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

4.4. Higgs plus four gluon amplitudes 127(− 1 − N f(−4 1 − N )f 〈12〉 2 [43]4N c 〈34〉ˆL 1 (s 134 , s 14 ))( [43]〈13pH 2〉(〈13p H 2〉 + 〈1432〉)ˆL 3 (s 134 , s 14 )N c 3〈34〉)] [] }+ (1 ↔ 3), (2 ↔ 4)− 〈12〉2 [43]ˆL 1 (s 134 , s 14 )3〈34〉〈ij〉↔[ij]{}+ (1 ↔ 2), (3 ↔ 4) . (4.42)The rational terms R 4 have the same symmetries [108],{[(R 4 (H, 1 − , 2 − , 3 + , 4 + ) = 1 − N ) (f [34]− 〈23〉〈1|p H|3] 2N c 3〈34〉 〈34〉[43][32]s 234− 〈14〉〈3|P 12|3]+ 〈12〉2〈34〉[12][32] 2〈34〉[43] − 〈12〉2[12] − 〈12〉〈2|P )]13|4]+ 〈12〉22[41]s 341 2s[] } {41}+ (1 ↔ 3), (2 ↔ 4) + (1 ↔ 2), (3 ↔ 4) . (4.43)〈ij〉↔[ij]4.4.3 The MHV amplitude A (1)4 (H, 1− , 2 + , 3 − , 4 + )The alternating helicity MHV configuration has the larger set of symmetries, (1 ↔3), (2 ↔ 4) and ((1 ↔ 3), (2 ↔ 4)). The finite cut-constructible contribution is [206](chapter 3),{[(F 4 (H, 1 − , 2 + , 3 − , 4 + 〈13〉 4) = −F 2me4F2〈12〉〈23〉〈34〉〈41〉(s 123, s 234 ; m 2 H , s 23)+ 1 2 F1m 4F (s 23, s 34 ; s 234 ) + 1 )2 F1m 4F (s 34, s 14 ; s 134 )(+4 1 − N )( (f− 〈13〉2 14N c 〈24〉 4〈24〉 F1m 4F (s 23, s 34 ; s 234 ))) (−[42]ˆL 1 (s 234 , s 23 ) + 2 1 − N f+ N )(s− 〈12〉〈41〉〈23〉〈34〉N c N c 〈24〉( 3)1×4〈24〉 F1m 4F (s 23, s 34 ; s 234 ) − [42]ˆL 1 (s 234 , s 23 )(− 〈23〉〈41〉[42]2 〈14〉〈23〉[42]ˆL 3 (s 234 , s 23 )〈24〉 3− 〈12〉〈34〉 ))] [] }ˆL 2 (s 234 , s 23 ) + (1 ↔ 2), (3 ↔ 4)2〈24〉〈ij〉↔[ij]{ } { } {}+ (1 ↔ 3) + (2 ↔ 4) + (1 ↔ 3), (2 ↔ 4) (4.44)