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B. Bellazzini, M. Lewandowski, and J. Serra, “Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity,” Phys. Rev. Lett
Original
1902
Earlier work this paper cites.
B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, “Massive Higher Spins: Effective Theory and Consistency,” JHEP
Original
1903
Earlier work this paper cites.
S. Melville, D. Roest, and D. Stefanyszyn, “UV Constraints on Massive Spinning Particles: Lessons from the Gravitino,” JHEP
Original
1911
Earlier work this paper cites.
M. Froissart, “Asymptotic Behavior and Subtractions in the Mandelstam Representation,” Phys. Rev
1961
Earlier work this paper cites.
A. Martin, “Unitarity and High-Energy Behavior of Scattering Amplitudes,” Phys. Rev
1963
Earlier work this paper cites.
J. Bros, H. Epstein, and V. J. Glaser, “Some rigorous analyticity properties of the four-point function in momentum space,” Nuovo Cim
1964
Earlier work this paper cites.
G. Cohen-Tannoudji, A. Morel, and H. Navelet, “Kinematical Singularities, Crossing Matrix and Kinematical Constraints for Two-Body Helicity Amplitudes,” Annals Phys
1968
Earlier work this paper cites.
A. I. Vainshtein, “To the Problem of Nonvanishing Gravitation Mass,” Phys. Lett. B
1972
Earlier work this paper cites.
A. Falkowski and G. Isabella, “Matter Coupling in Massive Gravity,” JHEP
Original
2001
Earlier work this paper cites.
C. Deffayet, G. R. Dvali, G. Gabadadze, and A. I. Vainshtein, “Nonperturbative Continuity in Graviton Mass Versus Perturbative Discontinuity,” Phys. Rev. D
2002
Earlier work this paper cites.
N. Arkani-Hamed, H. Georgi, and M. D. Schwartz, “Effective Field Theory for Massive Gravitons and Gravity in Theory Space,” Annals Phys
2003
Earlier work this paper cites.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, “Causality, Analyticity and an IR Obstruction to UV Completion,” JHEP
2006
Earlier work this paper cites.
C. de Rham and G. Gabadadze, “Generalization of the Fierz-Pauli Action,” Phys. Rev
Original
2010
Earlier work this paper cites.
M. Herrero-Valea, R. Santos-Garcia, and A. Tokareva, “Massless Positivity in Graviton Exchange,” 2011.11652
Original
2011
Earlier work this paper cites.
C. de Rham, G. Gabadadze, and A. J. Tolley, “Resummation of Massive Gravity,” Phys. Rev. Lett
Original
2011
Earlier work this paper cites.
A. Hebbar, D. Karateev, and J. Penedones, “Spinning S-Matrix Bootstrap in 4D,” 2011.11708
Original
2011
Earlier work this paper cites.
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau, and F. Riva, “Positive Moments for Scattering Amplitudes,” 2011.00037
Original
2011
Earlier work this paper cites.

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2023

Massive Gravity is not Positive

Bellazzini, Brando, Isabella, Giulia, Ricossa, Sara et al.

Understand

We derive new positivity bounds at finite momentum transfer, assuming a large separation between the mass $m$ of the lightest particle in the effective theory and the mass gap $M$ to new heavy states.

Massive gravity parametrically violates these bounds unless the cutoff is within one order of magnitude of the graviton mass $M\lesssim O(10)m$.
Non-gravitational effective theories of massive spin-2 particles are similarly bounded.

Built on

B. Bellazzini, M. Lewandowski, and J. Serra, “Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity,” Phys. Rev. Lett
Original
1902
Earlier work this paper cites.
B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, “Massive Higher Spins: Effective Theory and Consistency,” JHEP
Original
1903
Earlier work this paper cites.
S. Melville, D. Roest, and D. Stefanyszyn, “UV Constraints on Massive Spinning Particles: Lessons from the Gravitino,” JHEP
Original
1911
Earlier work this paper cites.
M. Froissart, “Asymptotic Behavior and Subtractions in the Mandelstam Representation,” Phys. Rev
1961
Earlier work this paper cites.
A. Martin, “Unitarity and High-Energy Behavior of Scattering Amplitudes,” Phys. Rev
1963
Earlier work this paper cites.
J. Bros, H. Epstein, and V. J. Glaser, “Some rigorous analyticity properties of the four-point function in momentum space,” Nuovo Cim
1964
Earlier work this paper cites.
G. Cohen-Tannoudji, A. Morel, and H. Navelet, “Kinematical Singularities, Crossing Matrix and Kinematical Constraints for Two-Body Helicity Amplitudes,” Annals Phys
1968
Earlier work this paper cites.
A. I. Vainshtein, “To the Problem of Nonvanishing Gravitation Mass,” Phys. Lett. B
1972
Earlier work this paper cites.
A. Falkowski and G. Isabella, “Matter Coupling in Massive Gravity,” JHEP
Original
2001
Earlier work this paper cites.
C. Deffayet, G. R. Dvali, G. Gabadadze, and A. I. Vainshtein, “Nonperturbative Continuity in Graviton Mass Versus Perturbative Discontinuity,” Phys. Rev. D
2002
Earlier work this paper cites.
N. Arkani-Hamed, H. Georgi, and M. D. Schwartz, “Effective Field Theory for Massive Gravitons and Gravity in Theory Space,” Annals Phys
2003
Earlier work this paper cites.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, “Causality, Analyticity and an IR Obstruction to UV Completion,” JHEP
2006
Earlier work this paper cites.
C. de Rham and G. Gabadadze, “Generalization of the Fierz-Pauli Action,” Phys. Rev
Original
2010
Earlier work this paper cites.
M. Herrero-Valea, R. Santos-Garcia, and A. Tokareva, “Massless Positivity in Graviton Exchange,” 2011.11652
Original
2011
Earlier work this paper cites.
C. de Rham, G. Gabadadze, and A. J. Tolley, “Resummation of Massive Gravity,” Phys. Rev. Lett
Original
2011
Earlier work this paper cites.
A. Hebbar, D. Karateev, and J. Penedones, “Spinning S-Matrix Bootstrap in 4D,” 2011.11708
Original
2011
Earlier work this paper cites.
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau, and F. Riva, “Positive Moments for Scattering Amplitudes,” 2011.00037
Original
2011
Earlier work this paper cites.