Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
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5.2. One-loop results 137= i A (0)4 (φ, 1 −¯q , 3 − g , 2 + q , 4 − g )+ terms antisymmetric <strong>in</strong> {3 ↔ 4} . (5.20)We note th<strong>at</strong> all <strong>of</strong> these amplitudes are f<strong>in</strong>ite because <strong>of</strong> the vanish<strong>in</strong>g <strong>of</strong> thecorrespond<strong>in</strong>g tree-level results (see section 5.1.2).5.2 One-loop resultsIn this section we present analytic expressions for the full one-loop corrections tothe process A (1)4 (φ, 1−¯q , 2 + q , 3− g , 4− g ). All expressions are presented un-renormalised <strong>in</strong>the four-dimensional helicity (FDH) scheme (sett<strong>in</strong>g δ R = 0) or ’t Ho<strong>of</strong>t-Veltmanscheme (sett<strong>in</strong>g δ R = 1).We employ the generalised unitarity method described <strong>in</strong> chapters 2 and 3 [120,122,123,127,128] to calcul<strong>at</strong>e the cut-constructible parts <strong>of</strong> the left-mov<strong>in</strong>g, rightmov<strong>in</strong>gand N f one-loop amplitudes. This relies on the familiar expansion <strong>of</strong> aone-loop amplitude <strong>in</strong> terms <strong>of</strong> scalar basis <strong>in</strong>tegrals,A cut−cons.4 (φ, 1 − q , 2+ q , 3− g , 4− g ) = ∑ iC 4;i I 4;i + ∑ iC 3;i I 3;i + ∑ iC 2;i I 2;i . (5.21)In this sum each j-po<strong>in</strong>t scalar basis <strong>in</strong>tegral (I j;i ) appears <strong>with</strong> a coefficient C j;i .The sum over i represents the sum over the partitions <strong>of</strong> the external momentaover the j legs <strong>of</strong> the basis <strong>in</strong>tegral. We use the methods described <strong>in</strong> previouschapters [120,122,132] to obta<strong>in</strong> the coefficients. Results were obta<strong>in</strong>ed us<strong>in</strong>g theQGRAF [207], FORM [210] and S@M [204] packages <strong>in</strong> order to control the extensivealgebra.5.2.1 Results for A 4;1 (φ, 1¯q , 2 q , 3 − g , 4 − g )The partial amplitude A 4;1 (φ, 1¯q , 2 q , 3 − g , 4− g ) is calcul<strong>at</strong>ed from three primitive amplitudesaccord<strong>in</strong>g to Eq. (5.4). We shall deal <strong>with</strong> each <strong>of</strong> these <strong>in</strong>gredients <strong>in</strong>turn.