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

Chapter 3One-loop φ-MHV amplitudes: thegeneral helicity case3.1 IntroductionIn this chapter we present the calculation of the φ-MHV amplitudes where thetwo negative helicity gluons are positioned arbitrarily. This builds on previous work[108] in which the two negative helicity gluons were constrained to be colour adjacent.We will use the methods of generalised unitarity to determine the cut-constructiblepieces of the amplitude. Coefficients associated with box integrals will be calculatedusing the four-cut method of Britto, Cachazo and Feng [120], which has been discussedin section 2.2. It will be shown that for the φ-MHV amplitudes only oneandtwo-mass easy boxes appear. The triangle coefficients will be determined usingForde’s Laurent expansion method [122] described in section 2.3 (we will alsoshow that one can use IR conditions to fix the triangles once the box coefficients areknown). Finally, the bubble (or 2-point) coefficients will be determined using Mastrolia’sStokes’ Theorem method [132], which was introduced in section 2.4. Due tothe simplicity of these methods it is easy to generalise the cut-constructible piecesto include n gluon multiplicities.The rational pieces will be calculated using the unitarity bootstrap approach69