Abstract
In this paper, we propose a new algorithm to systematically determine the missing boundary contributions, when one uses the BCFW on-shell recursion relation to calculate tree amplitudes for general quantum field theories. After an instruction of the algorithm, we will use several examples to demonstrate its application, including amplitudes of color-ordered ϕ 4 theory, Yang-Mills theory, Einstein-Maxwell theory and color-ordered Yukawa theory with ϕ 4 interaction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
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) 181602 [hep-th/0501052] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].
B. Feng and M. Luo, An Introduction to On-shell Recursion Relations, Front. Phys. 7 (2012) 533 [arXiv:1111.5759] [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
N. Arkani-Hamed and J. Kaplan, On Tree Amplitudes in Gauge Theory and Gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [INSPIRE].
C. Cheung, On-Shell Recursion Relations for Generic Theories, JHEP 03 (2010) 098 [arXiv:0808.0504] [INSPIRE].
P. Benincasa and F. Cachazo, Consistency Conditions on the S-matrix of Massless Particles, arXiv:0705.4305 [INSPIRE].
R.H. Boels, No triangles on the moduli space of maximally supersymmetric gauge theory, JHEP 05 (2010) 046 [arXiv:1003.2989] [INSPIRE].
B. Feng, J. Wang, Y. Wang and Z. Zhang, BCFW Recursion Relation with Nonzero Boundary Contribution, JHEP 01 (2010) 019 [arXiv:0911.0301] [INSPIRE].
B. Feng and C.-Y. Liu, A Note on the boundary contribution with bad deformation in gauge theory, JHEP 07 (2010) 093 [arXiv:1004.1282] [INSPIRE].
B. Feng and Z. Zhang, Boundary Contributions Using Fermion Pair Deformation, JHEP 12 (2011) 057 [arXiv:1109.1887] [INSPIRE].
P. Benincasa and E. Conde, On the Tree-Level Structure of Scattering Amplitudes of Massless Particles, JHEP 11 (2011) 074 [arXiv:1106.0166] [INSPIRE].
P. Benincasa and E. Conde, Exploring the S-matrix of Massless Particles, Phys. Rev. D 86 (2012) 025007 [arXiv:1108.3078] [INSPIRE].
B. Feng, Y. Jia, H. Lüo and M. Luo, Roots of Amplitudes, arXiv:1111.1547 [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-shell recurrence relations for one-loop QCD amplitudes, Phys. Rev. D 71 (2005) 105013 [hep-th/0501240] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Bootstrapping multi-parton loop amplitudes in QCD, Phys. Rev. D 73 (2006) 065013 [hep-ph/0507005] [INSPIRE].
C.F. Berger, Z. Bern, L.J. Dixon, D. Forde and D.A. Kosower, Bootstrapping One-Loop QCD Amplitudes with General Helicities, Phys. Rev. D 74 (2006) 036009 [hep-ph/0604195] [INSPIRE].
K. Zhou and C. Qiao, General tree-level amplitudes by factorization limits, arXiv:1410.5042 [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Progress in one loop QCD computations, Ann. Rev. Nucl. Part. Sci. 46 (1996) 109 [hep-ph/9602280] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The All-Loop Integrand For Scattering Amplitudes in Planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [INSPIRE].
C. Quigley and M. Rozali, Recursion relations, helicity amplitudes and dimensional regularization, JHEP 03 (2006) 004 [hep-ph/0510148] [INSPIRE].
M.-x. Luo and C.-k. Wen, Recursion relations for tree amplitudes in super gauge theories, JHEP 03 (2005) 004 [hep-th/0501121] [INSPIRE].
G. Georgiou and V.V. Khoze, Tree amplitudes in gauge theory as scalar MHV diagrams, JHEP 05 (2004) 070 [hep-th/0404072] [INSPIRE].
K. Risager, A Direct proof of the CSW rules, JHEP 12 (2005) 003 [hep-th/0508206] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
The unconventional order of authors is merely to satisfy the outdated requirement for Phy. Degree of the school. (Junjie Rao)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Feng, B., Zhou, K., Qiao, C. et al. Determination of boundary contributions in recursion relation. J. High Energ. Phys. 2015, 23 (2015). https://doi.org/10.1007/JHEP03(2015)023
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2015)023