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

6.2. Improvements from the semi-numeric code 148where σ(gg → H) is the total cross section. Setting x = 4m 2 t/m 2 Hthe correction forthe finite mass of the top quark in the region x > 1 is [72],[3x( [R = 1 − (x − 1) sin −1 1] 2 ) ] 2√x . (6.4)2This quantity when used to normalise an effective theory cross section providesa good approximation of the cross section from the full theory, see Ref. [66] andreferences therein. However for the case of Higgs + 1 jet it has been found thatthe effect of bottom quark loops and additional electroweak diagrams can also beimportant [92] and these effects should also be included. Our numerical results forthe Higgs cross section will not include the rescaling of Eqs. (6.3,6.4).6.2 Improvements from the semi-numeric codeThe phenomenology of the production of a Higgs boson in association with two jetshas been presented in Ref. [104, 105] for the case of the LHC operating at √ s =14 TeV. The NLO analysis in that paper was based on real matrix elements for theHiggs+5 parton processes given in Ref. [209], supplemented by the results of Ref. [95,146] in the cases where these latter results lead to more efficient code. In Ref. [105]the virtual matrix element corrections for the Higgs + 4 parton process were takenfrom Ref. [104]. For the Hgggg and Hq¯qgg sub-processes the virtual correctionswere based on a semi-numerical technique [211], whilst the matrix elements squaredfor the one-loop processes Hq¯qq ′¯q ′ and Hq¯qq¯q were given analytically in Ref. [104].In the three years since Ref. [105] was published a great deal of effort has beendevoted to the analytic calculation of one-loop corrections to Higgs + n-partonamplitudes, with particular emphasis on the n = 4 amplitudes which are relevantfor this study. The complete set of one-loop amplitudes for all Higgs + 4 partonprocesses is now available and analytic expressions can be found in the followingreferences:• Hgggg: (Chapter 3, Chapter 4) Refs. [106–108,206,208];• H¯qqgg: (Chapter 5) Refs. [109,212];