Abstract
We investigate the application of the BCFW recursion relation to scattering amplitudes with one off-shell particle in a Yang-Mills theory with fermions. We provide a set of conditions of applicability of the BCFW recursion, stressing some important differences with respect to the pure on-shell case. We show how the formulas for Maximally-Helicity-Violating (MHV) configurations with any number of partons, which are well known in the fully on-shell case, are generalized to this kinematic regime. We also derive analytic expressions for all the helicity configurations of the 5-point color-stripped tree-level amplitudes for any of the partons being off the mass shell.
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R. Kleiss and W.J. Stirling, Spinor Techniques for Calculating \( p\overline{p} \) → W ±/Z0 + Jets, Nucl. Phys. B 262 (1985) 235 [INSPIRE].
J.F. 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].
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].
F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
M.L. Mangano, S.J. Parke and Z. Xu, Duality and multi-gluon scattering, Nucl. Phys. B 298 (1988) 653 [INSPIRE].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [INSPIRE].
F.A. Berends, W.T. Giele and H. Kuijf, Exact and approximate expressions for multi-gluon scattering, Nucl. Phys. B 333 (1990) 120 [INSPIRE].
D.A. Kosower, Light Cone Recurrence Relations for QCD Amplitudes, Nucl. Phys. B 335 (1990) 23 [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].
M.-x. Luo and C.-k. Wen, Recursion relations for tree amplitudes in super gauge theories, JHEP 03 (2005) 004 [hep-th/0501121] [INSPIRE].
A. van Hameren, BCFW recursion for off-shell gluons, JHEP 07 (2014) 138 [arXiv:1404.7818] [INSPIRE].
S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135 [INSPIRE].
J.C. Collins and R.K. Ellis, Heavy quark production in very high-energy hadron collisions, Nucl. Phys. B 360 (1991) 3 [INSPIRE].
V.S. Fadin and L.N. Lipatov, Radiative corrections to QCD scattering amplitudes in a multi-Regge kinematics, Nucl. Phys. B 406 (1993) 259 [INSPIRE].
V.S. Fadin and L.N. Lipatov, Next-to-leading corrections to the BFKL equation from the gluon and quark production, Nucl. Phys. B 477 (1996) 767 [hep-ph/9602287] [INSPIRE].
L.N. Lipatov, Gauge invariant effective action for high-energy processes in QCD, Nucl. Phys. B 452 (1995) 369 [hep-ph/9502308] [INSPIRE].
E.N. Antonov, L.N. Lipatov, E.A. Kuraev and I.O. Cherednikov, Feynman rules for effective Regge action, Nucl. Phys. B 721 (2005) 111 [hep-ph/0411185] [INSPIRE].
A. van Hameren, P. Kotko and K. Kutak, Helicity amplitudes for high-energy scattering, JHEP 01 (2013) 078 [arXiv:1211.0961] [INSPIRE].
P. Kotko, Wilson lines and gauge invariant off-shell amplitudes, JHEP 07 (2014) 128 [arXiv:1403.4824] [INSPIRE].
L.N. Lipatov and M.I. Vyazovsky, QuasimultiRegge processes with a quark exchange in the t channel, Nucl. Phys. B 597 (2001) 399 [hep-ph/0009340] [INSPIRE].
A. van Hameren, K. Kutak and T. Salwa, Scattering amplitudes with off-shell quarks, Phys. Lett. B 727 (2013) 226 [arXiv:1308.2861] [INSPIRE].
M.A. Nefedov, V.A. Saleev and A.V. Shipilova, Dijet azimuthal decorrelations at the LHC in the parton Reggeization approach, Phys. Rev. D 87 (2013) 094030 [arXiv:1304.3549] [INSPIRE].
B.A. Kniehl, M.A. Nefedov and V.A. Saleev, Prompt-photon plus jet associated photoproduction at HERA in the parton Reggeization approach, Phys. Rev. D 89 (2014) 114016 [arXiv:1404.3513] [INSPIRE].
A.V. Karpishkov, M.A. Nefedov, V.A. Saleev and A.V. Shipilova, Open charm production in the parton Reggeization approach: Tevatron and the LHC, Phys. Rev. D 91 (2015) 054009 [arXiv:1410.7139] [INSPIRE].
A.V. Karpishkov, M.A. Nefedov, V.A. Saleev and A.V. Shipilova, B-meson production in the Parton Reggeization Approach at Tevatron and the LHC, Int. J. Mod. Phys. A 30 (2015) 1550023 [arXiv:1411.7672] [INSPIRE].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
M. Bury and A. van Hameren, Numerical evaluation of multi-gluon amplitudes for High Energy Factorization, arXiv:1503.08612 [INSPIRE].
M. Deak, F. Hautmann, H. Jung and K. Kutak, Forward Jet Production at the Large Hadron Collider, JHEP 09 (2009) 121 [arXiv:0908.0538] [INSPIRE].
K. Kutak and S. Sapeta, Gluon saturation in dijet production in p-Pb collisions at Large Hadron Collider, Phys. Rev. D 86 (2012) 094043 [arXiv:1205.5035] [INSPIRE].
M.D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, Cambridge U.K. (2013).
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van Hameren, A., Serino, M. BCFW recursion for TMD parton scattering. J. High Energ. Phys. 2015, 10 (2015). https://doi.org/10.1007/JHEP07(2015)010
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DOI: https://doi.org/10.1007/JHEP07(2015)010