On Multi-step BCFW Recursion Relations
arXiv:1504.06306 · doi:10.1007/JHEP07(2015)058
Abstract
In this paper, we extensively investigate the new algorithm known as the multi-step BCFW recursion relations. Many interesting mathematical properties are found and understanding these aspects, one can find a systematic way to complete the calculation of amplitude after finite, definite steps and get the correct answer, without recourse to any specific knowledge from field theories, besides mass dimension and helicities. This process consists of the pole concentration and inconsistency elimination. Terms that survive inconsistency elimination cannot be determined by the new algorithm. They include polynomials and their generalizations, which turn out to be useful objects to be explored. Afterwards, we apply it to the Standard Model plus gravity to illustrate its power and limitation. Ensuring its workability, we also tentatively discuss how to improve its efficiency by reducing the steps.
38 pages, 13 figures, 3 appendices
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Cited by in corpus (10)
- Expansion of Einstein-Yang-Mills Amplitude
- Recursion relations from soft theorems
- An Algebraic Approach to the Scattering Equations
- The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
- On-shell diagrammatics and the perturbative structure of planar gauge theories
- Form Factor and Boundary Contribution of Amplitude
- Boundary Operators of BCFW Recursion Relation
- Note on recursion relations for the -cut representation
- Wilson Lines and Boundary Operators of BCFW Shifts
- Boundary Contributions of On-shell Recursion Relations With Multiple-line Deformation