Abstract
We analyze the validity of BCFW recursion relations for currents of n − 2 gluons and two massive quarks, where one of the quarks is off shell and the remaining particles are on shell. These currents are gauge-dependent and can be used as ingredients in the unitarity-based approach to computing one-loop amplitudes. The validity of BCFW recursion relations is well known to depend on the so-called boundary behavior of the currents as the momentum shift parameter goes to infinity. With off-shell currents, a new potential problem arises, namely unphysical poles that depend on the choice of gauge. We identify conditions under which boundary terms are absent and unphysical poles are avoided, so that there is a natural recursion relation. In particular, we are able to choose a gauge in which we construct a valid shift for currents with at least n − 3 gluons of the same helicity. We derive an analytic formula in the case where all gluons have the same helicity. As by-products, we prove the vanishing boundary behavior of general off-shell objects in Feynman gauge, and we find a compact generalization of Berends-Giele gluon currents with a generic reference spinor.
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References
F.A. Berends and W. Giele, Recursive calculations for processes with N gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
D.A. Kosower, Light cone recurrence relations for QCD amplitudes, Nucl. Phys. B 335 (1990) 23 [INSPIRE].
B. Feng and Z. Zhang, Boundary contributions using fermion pair deformation, JHEP 12 (2011) 057 [arXiv:1109.1887] [INSPIRE].
R. Britto and E. Mirabella, External leg corrections in the unitarity method, JHEP 01 (2012) 045 [arXiv:1109.5106] [INSPIRE].
G. Rodrigo, Multigluonic scattering amplitudes of heavy quarks, JHEP 09 (2005) 079 [hep-ph/0508138] [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].
S. Badger, E.N. Glover and V.V. Khoze, Recursion relations for gauge theory amplitudes with massive vector bosons and fermions, JHEP 01 (2006) 066 [hep-th/0507161] [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].
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].
C. Quigley and M. Rozali, Recursion relations, helicity amplitudes and dimensional regularization, JHEP 03 (2006) 004 [hep-ph/0510148] [INSPIRE].
C. Schwinn and S. Weinzierl, SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks, JHEP 03 (2006) 030 [hep-th/0602012] [INSPIRE].
K. Ozeren and W. Stirling, Scattering amplitudes with massive fermions using BCFW recursion, Eur. Phys. J. C 48 (2006) 159 [hep-ph/0603071] [INSPIRE].
P. Ferrario, G. Rodrigo and P. Talavera, Compact multigluonic scattering amplitudes with heavy scalars and fermions, Phys. Rev. Lett. 96 (2006) 182001 [hep-th/0602043] [INSPIRE].
C. Schwinn and S. Weinzierl, On-shell recursion relations for all Born QCD amplitudes, JHEP 04 (2007) 072 [hep-ph/0703021] [INSPIRE].
A. Hall, Massive quark-gluon scattering amplitudes at tree level, Phys. Rev. D 77 (2008) 025011 [arXiv:0710.1300] [INSPIRE].
G. Chen, Recursion relations for the general tree-level amplitudes in QCD with massive Dirac fields, Phys. Rev. D 83 (2011) 125005 [arXiv:1103.2518] [INSPIRE].
R.H. Boels and C. Schwinn, On-shell supersymmetry for massive multiplets, Phys. Rev. D 84 (2011) 065006 [arXiv:1104.2280] [INSPIRE].
J.-H. Huang and W. Wang, Multigluon tree amplitudes with a pair of massive fermions, Eur. Phys. J. C 72 (2012) 2050 [arXiv:1204.0068] [INSPIRE].
F.A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans and T.T. Wu, Single Bremsstrahlung processes in gauge theories, Phys. Lett. B 103 (1981) 124 [INSPIRE].
P. De Causmaecker, R. Gastmans, W. Troost and T.T. Wu, Multiple Bremsstrahlung in gauge theories at high-energies. 1. General formalism for quantum electrodynamics, Nucl. Phys. B 206 (1982) 53 [INSPIRE].
R. Kleiss and W.J. Stirling, Spinor techniques for calculating \( p\overline{p}\to {{{{W^{+- }}}} \left/ {{{Z_0}+}} \right.} \) jets, Nucl. Phys. B 262 (1985) 235 [INSPIRE].
Z. Xu, D.-H. Zhang and L. Chang, Helicity amplitudes for multiple Bremsstrahlung in massless nonabelian gauge theories, Nucl. Phys. B 291 (1987) 392 [INSPIRE].
J. Gunion and Z. Kunszt, Improved analytic techniques for tree graph calculations and the \( ggq\overline{q} \) lepton anti-lepton subprocess, Phys. Lett. B 161 (1985) 333 [INSPIRE].
C. Schwinn and S. Weinzierl, Scalar diagrammatic rules for Born amplitudes in QCD, JHEP 05 (2005) 006 [hep-th/0503015] [INSPIRE].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
R.H. Boels and R.S. Isermann, Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts, JHEP 03 (2012) 051 [arXiv:1110.4462] [INSPIRE].
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ArXiv ePrint: 1210.1755
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Britto, R., Ochirov, A. On-shell recursion for massive fermion currents. J. High Energ. Phys. 2013, 2 (2013). https://doi.org/10.1007/JHEP01(2013)002
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DOI: https://doi.org/10.1007/JHEP01(2013)002