Abstract
In a recent paper [1], three-particle interactions without invariance under Lorentz boosts were constrained by demanding that they yield tree-level four-particle scattering amplitudes with singularities as dictated by unitarity and locality. In this brief note, we show how to obtain an independent verification and consistency check of these boostless bootstrap results using BCFW momentum shifts. We point out that the constructibility criterion, related to the behaviour of the deformed amplitude at infinite BCFW parameter z, is not strictly necessary to obtain non-trivial constraints for the three-particle interactions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Pajer, D. Stefanyszyn and J. Supeł, The boostless bootstrap: amplitudes without Lorentz boosts, JHEP 12 (2020) 198 [arXiv:2007.00027] [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering amplitudes, arXiv:1308.1697 [INSPIRE].
C. Cheung, TASI lectures on scattering amplitudes, in Proceedings, Theoretical Advanced Study Institute in elementary particle physics: anticipating the next discoveries in particle physics (TASI 2016), Boulder, CO, U.S.A., 6 June–1 July 2016, R. Essig and I. Low eds., World Scientific, Singapore (2018), pg. 571 [arXiv:1708.03872] [INSPIRE].
P. Benincasa, New structures in scattering amplitudes: a review, Int. J. Mod. Phys. A 29 (2014) 1430005 [arXiv:1312.5583] [INSPIRE].
S. Weinberg, Photons and gravitons in S-matrix theory: derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev. 135 (1964) B1049 [INSPIRE].
S. Weinberg, Photons and gravitons in perturbation theory: derivation of Maxwell’s and Einstein’s equations, Phys. Rev. 138 (1965) B988 [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].
P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, Scattering amplitudes for all masses and spins, arXiv:1709.04891 [INSPIRE].
D. A. McGady and L. Rodina, Higher-spin massless S-matrices in four-dimensions, Phys. Rev. D 90 (2014) 084048 [arXiv:1311.2938] [INSPIRE].
P. C. Schuster and N. Toro, Constructing the tree-level Yang-Mills S-matrix using complex factorization, JHEP 06 (2009) 079 [arXiv:0811.3207] [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].
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, The cosmological bootstrap: weight-shifting operators and scalar seeds, JHEP 12 (2020) 204 [arXiv:1910.14051] [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043 [INSPIRE].
C. Sleight, A Mellin space approach to cosmological correlators, JHEP 01 (2020) 090 [arXiv:1906.12302] [INSPIRE].
C. Sleight and M. Taronna, Bootstrapping inflationary correlators in Mellin space, JHEP 02 (2020) 098 [arXiv:1907.01143] [INSPIRE].
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, The cosmological bootstrap: spinning correlators from symmetries and factorization, arXiv:2005.04234 [INSPIRE].
D. Green and E. Pajer, On the symmetries of cosmological perturbations, JCAP 09 (2020) 032 [arXiv:2004.09587] [INSPIRE].
I. Mata, S. Raju and S. Trivedi, CMB from CFT, JHEP 07 (2013) 015 [arXiv:1211.5482] [INSPIRE].
A. Ghosh, N. Kundu, S. Raju and S. P. Trivedi, Conformal invariance and the four point scalar correlator in slow-roll inflation, JHEP 07 (2014) 011 [arXiv:1401.1426] [INSPIRE].
N. Kundu, A. Shukla and S. P. Trivedi, Constraints from conformal symmetry on the three point scalar correlator in inflation, JHEP 04 (2015) 061 [arXiv:1410.2606] [INSPIRE].
N. Arkani-Hamed, P. Benincasa and A. Postnikov, Cosmological polytopes and the wavefunction of the universe, arXiv:1709.02813 [INSPIRE].
N. Arkani-Hamed and P. Benincasa, On the emergence of Lorentz invariance and unitarity from the scattering facet of cosmological polytopes, arXiv:1811.01125 [INSPIRE].
P. Benincasa, From the flat-space S-matrix to the wavefunction of the universe, arXiv:1811.02515 [INSPIRE].
P. Benincasa, Cosmological polytopes and the wavefuncton of the universe for light states, arXiv:1909.02517 [INSPIRE].
A. Hillman, Symbol recursion for the dS wave function, arXiv:1912.09450 [INSPIRE].
P. Benincasa, A. J. McLeod and C. Vergu, Steinmann relations and the wavefunction of the universe, Phys. Rev. D 102 (2020) 125004 [arXiv:2009.03047] [INSPIRE].
H. Goodhew, S. Jazayeri and E. Pajer, The cosmological optical theorem, arXiv:2009.02898 [INSPIRE].
J. M. Maldacena and G. L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [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].
M. P. Hertzberg, J. A. Litterer and M. Sandora, Symmetries from locality. II. Gravitation and Lorentz boosts, Phys. Rev. D 102 (2020) 025023 [arXiv:2005.01744] [INSPIRE].
J. Khoury, G. E. J. Miller and A. J. Tolley, On the origin of gravitational Lorentz covariance, Class. Quant. Grav. 31 (2014) 135011 [arXiv:1305.0822] [INSPIRE].
M. P. Hertzberg and J. A. Litterer, Symmetries from locality. III. Massless spin-2 gravitons and time translations, Phys. Rev. D 102 (2020) 085007 [arXiv:2008.06510] [INSPIRE].
M. P. Hertzberg and M. Sandora, Special relativity from soft gravitons, Phys. Rev. D 96 (2017) 084048 [arXiv:1704.05071] [INSPIRE].
H. K. Dreiner, H. E. Haber and S. P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv:0812.1594] [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].
P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming tree amplitudes in general relativity, JHEP 11 (2007) 057 [hep-th/0702032] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, On-shell recursion relations for effective field theories, Phys. Rev. Lett. 116 (2016) 041601 [arXiv:1509.03309] [INSPIRE].
A. Padilla, D. Stefanyszyn and T. Wilson, Probing scalar effective field theories with the soft limits of scattering amplitudes, JHEP 04 (2017) 015 [arXiv:1612.04283] [INSPIRE].
B. Feng, K. Zhou, C. Qiao and J. Rao, Determination of boundary contributions in recursion relation, JHEP 03 (2015) 023 [arXiv:1411.0452] [INSPIRE].
S. Raju, Four point functions of the stress tensor and conserved currents in AdS4/CFT3, Phys. Rev. D 85 (2012) 126008 [arXiv:1201.6452] [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].
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: 2009.14289
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
Stefanyszyn, D., Supeł, J. The boostless bootstrap and BCFW momentum shifts. J. High Energ. Phys. 2021, 91 (2021). https://doi.org/10.1007/JHEP03(2021)091
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)091