Abstract
Our work focuses on utilizing the Berends-Giele currents to construct differential operators and unifying relations for 1-loop Feynman integrands. We successfully reproduce the known results for the unifying relations between Yang-Mills theory and Yang-Mills scalar theory, and extend the discussion to the (A)dS case for the scalar theory with minimal coupling to gluons.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Cheung, C.-H. Shen and C. Wen, Unifying Relations for Scattering Amplitudes, JHEP 02 (2018) 095 [arXiv:1705.03025] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [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].
F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:1412.3479] [INSPIRE].
K. Zhou and B. Feng, Note on differential operators, CHY integrands, and unifying relations for amplitudes, JHEP 09 (2018) 160 [arXiv:1808.06835] [INSPIRE].
K. Zhou, Unified web for expansions of amplitudes, JHEP 10 (2019) 195 [arXiv:1908.10272] [INSPIRE].
J. Dong, S. He and L. Hou, Universal expansions of scattering amplitudes for gravitons, gluons, and Goldstone particles, Phys. Rev. D 105 (2022) 105007 [arXiv:2111.10525] [INSPIRE].
Y.-X. Tao and Q. Chen, A type of unifying relation in (A)dS spacetime, JHEP 02 (2023) 030 [arXiv:2210.15411] [INSPIRE].
F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
S. Raju, BCFW for Witten Diagrams, Phys. Rev. Lett. 106 (2011) 091601 [arXiv:1011.0780] [INSPIRE].
S. Raju, Recursion Relations for AdS/CFT Correlators, Phys. Rev. D 83 (2011) 126002 [arXiv:1102.4724] [INSPIRE].
S. Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators, Phys. Rev. D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
S. Albayrak, C. Chowdhury and S. Kharel, New relation for Witten diagrams, JHEP 10 (2019) 274 [arXiv:1904.10043] [INSPIRE].
D. Baumann et al., The cosmological bootstrap: weight-shifting operators and scalar seeds, JHEP 12 (2020) 204 [arXiv:1910.14051] [INSPIRE].
D. Baumann et al., The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization, SciPost Phys. 11 (2021) 071 [arXiv:2005.04234] [INSPIRE].
D. Baumann, C. Duaso Pueyo and A. Joyce, Bootstrapping Cosmological Correlations, AAPPS Bull. 30 (2020) 2 [INSPIRE].
D. Baumann et al., Snowmass White Paper: The Cosmological Bootstrap, in the proceedings of the Snowmass 2021, Seattle U.S.A, July 17–26 (2022) [arXiv:2203.08121] [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities, JHEP 04 (2020) 105 [arXiv:1811.00024] [INSPIRE].
H. Gomez, R. Lipinski Jusinskas, C. Lopez-Arcos and A. Quintero Velez, One-Loop Off-Shell Amplitudes from Classical Equations of Motion, Phys. Rev. Lett. 130 (2023) 081601 [arXiv:2208.02831] [INSPIRE].
N. Arkani-Hamed et al., The All-Loop Integrand For Scattering Amplitudes in Planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [INSPIRE].
R.H. Boels, On BCFW shifts of integrands and integrals, JHEP 11 (2010) 113 [arXiv:1008.3101] [INSPIRE].
J.A. Farrow et al., Propagators, BCFW recursion and new scattering equations at one loop, JHEP 10 (2020) 074 [arXiv:2007.00623] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, One-Loop Corrections from Higher Dimensional Tree Amplitudes, JHEP 08 (2016) 008 [arXiv:1512.05001] [INSPIRE].
S. He and E.Y. Yuan, One-loop Scattering Equations and Amplitudes from Forward Limit, Phys. Rev. D 92 (2015) 105004 [arXiv:1508.06027] [INSPIRE].
K. Zhou, On differential operators and unifying relations for 1-loop Feynman integrands, JHEP 10 (2021) 150 [arXiv:2108.04025] [INSPIRE].
K. Lee, Quantum off-shell recursion relation, JHEP 05 (2022) 051 [arXiv:2202.08133] [INSPIRE].
S. Albayrak and S. Kharel, Spinning loop amplitudes in anti-de Sitter space, Phys. Rev. D 103 (2021) 026004 [arXiv:2006.12540] [INSPIRE].
M. Bollmann and L. Ferro, Transmuting CHY formulae, JHEP 01 (2019) 180 [arXiv:1808.07451] [INSPIRE].
K. Zhou, Transmutation operators and expansions for one-loop Feynman integrands, Phys. Rev. D 106 (2022) 025014 [arXiv:2201.01552] [INSPIRE].
C. Armstrong et al., New recursion relations for tree-level correlators in anti-de Sitter spacetime, Phys. Rev. D 106 (2022) L121701 [arXiv:2209.02709] [INSPIRE].
S. Lee, C.R. Mafra and O. Schlotterer, Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality, JHEP 03 (2016) 090 [arXiv:1510.08843] [INSPIRE].
C.R. Mafra, Berends-Giele recursion for double-color-ordered amplitudes, JHEP 07 (2016) 080 [arXiv:1603.09731] [INSPIRE].
K.G. Selivanov, Post-classicism in Tree Amplitudes, in the proceedings of the 34th Rencontres de Moriond: Electroweak Interactions and Unified Theories, Les Arcs France, March 13–20 (1999), p. 473–478 [hep-th/9905128] [INSPIRE].
R. Kleiss and H. Kuijf, Multi-Gluon Cross-sections and Five Jet Production at Hadron Colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
S. Mizera and B. Skrzypek, Perturbiner Methods for Effective Field Theories and the Double Copy, JHEP 10 (2018) 018 [arXiv:1809.02096] [INSPIRE].
H. Frost, C.R. Mafra and L. Mason, A Lie bracket for the momentum kernel, arXiv:2012.00519 [https://doi.org/10.1007/s00220-023-04748-z] [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].
Y.-J. Du, B. Feng and C.-H. Fu, Dual-color decompositions at one-loop level in Yang-Mills theory, JHEP 06 (2014) 157 [arXiv:1402.6805] [INSPIRE].
S. Albayrak and S. Kharel, Towards the higher point holographic momentum space amplitudes, JHEP 02 (2019) 040 [arXiv:1810.12459] [INSPIRE].
H. Gomez and R.L. Jusinskas, Multiparticle Solutions to Einstein’s Equations, Phys. Rev. Lett. 127 (2021) 181603 [arXiv:2106.12584] [INSPIRE].
H. Lee and X. Wang, Cosmological Double-Copy Relations, arXiv:2212.11282 [INSPIRE].
S. Albayrak, S. Kharel and D. Meltzer, On duality of color and kinematics in (A)dS momentum space, JHEP 03 (2021) 249 [arXiv:2012.10460] [INSPIRE].
Y.-Z. Li, Flat-space structure of gluons and gravitons in AdS spacetime, Phys. Rev. D 107 (2023) 125018 [arXiv:2212.13195] [INSPIRE].
K. Cho, K. Kim and K. Lee, The off-shell recursion for gravity and the classical double copy for currents, JHEP 01 (2022) 186 [arXiv:2109.06392] [INSPIRE].
J.A. Farrow, A.E. Lipstein and P. McFadden, Double copy structure of CFT correlators, JHEP 02 (2019) 130 [arXiv:1812.11129] [INSPIRE].
C. Armstrong, A.E. Lipstein and J. Mei, Color/kinematics duality in AdS4, JHEP 02 (2021) 194 [arXiv:2012.02059] [INSPIRE].
Acknowledgments
We would like to thank Yi-Jian Du and Kang Zhou for useful comments on the draft. QC is partly supported by National Key R&D Program of China (Grant No. 2017YFA0402204). YT is partly supported by National Key R&D Program of China (NO. 2020YFA0713000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2301.08043
Rights and permissions
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.
About this article
Cite this article
Chen, Q., Tao, YX. Differential operators and unifying relations for 1-loop Feynman integrands from Berends-Giele currents. J. High Energ. Phys. 2023, 38 (2023). https://doi.org/10.1007/JHEP08(2023)038
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)038