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

5.2. One-loop results 140with K 1 = −p 1 −p 2 −p 3 −p 4 , K 2 = −p 1 −p 4 and K ♭ 1 given in terms of these vectorsby Eq. (5.26).The definitions of the box integral functions F 1m4Fand F2mh 4Fcan be found inAppendix B, together with expressions for ˆL 1 , ˆL 2 and ˆL 3 . In addition to logarithmsand polynomial denominators, the latter functions also contain rational terms thatprotect them from unphysical singularities. Thus, for example,(log (s/t)ˆL 2 (s, t) =(s − t) − 1 1 2 2(s − t) s + 1 ),twhich is finite in the limit that s → t.A R 4 (φ, 1 −¯q , 2 + q , 3 − g , 4 − g )The result for the right-moving amplitude, A R 4 (φ, 1−¯q , 2 + q , 3− g , 4− g ) is,−iA R 4 (φ, 1 −¯q , 2 + q , 3 − g , 4 − g ) = −iA (0)4 (φ, 1 −¯q , 2 + q , 3 − g , 4 − g ) × V R+ [1 2]2 〈4 |p φ | 3] 22[1 3] 3 [2 3]s 123F 1m4F (s 12, s 23 ; s 123 ) + 〈3 |p φ| 2] 22 [1 4][2 4]s 124F 1m4F (s 14, s 12 ; s 124 )+〈1 |p φ | 2] 22[2 3][3 4]〈1 |p φ | 4] F2mh 4F (s 14, s 234 ; s 23 , m 2 φ )s 2 134−2[1 4][3 4]〈2 |p φ | 3] F2mh 4F (s 23, s 134 ; s 14 , m 2 φ )− C 3;φ|41|23 (φ, 1 −¯q , 2+ q , 3− g , 4− g ) F3m 3 (s 23, s 14 , m 2 φ )− 1 〈1 4〉 2 [1 2] 2 〈3 |p φ | 4] 2ˆL2 (s 124 , s 12 )2 [1 4][2 4]s 124− 2 〈3 4〉 〈3 |p φ| 2]ˆL 1 (s 124 , s 12 ) + 1 〈3 |p φ | 2] 2ˆL0 (s 124 , s 12 )[1 4]2 [1 4][2 4]s 124+ 1 〈1 4〉 2 [2 4] 2 s 2 2342 [2 3][3 4] 〈1 |p φ | 4] ˆL 2 (s 234 , s 23 ) + 2 〈3 4〉 〈1 |p φ| 2]ˆL 1 (s 234 , s 23 )[3 4]− 1 〈1 |p φ | 2] 22 [2 3][3 4] 〈1 |p φ | 4] ˆL 0 (s 234 , s 23 )(2− 1 〈1 2〉 [1 2] 〈4 |p φ | 1])[2 3]2 [1 3] 3 ˆL2 (s 123 , s 23 )s 123+ 2 〈1 3〉 [1 2] 〈4 |p φ| 3] 〈4 |p φ | 1]ˆL〈2 3〉 [1 3] 2 1 (s 123 , s 23 )[2 3][+ − 2 〈1 3〉[1 2] 〈4 |p φ| 3] 〈4 |p φ | 1]s 123 [1 3] 2 + 1 〈4 |p φ | 1] 2 [2 3]]ˆL0〈2 3〉[2 3] 2 [1 3] 3 (s 123 , s 23 )s 123