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

3.2. The cut-constructible parts 92i+ −± ∓− ++ −∓ ±− +(a)j(b) (c)±∓∓±−−+− ++ − +(d) (e) (f)Figure 3.11: Double cut topologies which can appear in φ-MHV amplitudes. Diagramswhich allow both fermions and gluons to propagate in the loop are colouredblue. The remaining diagrams only allow gluons to propagate in the loop.In eq. (3.76)-(3.78) F 2me4Fin Appendix B. The coefficients b ij1mrepresents the finite part of a two-mass box and is definedare defined by eq. (3.46).3.2.4 φ-MHV Double cutsWith the calculation of the box and triangle coefficients now complete we turn ourattention to determining the coefficients of the various two point functions thatappear in φ-MHV amplitudes. The general double cut topologies are depicted inFig. 3.11, and, as was found with the four and three cut topologies, the position ofthe two negative helicity gluons determines what species of particle can propagatein the loop.We begin by considering diagram 3.11(a), this diagram only allows gluonic contributions,D (a) = A (0)n+2−(j−i) (φ, l+ 1 , (j + 1)+ , . . .,1 − , . . .,m − , . . .,(i − 1) + , l + 2 )= −×A (0)(j−i)+2 (l− 2 , i+ , . . ., j + , l − 1 )〈1m〉 4 〈l 2 l 1 〉 2〈l 1 (j + 1)〉 ∏ i−2α=(j+1) 〈α(α + 1)〉〈(i − 1)l 2〉〈l 2 i〉 ∏ j−1β=i 〈β(β + 1)〉〈l 1j〉= −A (0 〈l 1 l 2 〉 2 〈(i − 1)i〉〈j(j + 1)〉n〈l 1 (j + 1)〉〈(i − 1)l 2 〉〈l 2 i〉〈l 1 j〉 . (3.79)