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

eplacemenB.2. Box Integral Functions 179tM 2 2F 1m3 F 2m3F 3m3M 2 3ssM 2 1Figure B.2: Conventions for labelling the three scalar triangle integrals appearingin the one-loop H plus parton amplitudes.(B.2.17)where,∆ =3∑−Mk 4 + 2M2 k M2 k+1k=1(B.2.18)δ k = M2 k − M2 k+1 − M2 k+2√ . (B.2.19)∆Alternative representations for these integrals can be found in references [186,220,221].B.2.2Bubble basis integralsThe two point bubble integral integrates to the following,( )1 µ2 ǫI 2 (s) =. (B.2.20)ǫ(1 − 2ǫ) −sin this thesis we combine bubble integrals to produce the following basis functions,L k (s, t) =log (s/t)(s − t) k , (B.2.21)which we then complete to avoid the presence of spurious (s → t) singularities.(L 3 (s, t) → ˆL 1 13 (s, t) = L 3 (s, t) −2(s − t) 2 s + 1 ),t