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

2.6. The unitarity-bootstrap 60of our results we shift (or complete) the basis such that no basis functions developunphysical singularities. The completed basis has the following form,(L 3 (s, t) → ˆL 1 13 (s, t) = L 3 (s, t) −2(s − t) 2 s + 1 ),tL 2 (s, t) → ˆL 1 12 (s, t) = L 2 (s, t) −2(s − t)(s + 1 ),tL 1 (s, t) → ˆL 1 (s, t) = L 1 (s, t),L 0 (s, t) → ˆL 0 (s, t) = L 0 (s, t). (2.104)The rational pieces associated with the above functions are called the cut-completionterms, we will use the following notation to describe the various pieces of the amplitude.The rational pieces are those left when all of the logs, dilogs and π 2 termsvanish,R n (z) = 1 ∣∣∣∣log,Li,πA n , (2.105)c Γ 2 →0so that the total (z dependent) amplitude is defined asA n (z) = c Γ (C n (z) + R n (z)). (2.106)As described above the cut-constructible pieces can be completed by including somerational terms,Ĉ n (z) = C n (z) + ĈR n(z) (2.107)whereĈR n (z) = Ĉn(z)∣ . (2.108)ratOf course the total rational piece R n is the sum of completion terms CR n and theremaining rational piecesR n (z) = ĈR n(z) + ̂R n (z). (2.109)We now wish to consider the following integral∫Bdzz Disc BĈn(z) (2.110)