Abstract
The appearance of BCFW on-shell recursion relation has deepen our understanding of quantum field theory, especially the one with gauge boson and graviton. To be able to write the BCFW recursion relation, the knowledge of boundary contributions is needed. So far, most applications have been constrained to the cases where the boundary contribution is zero. In this paper, we show that for some theories, although there is no proper deformation to annihilate the boundary contribution, its effects can be analyzed in simple way, thus we do able to write down the BCFW recursion relation with boundary contributions. The examples we will present in this paper include the λφ4 theory and Yukawa coupling between fermions and scalars.
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] [SPIRES].
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] [SPIRES].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [SPIRES].
P. Benincasa and F. Cachazo, Consistancy conditions on the S-matix of massless particles, arXiv:0705.4305 [SPIRES].
N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [SPIRES].
D. Vaman and Y.-P. Yao, QCD recursion relations from the largest time equation, JHEP 04 (2006) 030 [hep-th/0512031] [SPIRES].
P.D. Draggiotis, R.H.P. Kleiss, A. Lazopoulos and C.G. Papadopoulos, Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD, Eur. Phys. J. C 46 (2006) 741 [hep-ph/0511288] [SPIRES].
P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming tree amplitudes in general relativity, JHEP 11 (2007) 057 [hep-th/0702032] [SPIRES].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, arXiv:0808.1446 [SPIRES].
C. Cheung, On-shell recursion relations for generic theories, arXiv:0808.0504 [SPIRES].
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] [SPIRES].
Z. Bern, L.J. Dixon and D.A. Kosower, The last of the finite loop amplitudes in QCD, Phys. Rev. D 72 (2005) 125003 [hep-ph/0505055] [SPIRES].
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] [SPIRES].
Z. Bern, N.E.J. Bjerrum-Bohr, D.C. Dunbar and H. Ita, Recursive calculation of one-loop QCD integral coefficients, JHEP 11 (2005) 027 [hep-ph/0507019] [SPIRES].
C.F. Berger, Z. Bern, L.J. Dixon, D. Forde and D.A. Kosower, All one-loop maximally helicity violating gluonic amplitudes in QCD, Phys. Rev. D 75 (2007) 016006 [hep-ph/0607014] [SPIRES].
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] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 0911.0301
Rights and permissions
About this article
Cite this article
Feng, B., Wang, J., Wang, Y. et al. BCFW recursion relation with nonzero boundary contribution. J. High Energ. Phys. 2010, 19 (2010). https://doi.org/10.1007/JHEP01(2010)019
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2010)019