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

1.4. Effective coupling between gluons and a Higgs in the limit of aheavy top quark 26element takes the following form,M FTm t→∞ (H → gg) = −i α s6πv g µνp 1 · p 2 ǫ ∗µ1 ǫ∗ν 2 + . . . (1.51)where . . . represent pieces which are suppressed in the large top limit. We candetermine the coefficient C by matching eq. (1.50) and eq. (1.51).C α S= α S6πv(1.52)To compute C to higher orders in α S one must calculate M FTm t→∞(H → gg) athigher loops, The effective coupling C has been calculated up to order O(αs 3 ) in [70].However, for our purposes we need it only up to order O(αs) 2 [71],(αC α2 sS = 1 + 11 )6πv 4π α s + O(αs 3 ) (1.53)One can also define the following quantity R which is given by the ratioR =σ(H → gg)σ mt→∞(H → gg) , (1.54)where σ(gg → H) is the total cross section. Setting x = 4m 2 t /m2 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 . (1.55)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.It has been known for a long time that the radiative corrections to Higgs productionthrough gluon fusion are large [72–74]. These NLO studies showed thatgoing beyond NLO was essential and impressively fully differential cross-sectionsat NNLO have now been calculated [75–82]. Recent calculations have studied theeffect of finite top masses on the NNLO calculations [83–88]. They found themto be reasonably small, indicating that for Higgs production through gluon fusionthe effective theory works well. The NNLO results can also be improved by includingnext-to-next-to-leading logarithmic (NNLL) soft gluon resummation [89] 5 .5 At the Tevatron this results in an increase in cross section of around 13%.