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2014

Recursion Relation for Boundary Contribution

Jin, Qingjun, Feng, Bo

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It is well known that under a BCFW-deformation, there is a boundary contribution when the amplitude scales as O(1) or worse.

We show that boundary contributions have a similar recursion relation as scattering amplitude.
Just like the BCFW recursion relation, where scattering amplitudes are expressed as the products of two on-shell sub-amplitudes (plus possible boundary contributions), our new recursion relation expresses boundary contributions as products of sub-amplitudes and boundary contributions with less legs, plus yet another possible boundary contribution.
In other words, the complete scattering amplitude, including boundary contributions, can be obtained by multiple steps of recursions, unless the boundary contributions are still non-zero when all possible deformations are exploited.

Recursion Relation for Boundary Contribution · Around

Built on

R. Britto, F. Cachazo and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys. B 715
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R. Britto, F. Cachazo, B. Feng and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett. 94
2005
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K. Risager, “A Direct proof of the CSW rules,” JHEP 0512
2005
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Z. Bern, L. J. Dixon and D. A. Kosower, “On-Shell Methods in Perturbative QCD,” Annals Phys. 322
Original
2007
Earlier work this paper cites.
N. Arkani-Hamed and J. Kaplan, “On Tree Amplitudes in Gauge Theory and Gravity,” JHEP 0804
Original
2008
Earlier work this paper cites.

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Then

N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, “A Duality For The S Matrix,” JHEP 1003
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2010
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B. Feng and Z. Zhang, “Boundary Contributions Using Fermion Pair Deformation,” JHEP 1112
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B. Feng and M. Luo, “An Introduction to On-shell Recursion Relations,” Front. Phys. 7
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M. Sogaard and Y. Zhang, “Unitarity Cuts of Integrals with Doubled Propagators,” JHEP 1407
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