Built on

A. Brandhuber and G. Travaglini, On higher-derivative effects on the gravitational potential and particle bending , JHEP 01
Original
1905
Earlier work this paper cites.
M. Ruhdorfer, J. Serra and A. Weiler, Effective Field Theory of Gravity to All Orders , JHEP 05
Original
1908
Earlier work this paper cites.
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A. J. Tolley, Positivity Constraints on Interacting Spin-2 Fields , JHEP 03
Original
1910
Earlier work this paper cites.
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A. J. Tolley, Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields , JHEP 07
Original
1912
Earlier work this paper cites.
N. Sennett, R. Brito, A. Buonanno, V. Gorbenko and L. Senatore, Gravitational-Wave Constraints on an Effective Field-Theory Extension of General Relativity , Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
S. Mandelstam, Determination of the pion - nucleon scattering amplitude from dispersion relations and unitarity. General theory , Phys. Rev. 112
1958
Earlier work this paper cites.
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation , Phys. Rev. 123
1961
Earlier work this paper cites.
K. Igi, pi-N Scattering Length and Singularities in the Complex J Plane , Phys. Rev. Lett. 9
1962
Earlier work this paper cites.
Y. S. Jin and A. Martin, Connection Between the Asymptotic Behavior and the Sign of the Discontinuity in One-Dimensional Dispersion Relations , Phys. Rev. 135
1964
Earlier work this paper cites.
A. A. Logunov, L. D. Soloviev and A. N. Tavkhelidze, Dispersion sum rules and high-energy scattering , Phys. Lett. B 24
1967
Earlier work this paper cites.
K. Igi and S. Matsuda, Some Consequences from Superconvergence for pi N Scattering , Phys. Rev. 163
1967
Earlier work this paper cites.
K. Igi and S. Matsuda, New Sum Rules and Singularities in the Complex J Plane , Phys. Rev. Lett. 18
1967
Earlier work this paper cites.
Y.-C. Liu and S. Okubo, Tests of New π \pi − - N Superconvergent Dispersion Relations , Phys. Rev. Lett. 19
1967
Earlier work this paper cites.
R. Dolen, D. Horn and C. Schmid, Finite energy sum rules and their application to pi N charge exchange , Phys. Rev. 166
1968
Earlier work this paper cites.
M. G. Olsson, On the decoupling of a second RHO in forward π \pi N scattering , Phys. Lett. B 26
1968
Earlier work this paper cites.
G. Veneziano, Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories , Nuovo Cim. A 57
1968
Earlier work this paper cites.
J. D. Jackson, Models for high-energy processes , Rev. Mod. Phys. 42
1970
Earlier work this paper cites.
G. Auberson and N. N. Khuri, Rigorous parametric dispersion representation with three-channel symmetry , Phys. Rev. D 6
1972
Earlier work this paper cites.
G. Mahoux, S. M. Roy and G. Wanders, Physical pion pion partial-wave equations based on three channel crossing symmetry , Nucl. Phys. B 70
1974
Earlier work this paper cites.
T. N. Pham and T. N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation , Phys. Rev. D31
1985
Earlier work this paper cites.
D. J. Gross and E. Witten, Superstring Modifications of Einstein’s Equations , Nucl. Phys. B 277
1986
Earlier work this paper cites.
H. Kawai, D. C. Lewellen and S. H. H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings , Nucl. Phys. B 269
1986
Earlier work this paper cites.
R. R. Metsaev and A. A. Tseytlin, Curvature Cubed Terms in String Theory Effective Actions , Phys. Lett. B 185
1987
Earlier work this paper cites.
J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections , Phys. Rev. D 50
1994
Earlier work this paper cites.
J. F. Donoghue, Introduction to the effective field theory description of gravity , in Advanced School on Effective Theories , 6, 1995, gr-qc/9512024
1995
Earlier work this paper cites.
B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints , Phys. Rev. D51
1995
Earlier work this paper cites.
M. R. Pennington and J. Portoles, The Chiral Lagrangian parameters, l1, l2, are determined by the rho resonance , Phys. Lett. B 344
1995
Earlier work this paper cites.

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C. P. Burgess, Quantum gravity in everyday life: General relativity as an effective field theory , Living Rev. Rel. 7
2004
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C. de Rham, J. Francfort and J. Zhang, Black Hole Gravitational Waves in the Effective Field Theory of Gravity , Phys. Rev. D 102
Original
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Original
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Then

C. de Rham, S. Melville, A. J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories , Phys. Rev. D96
Original
2017
Later among the works it cites.
S. Endlich, V. Gorbenko, J. Huang and L. Senatore, An effective formalism for testing extensions to General Relativity with gravitational waves , JHEP 09
Original
2017
Later among the works it cites.
C. de Rham, S. Melville, A. J. Tolley and S.-Y. Zhou, Massive Galileon Positivity Bounds , JHEP 09
Original
2017
Later among the works it cites.
B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, …: Higher dimension operators in the SM EFT , JHEP 08
Original
2017
Later among the works it cites.
B. Henning, X. Lu, T. Melia and H. Murayama, Operator bases, S S -matrices, and their partition functions , JHEP 10

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2022

Constraints on Regge behaviour from IR physics

de Rham, Claudia, Jaitly, Sumer, Tolley, Andrew J.

Understand

We consider positivity constraints applicable to the Effective Field Theory (EFT) of gravity in arbitrary dimensions.

By considering scattering of indefinite initial and final states, we highlight the existence of a gravitational scattering amplitude for which full crossing symmetry is manifest and utilize the recently developed crossing symmetric dispersion relations to derive compact non-linear bounds.
We show that the null constraints built into these dispersion relations lead to a finite energy sum rule for gravity which may be extended to a one-parameter family of continuous moment sum rules.
These sum rules enforce a UV-IR relation which imposes constraints on both the Regge trajectory and residue.

Built on

A. Brandhuber and G. Travaglini, On higher-derivative effects on the gravitational potential and particle bending , JHEP 01
Original
1905
Earlier work this paper cites.
M. Ruhdorfer, J. Serra and A. Weiler, Effective Field Theory of Gravity to All Orders , JHEP 05
Original
1908
Earlier work this paper cites.
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A. J. Tolley, Positivity Constraints on Interacting Spin-2 Fields , JHEP 03
Original
1910
Earlier work this paper cites.
L. Alberte, C. de Rham, A. Momeni, J. Rumbutis and A. J. Tolley, Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields , JHEP 07
Original
1912
Earlier work this paper cites.
N. Sennett, R. Brito, A. Buonanno, V. Gorbenko and L. Senatore, Gravitational-Wave Constraints on an Effective Field-Theory Extension of General Relativity , Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
S. Mandelstam, Determination of the pion - nucleon scattering amplitude from dispersion relations and unitarity. General theory , Phys. Rev. 112
1958
Earlier work this paper cites.
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation , Phys. Rev. 123
1961
Earlier work this paper cites.
K. Igi, pi-N Scattering Length and Singularities in the Complex J Plane , Phys. Rev. Lett. 9
1962
Earlier work this paper cites.
Y. S. Jin and A. Martin, Connection Between the Asymptotic Behavior and the Sign of the Discontinuity in One-Dimensional Dispersion Relations , Phys. Rev. 135
1964
Earlier work this paper cites.
A. A. Logunov, L. D. Soloviev and A. N. Tavkhelidze, Dispersion sum rules and high-energy scattering , Phys. Lett. B 24
1967
Earlier work this paper cites.
K. Igi and S. Matsuda, Some Consequences from Superconvergence for pi N Scattering , Phys. Rev. 163
1967
Earlier work this paper cites.
K. Igi and S. Matsuda, New Sum Rules and Singularities in the Complex J Plane , Phys. Rev. Lett. 18
1967
Earlier work this paper cites.
Y.-C. Liu and S. Okubo, Tests of New π \pi − - N Superconvergent Dispersion Relations , Phys. Rev. Lett. 19
1967
Earlier work this paper cites.
R. Dolen, D. Horn and C. Schmid, Finite energy sum rules and their application to pi N charge exchange , Phys. Rev. 166
1968
Earlier work this paper cites.
M. G. Olsson, On the decoupling of a second RHO in forward π \pi N scattering , Phys. Lett. B 26
1968
Earlier work this paper cites.
G. Veneziano, Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories , Nuovo Cim. A 57
1968
Earlier work this paper cites.
J. D. Jackson, Models for high-energy processes , Rev. Mod. Phys. 42
1970
Earlier work this paper cites.
G. Auberson and N. N. Khuri, Rigorous parametric dispersion representation with three-channel symmetry , Phys. Rev. D 6
1972
Earlier work this paper cites.
G. Mahoux, S. M. Roy and G. Wanders, Physical pion pion partial-wave equations based on three channel crossing symmetry , Nucl. Phys. B 70
1974
Earlier work this paper cites.
T. N. Pham and T. N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation , Phys. Rev. D31
1985
Earlier work this paper cites.
D. J. Gross and E. Witten, Superstring Modifications of Einstein’s Equations , Nucl. Phys. B 277
1986
Earlier work this paper cites.
H. Kawai, D. C. Lewellen and S. H. H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings , Nucl. Phys. B 269
1986
Earlier work this paper cites.
R. R. Metsaev and A. A. Tseytlin, Curvature Cubed Terms in String Theory Effective Actions , Phys. Lett. B 185
1987
Earlier work this paper cites.
J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections , Phys. Rev. D 50
1994
Earlier work this paper cites.
J. F. Donoghue, Introduction to the effective field theory description of gravity , in Advanced School on Effective Theories , 6, 1995, gr-qc/9512024
1995
Earlier work this paper cites.
B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints , Phys. Rev. D51
1995
Earlier work this paper cites.
M. R. Pennington and J. Portoles, The Chiral Lagrangian parameters, l1, l2, are determined by the rho resonance , Phys. Lett. B 344
1995
Earlier work this paper cites.

Similar

C. P. Burgess, Quantum gravity in everyday life: General relativity as an effective field theory , Living Rev. Rel. 7
2004
Cited alongside, same era.
C. de Rham, J. Francfort and J. Zhang, Black Hole Gravitational Waves in the Effective Field Theory of Gravity , Phys. Rev. D 102
Original
2005
Cited alongside, same era.
Cambridge university press, 2005
M. Ismail, M. E. Ismail and W. van Assche, Classical and quantum orthogonal polynomials in one variable , vol. 13 · 2005
Cited alongside, same era.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion , JHEP 10
2006
Cited alongside, same era.
M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini, Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity , Phys. Rev. D 102
Original
2006