Abstract
We investigate how the speed of propagation of physical excitations is encoded in the coefficients of five-point interactions. This leads to a superluminality bound on scalar five-point interactions, which we present here for the first time. To substantiate our result, we also consider the case of four-point interactions for which bounds from S-matrix sum rules exist and show that these are parametrically equivalent to the bounds obtained within our analysis. Finally, we extend the discussion to a class of higher-point interactions.
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T.N. Pham and T.N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation, Phys. Rev. D 31 (1985) 3027 [INSPIRE].
A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
J. Bros, H. Epstein and V.J. Glaser, Some rigorous analyticity properties of the four-point function in momentum space, Nuovo Cim. 31 (1964) 1265 [INSPIRE].
S. Mizera, Physics of the analytic S-matrix, Phys. Rept. 1047 (2024) 1 [arXiv:2306.05395] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP 05 (2010) 095 [Erratum ibid. 11 (2011) 128] [arXiv:0912.4258] [INSPIRE].
B. Bellazzini, Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034 [arXiv:1605.06111] [INSPIRE].
B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Beyond Positivity Bounds and the Fate of Massive Gravity, Phys. Rev. Lett. 120 (2018) 161101 [arXiv:1710.02539] [INSPIRE].
B. Bellazzini et al., Positive moments for scattering amplitudes, Phys. Rev. D 104 (2021) 036006 [arXiv:2011.00037] [INSPIRE].
A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry, JHEP 05 (2021) 255 [arXiv:2011.02400] [INSPIRE].
S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories, JHEP 05 (2021) 280 [arXiv:2011.02957] [INSPIRE].
B. Bellazzini, M. Riembau and F. Riva, IR side of positivity bounds, Phys. Rev. D 106 (2022) 105008 [arXiv:2112.12561] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Sharp boundaries for the swampland, JHEP 07 (2021) 110 [arXiv:2102.08951] [INSPIRE].
L.-Y. Chiang et al., Into the EFThedron and UV constraints from IR consistency, JHEP 03 (2022) 063 [arXiv:2105.02862] [INSPIRE].
S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez and D. Simmons-Duffin, Causality constraints on corrections to Einstein gravity, JHEP 05 (2023) 122 [arXiv:2201.06602] [INSPIRE].
D.-Y. Hong, Z.-H. Wang and S.-Y. Zhou, Causality bounds on scalar-tensor EFTs, JHEP 10 (2023) 135 [arXiv:2304.01259] [INSPIRE].
J. Bros, V. Glaser and H. Epstein, Local analyticity properties of the n particle scattering amplitude, Helv. Phys. Acta 45 (1972) 149 [INSPIRE].
S. Caron-Huot, M. Giroux, H.S. Hannesdottir and S. Mizera, What can be measured asymptotically?, JHEP 01 (2024) 139 [arXiv:2308.02125] [INSPIRE].
S. Caron-Huot, M. Giroux, H.S. Hannesdottir and S. Mizera, Crossing beyond scattering amplitudes, JHEP 04 (2024) 060 [arXiv:2310.12199] [INSPIRE].
J. Bros, Derivation of asymptotic crossing domains for multiparticle processes in axiomatic quantum field theory: A general approach and a complete proof for 2 → 3 particle processes, Phys. Rept. 134 (1986) 325 [INSPIRE].
V. Chandrasekaran, G.N. Remmen and A. Shahbazi-Moghaddam, Higher-Point Positivity, JHEP 11 (2018) 015 [arXiv:1804.03153] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
M. Carrillo González, C. de Rham, V. Pozsgay and A.J. Tolley, Causal effective field theories, Phys. Rev. D 106 (2022) 105018 [arXiv:2207.03491] [INSPIRE].
F. Serra, J. Serra, E. Trincherini and L.G. Trombetta, Causality constraints on black holes beyond GR, JHEP 08 (2022) 157 [arXiv:2205.08551] [INSPIRE].
M. Carrillo González et al., Positivity-causality competition: a road to ultimate EFT consistency constraints, arXiv:2307.04784 [INSPIRE].
B. Greene, D. Kabat, J. Levin and M. Porrati, Back to the future: Causality on a moving braneworld, Phys. Rev. D 107 (2023) 025016 [arXiv:2208.09014] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
L. Maiani and M. Testa, Unstable systems in relativistic quantum field theory, Annals Phys. 263 (1998) 353 [hep-th/9709110] [INSPIRE].
E. Curiel, A Primer on Energy Conditions, Einstein Stud. 13 (2017) 43 [arXiv:1405.0403] [INSPIRE].
K. Kampf, J. Novotny, F. Preucil and J. Trnka, Multi-spin soft bootstrap and scalar-vector Galileon, JHEP 07 (2021) 153 [arXiv:2104.10693] [INSPIRE].
M.A. Luty, M. Porrati and R. Rattazzi, Strong interactions and stability in the DGP model, JHEP 09 (2003) 029 [hep-th/0303116] [INSPIRE].
L. Heisenberg and C.F. Steinwachs, Geometrized quantum Galileons, JCAP 02 (2020) 031 [arXiv:1909.07111] [INSPIRE].
Acknowledgments
The authors would like to thank B. Bellazzini, D. E. Kaplan, D. Kosmopoulos, S. Rajendran, S. Ramazanov, J. Serra, G. Trenkler, A. Vikman for useful discussions, and especially I. Sawicki and E. Trincherini for helpful discussions and comments on the manuscript. The work of F.S. was supported by the U.S. Department of Energy (DOE), Office of Science, National Quantum Information Science Research Centers, Superconducting Quantum Materials and Systems Center (SQMS) under Contract No. DE-AC02-07CH11359 as well as by the Simons Investigator Award No. 827042 (P.I.: Surjeet Rajendran). The work of L.G.T. was supported by European Union (Grant No. 101063210). We also thank the hospitality of the Centro de Ciencias de Benasque Pedro Pascual during the initial stages of this work.
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Serra, F., Trombetta, L.G. Five-point superluminality bounds. J. High Energ. Phys. 2024, 117 (2024). https://doi.org/10.1007/JHEP06(2024)117
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DOI: https://doi.org/10.1007/JHEP06(2024)117