Abstract
We compute the 2 → 2 gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass m3/2) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as \( {\kappa}^2{E}^4/{m}_{3/2}^2 \), signaling a potential breakdown of unitarity at a scale \( {\Lambda}^2\sim {m}_{3/2}/\kappa \sim {M}_{\textrm{SUSY}}^2 \). As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos D-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff Λ ~ MSUSY where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.
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References
J. Polonyi, Generalization of the massive scalar multiplet coupling to the supergravity, [INSPIRE].
P. Fayet and J. Iliopoulos, Spontaneously broken supergauge symmetries and Goldstone spinors, Phys. Lett. B 51 (1974) 461 [INSPIRE].
D.Z. Freedman, Supergravity with axial gauge invariance, Phys. Rev. D 15 (1977) 1173 [INSPIRE].
R. Barbieri, S. Ferrara, D.V. Nanopoulos and K.S. Stelle, Supergravity, R invariance and spontaneous supersymmetry breaking, Phys. Lett. B 113 (1982) 219 [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on the Fayet-Iliopoulos term in field theory and supergravity, JHEP 06 (2009) 007 [arXiv:0904.1159] [INSPIRE].
K.R. Dienes and B. Thomas, On the inconsistency of Fayet-Iliopoulos terms in supergravity theories, Phys. Rev. D 81 (2010) 065023 [arXiv:0911.0677] [INSPIRE].
N. Cribiori, F. Farakos, M. Tournoy and A. van Proeyen, Fayet-Iliopoulos terms in supergravity without gauged R-symmetry, JHEP 04 (2018) 032 [arXiv:1712.08601] [INSPIRE].
N. Cribiori, F. Farakos and M. Tournoy, Supersymmetric Born-Infeld actions and new Fayet-Iliopoulos terms, JHEP 03 (2019) 050 [arXiv:1811.08424] [INSPIRE].
I. Antoniadis, A. Chatrabhuti, H. Isono and R. Knoops, Fayet-Iliopoulos terms in supergravity and D-term inflation, Eur. Phys. J. C 78 (2018) 366 [arXiv:1803.03817] [INSPIRE].
I. Antoniadis, A. Chatrabhuti, H. Isono and R. Knoops, The cosmological constant in supergravity, Eur. Phys. J. C 78 (2018) 718 [arXiv:1805.00852] [INSPIRE].
I. Antoniadis and F. Rondeau, New Kähler invariant Fayet-Iliopoulos terms in supergravity and cosmological applications, Eur. Phys. J. C 80 (2020) 346 [arXiv:1912.08117] [INSPIRE].
H. Jang and M. Porrati, Inflation, gravity mediated supersymmetry breaking, and de Sitter vacua in supergravity with a Kähler-invariant Fayet-Iliopoulos term, Phys. Rev. D 103 (2021) 105006 [arXiv:2102.11358] [INSPIRE].
H. Jang and M. Porrati, Realization of slow-roll inflation and the MSSM in supergravity theories with new Fayet-Iliopoulos terms, Phys. Rev. D 106 (2022) 045024 [arXiv:2207.01889] [INSPIRE].
H. Jang and M. Porrati, Component actions of liberated N = 1 supergravity and new Fayet-Iliopoulos terms in superconformal tensor calculus, JHEP 11 (2021) 075 [arXiv:2108.04469] [INSPIRE].
M.D. Schwartz, Quantum field theory and the Standard Model, Cambridge University Press (2014).
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press (2012).
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
N.E.J. Bjerrum-Bohr and O.T. Engelund, Gravitino interactions from Yang-Mills theory, Phys. Rev. D 81 (2010) 105009 [arXiv:1002.2279] [INSPIRE].
T. Moroi, Effects of the gravitino on the inflationary universe, Ph.D. thesis, Tohoku University, Sendai, Japan (1995) [hep-ph/9503210] [INSPIRE].
S. Ferrara, R. Kallosh, A. Van Proeyen and T. Wrase, Linear versus non-linear supersymmetry, in general, JHEP 04 (2016) 065 [arXiv:1603.02653] [INSPIRE].
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Antoniadis, I., Guillen, A. & Rondeau, F. Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms. J. High Energ. Phys. 2023, 43 (2023). https://doi.org/10.1007/JHEP01(2023)043
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DOI: https://doi.org/10.1007/JHEP01(2023)043