Abstract
We use the recently developed massive spinor-helicity formalism [1] of Arkani-Hamed et al. to study a new class of recursion relations for tree-level amplitudes in gauge theories. These relations are based on a combined complex deformation of massless as well as massive external momenta. We use these relations to study tree-level amplitudes in scalar QCD as well as amplitudes involving massive vector bosons in the Higgsed phase of Yang-Mills theory. We prove the validity of our proposal by showing that in the limit of infinite momenta of two of the external particles, the amplitude once again is controlled by an enhanced Spin-Lorentz symmetry paralleling the proof of BCFW shift for massless gauge theories. Simple examples illustrate that the proposed shift may lead to an efficient computation of tree-level amplitudes.
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References
N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang, Scattering Amplitudes For All Masses and Spins, arXiv:1709.04891 [INSPIRE].
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges and J. Trnka, A Note on Polytopes for Scattering Amplitudes, JHEP 04 (2012) 081 [arXiv:1012.6030] [INSPIRE].
N. Arkani-Hamed and J. Trnka, The Amplituhedron, JHEP 10 (2014) 030 [arXiv:1312.2007] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001 [arXiv:1306.6575] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [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 and Y.-t. Huang, Basics of Generalized Unitarity, J. Phys. A 44 (2011) 454003 [arXiv:1103.1869] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng, Black Hole Binary Dynamics from the Double Copy and Effective Theory, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge University Press (2015) [DOI].
R. Kleiss and W. J. Stirling, Spinor Techniques for Calculating \( p\overline{p} \) → W ± /Z 0 + Jets, Nucl. Phys. B 262 (1985) 235 [INSPIRE].
C. Schwinn and S. Weinzierl, Scalar diagrammatic rules for Born amplitudes in QCD, JHEP 05 (2005) 006 [hep-th/0503015] [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].
S. D. Badger, E. W. 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].
K. J. Ozeren and W. J. Stirling, Scattering amplitudes with massive fermions using BCFW recursion, Eur. Phys. J. C 48 (2006) 159 [hep-ph/0603071] [INSPIRE].
S. D. Badger, E. W. N. Glover, V. V. Khoze and P. Svrček, Recursion relations for gauge theory amplitudes with massive particles, JHEP 07 (2005) 025 [hep-th/0504159] [INSPIRE].
A. Ochirov, Helicity amplitudes for QCD with massive quarks, JHEP 04 (2018) 089 [arXiv:1802.06730] [INSPIRE].
C. Schwinn and S. Weinzierl, On-shell recursion relations for all Born QCD amplitudes, JHEP 04 (2007) 072 [hep-ph/0703021] [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].
R. Franken and C. Schwinn, On-shell constructibility of Born amplitudes in spontaneously broken gauge theories, JHEP 02 (2020) 073 [arXiv:1910.13407] [INSPIRE].
A. Falkowski and C. S. Machado, Soft Matters, or the Recursions with Massive Spinors, arXiv:2005.08981 [INSPIRE].
A. Herderschee, S. Koren and T. Trott, Massive On-Shell Supersymmetric Scattering Amplitudes, JHEP 10 (2019) 092 [arXiv:1902.07204] [INSPIRE].
A. Herderschee, S. Koren and T. Trott, Constructing \( \mathcal{N} \) = 4 Coulomb branch superamplitudes, JHEP 08 (2019) 107 [arXiv:1902.07205] [INSPIRE].
R. Aoude and C. S. Machado, The Rise of SMEFT On-shell Amplitudes, JHEP 12 (2019) 058 [arXiv:1905.11433] [INSPIRE].
N. Arkani-Hamed and J. Kaplan, On Tree Amplitudes in Gauge Theory and Gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP 09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP 04 (2019) 156 [arXiv:1812.08752] [INSPIRE].
V. Del Duca, L. J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [INSPIRE].
L. J. Dixon, Calculating scattering amplitudes efficiently, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95): QCD and Beyond, (1996) [hep-ph/9601359] [INSPIRE].
H. Johansson and A. Ochirov, Color-Kinematics Duality for QCD Amplitudes, JHEP 01 (2016) 170 [arXiv:1507.00332] [INSPIRE].
A. Ochirov and B. Page, Multi-Quark Colour Decompositions from Unitarity, JHEP 10 (2019) 058 [arXiv:1908.02695] [INSPIRE].
F. Maltoni, K. Paul, T. Stelzer and S. Willenbrock, Color Flow Decomposition of QCD Amplitudes, Phys. Rev. D 67 (2003) 014026 [hep-ph/0209271] [INSPIRE].
T. Melia, Proof of a new colour decomposition for QCD amplitudes, JHEP 12 (2015) 107 [arXiv:1509.03297] [INSPIRE].
S. J. Parke and T. R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
H. Johansson and A. Ochirov, Double copy for massive quantum particles with spin, JHEP 09 (2019) 040 [arXiv:1906.12292] [INSPIRE].
T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP 04 (2011) 053 [arXiv:1010.0257] [INSPIRE].
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Ballav, S., Manna, A. Recursion relations for scattering amplitudes with massive particles. J. High Energ. Phys. 2021, 295 (2021). https://doi.org/10.1007/JHEP03(2021)295
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DOI: https://doi.org/10.1007/JHEP03(2021)295