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

3.3. The rational pieces 102+R(4 + , ˆ1 − , 2 + , − ˆP 412) + 1 A (0) (φ,s ˆP 412, − ˆ3 − )412+R(φ, ˆ1 − , 2 + , − ˆP 34, + ) 1 A (0) (s ˆP 34, − ˆ3 − , 4 + )34+R(φ, ˆ1 − , 4 + , − ˆP 23) + 1 A (0) (s ˆP 23, − 2 + , ˆ3 − )23+A (0) (ˆ1 − , ˆP 41, + 4 + ) 1 R(φ, −s ˆP 41, − 2 + , ˆ3 − )41+A (0) (ˆ1 − , ˆP 12 + , 2+ ) 1 R(φ, −s ˆP 12 − , ˆ3 − , 4 + ), (3.126)12where we recycle the known lower point amplitudes. For the four-point amplitude,we require the rational parts of the φ amplitude with one minus and two positivehelicity gluons (3.121), the two and three-point φ-MHV amplitudes given ineqs. (3.123), (3.124) and (3.125), as well as the pure four-gluon QCD amplitudewith a single negative helicity of eq. (3.122).We find thatSimilarly,In the other channels,R4 234 = N P m 4 H 〈2 4〉 [2 4] 〈3 |P 234 | 1] 26 s 234 〈4 |P 234 | 1] 2 〈2 |P 234 | 1]2. (3.127)R4 23 = −2A(0) (φ † , 4 + , 2 + , 3 − , 1 − ) − N P6 s [2 4][2 1] 〈4 |P 123 | 2]123[3 1][2 3] 〈4 |P 123 | 1]2, (3.128)R4 34 = R4 23 (2 ↔ 4). (3.129)R 414 = −2A (0) (φ, 1 − , 3 − , 2 + , 4 + ) (3.130)R 124 = R 414 (4 ↔ 2), (3.131)and finally,R4 412 = N P [2 4] 3 〈3 |P 412 | 1] 26 s 412 〈2 4〉[1 2] 2 [4 1]2. (3.132)3.3.3 The overlap termsThe overlap terms are defined as [108,124],O n = ∑ iCR n (z)Res z=zi . (3.133)z