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

3.4. Cross Checks and Limits 107(3.157)Split (1),C (−K − , 1 − , 2 − ) = 0, (3.158)Split (1),R (−K ± , 1 − , 2 + ) = 0, (3.159)Split (1),R (−K + , 1 − , 2 − ) = N √P z(1 − z), (3.160)96π 2 [1 2]Split (1),R (−K − , 1 − , 2 − ) = N P96π 2 √z(1 − z) 〈1 2〉[1 2] 2 . (3.161)Explicitly, the cut-constructible parts should satisfy,C n (. . .,i λ i, i + 1 λ i+1, . . .) i‖i+−→ 1 ∑ h=±C n−1 (. . .,i − 1 λ i−1, K h , i + 2 λ i+2, . . .) Split (0) (−K −h ; i λ i, i + 1 λ i+1)+A (0)n−1 (. . .,i − 1λ i−1, K h , i + 2 λ i+2, . . .) Split (1),C (−K −h ; i λ i, i + 1 λ i+1),(3.162)while the rational pieces obey,R n (. . .,i λ i, i + 1 λ i+1, . . .) i‖i+ −−→ 1 ∑ h=±R n−1 (. . .,i − 1 λ i−1, K h , i + 2 λ i+2, . . .) Split (0) (−K −h ; i λ i, i + 1 λ i+1)+A (0)n−1(. . .,i − 1 λ i−1, K h , i + 2 λ i+2, . . .) Split (1),R (−K −h ; i λ i, i + 1 λ i+1).(3.163)3.4.2 Collinear factorisation of the cut-constructible contributionsIn Ref. [108], it was demonstrated that the helicity independent cut-constructiblegluonic contribution obeys,Cnφ{G} (. . .,i λ i, i + 1 λ i+1, . . .) i‖i+ −→ 1 ∑ h=±C φ{G}n−1 (. . .,i − 1 λ i−1, K h , i + 2 λ i+2, . . .) Split (0) (−K −h ; i λ i, i + 1 λ i+1)+A (0)n−1(. . .,i − 1 λ i−1, K h , i + 2 λ i+2, . . .) Split (1),C (−K −h ; i λ i, i + 1 λ i+1).(3.164)