Bootstrapping multiparton loop amplitudes in QCD

Stanford University, Palo Alto, California, United States
Physical Review D (Impact Factor: 4.64). 03/2006; 73(6). DOI: 10.1103/PhysRevD.73.065013
Source: arXiv


We present a new method for computing complete one-loop amplitudes, including their rational parts, in nonsupersymmetric gauge theory. This method merges the unitarity method with on-shell recursion relations. It systematizes a unitarity-factorization bootstrap approach previously applied by the authors to the one-loop amplitudes required for next-to-leading order QCD corrections to the processes e+e-→Z,γ*→4 jets and pp→W+2 jets. We illustrate the method by reproducing the one-loop color-ordered five-gluon helicity amplitudes in QCD that interfere with the tree amplitude, namely A5;1(1-,2-,3+,4+,5+) and A5;1(1-,2+,3-,4+,5+). Then we describe the construction of the six- and seven-gluon amplitudes with two adjacent negative-helicity gluons, A6;1(1-,2-,3+,4+,5+,6+) and A7;1(1-,2-,3+,4+,5+,6+,7+), which uses the previously-computed logarithmic parts of the amplitudes as input. We present a compact expression for the six-gluon amplitude. No loop integrals are required to obtain the rational parts.

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    • "Since all pole parts have been found, the remaining part must be zero, then the boundary contributions are fully determined. The use of auxiliary deformations has also appeared in the study of one-loop rational parts in [17] [18] [19]. "
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    • "One possible application of our results is following. Since our results are complete, i.e., there are (µ 2 ) n -terms corresponding to rational part as mentioned in section 2, we could use our result to calculate the rational terms and compare with results from the recursion relation given in [39] [40] [41]. We believe this calculation will help to us to clarify some points in the recursion relation. "
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    • "Basically all new methods need a special treatment of the contributions that are not proportional to the scalar 1-loop functions, the so called rational terms [38] [39] [40] [41]. That is achieved, in Unitarity and Generalized Unitarity methods, by computing the entire amplitude in different numbers of space-time dimensions [42], or via bootstrapping techniques [43] [44], or through d-dimensional cuts [45]. The OPP approach requires, instead, the computation (once for all for the theory at hand) of a special set of tree level Feynman rules [46] [47] [48] [49] [50] up to 4-point interactions 1 . "
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