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

1.4. Effective coupling between gluons and a Higgs in the limit of aheavy top quark 27These calculations have been confirmed by calculation of soft terms to N 3 LO accuracy[90,91].When more partons are considered in the final state top mass effects becomemore pronounced. It has been shown that top and bottom quark mass effects canplay an important role [92] in deviations from the effective theory results [93,94] forHiggs plus jet calculations at NLO. We discuss the role of additional jets further(with an emphasis on two jets) in section 1.5.1.4.2 φ, φ † splitting of the Effective LagrangianWhen we look at a simple Higgs plus gluon helicity amplitude at tree-level a hint ofstructure jumps out at us,A (0)4 (φ, 1 − , 2 + , 3 − , 4 + ) =〈13〉 4〈12〉〈23〉〈34〉〈41〉 + [24] 4[12][23][34][41] . (1.56)Here we have used the spinor helicity formalism, which is described in Appendix A.Eq. (1.56) has a clear structure, if momentum were conserved amongst the gluons(p H → 0) then the two terms would be conjugates of each other. With this in mindwe make the following definitions, [95],φ =(H + iA), φ † =2(H − iA). (1.57)2Here A is a massive pseudo-scalar. We also wish to divide the gluon field strengthtensor G µν into self-dual (SD) and anti-self dual (ASD) pieces,G µνSD = 1 2 (Gµν + ∗ G µν ) G µνASD = 1 2 (Gµν − ∗ G µν ), (1.58)with∗ G µν = i 2 ǫµνρσ G ρσ . (1.59)In terms of these definitions the Lagrangian takes the following form,][HtrG µν G µν + iAtrG ∗ µνG µνL intH,A = C 2= C[]φtrG SD µν G µ,νSD + φ† trG ASD µν G µ,νASD. (1.60)