also note the vanishing of the following amplitudes,(A.3.28)A (0)n (1± , 2 + , . . .,n + ) = 0A (0)n (1− q , 2+ , . . .,n + q ) = 0(A.3.29)(A.3.30)