Built on

W.-M. Chen, Y.-T. Huang, T. Noumi and C. Wen, Unitarity bounds on charged/neutral state mass ratios , Phys. Rev. D 100
Original
1901
Earlier work this paper cites.
Q. Bi, C. Zhang and S.-Y. Zhou, Positivity constraints on aQGC: carving out the physical parameter space , JHEP 06
Original
1902
Earlier work this paper cites.
B. Bellazzini, M. Lewandowski and J. Serra, Amplitudes’ Positivity, Weak Gravity Conjecture, and Modified Gravity , 1902.03250
Original
1902
Earlier work this paper cites.
S. Melville and J. Noller, Positivity in the sky , 1904.05874
Original
1904
Earlier work this paper cites.
G. N. Remmen and N. L. Rodd, Consistency of the Standard Model Effective Field Theory , JHEP 12
Original
1908
Earlier work this paper cites.
M. B. Green and C. Wen, Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values , JHEP 11
Original
1908
Earlier work this paper cites.
C. de Rham and A. J. Tolley, Speed of gravity , Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
G. J. Loges, T. Noumi and G. Shiu, Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture , 1909.01352
Original
1909
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 , 1910.11799
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 , 1912.10018
Original
1912
Earlier work this paper cites.
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation , Phys. Rev. 123
1961
Earlier work this paper cites.
A. Martin, Unitarity and high-energy behavior of scattering amplitudes , Phys. Rev. 129
1963
Earlier work this paper cites.
Y. S. Jin and A. Martin, Number of Subtractions in Fixed-Transfer Dispersion Relations , Phys. Rev. 135
1964
Earlier work this paper cites.
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1. , Nuovo Cim. A42
1965
Earlier work this paper cites.
S. Weinberg, Pion scattering lengths , Phys. Rev. Lett. 17
1966
Earlier work this paper cites.
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop , Annals Phys. 158
1984
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.
M. R. Pennington and J. Portoles, The Chiral Lagrangian parameters, l1, l2, are determined by the rho resonance , Phys. Lett. B344
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.
J. Comellas, J. I. Latorre and J. Taron, Constraints on chiral perturbation theory parameters from QCD inequalities , Phys. Lett. B360
1995
Earlier work this paper cites.
J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. E. Sainio, Elastic pi pi scattering to two loops , Phys. Lett. B374
1996
Earlier work this paper cites.

Similar

L. Girlanda, M. Knecht, B. Moussallam and J. Stern, Comment on the prediction of two loop standard chiral perturbation theory for low-energy π π \pi\pi scattering , Phys. Lett. B409
1997
Cited alongside, same era.
G. R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space , Phys. Lett. B485
2000
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G. Amoros, J. Bijnens and P. Talavera, K ℓ 4 K_{\ell 4} form-factors and π \pi - π \pi scattering , Nucl. Phys. B585
2000
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G. Colangelo, J. Gasser and H. Leutwyler, π π \pi\pi scattering , Nucl. Phys. B603
2001
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2003
Cited alongside, same era.

Then

C. Burrage, C. de Rham, D. Seery and A. J. Tolley, Galileon inflation , JCAP 01
Original
2011
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B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive Moments for Scattering Amplitudes , 2011.00037
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2011
Later among the works it cites.
S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories , 2011.02957
Original
2011
Later among the works it cites.
A. Guerrieri, J. Penedones and P. Vieira, S-matrix Bootstrap for Effective Field Theories: Massless Pions , 2011.02802
Original
2011
Later among the works it cites.
K. Hinterbichler and A. Joyce, Goldstones with Extended Shift Symmetries , Int. J. Mod. Phys. D 23

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2020

New positivity bounds from full crossing symmetry

Tolley, Andrew J., Wang, Zi-Yue, Zhou, Shuang-Yong

Understand

Positivity bounds are powerful tools to constrain effective field theories.

Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: We refer to these as the $PQ$, $D^{\rm su}$, $D^{\rm stu}$ and $\bar{D}^{\rm stu}$ bounds.
While the $PQ$ bounds and $D^{\rm su}$ bounds only make use of the $s\leftrightarrow u$ dispersion relation, the $D^{\rm stu}$ and $\bar{D}^{\rm stu}$ bounds are obtained by further imposing the $s\leftrightarrow t$ crossing symmetry.
In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders.

Built on

W.-M. Chen, Y.-T. Huang, T. Noumi and C. Wen, Unitarity bounds on charged/neutral state mass ratios , Phys. Rev. D 100
Original
1901
Earlier work this paper cites.
Q. Bi, C. Zhang and S.-Y. Zhou, Positivity constraints on aQGC: carving out the physical parameter space , JHEP 06
Original
1902
Earlier work this paper cites.
B. Bellazzini, M. Lewandowski and J. Serra, Amplitudes’ Positivity, Weak Gravity Conjecture, and Modified Gravity , 1902.03250
Original
1902
Earlier work this paper cites.
S. Melville and J. Noller, Positivity in the sky , 1904.05874
Original
1904
Earlier work this paper cites.
G. N. Remmen and N. L. Rodd, Consistency of the Standard Model Effective Field Theory , JHEP 12
Original
1908
Earlier work this paper cites.
M. B. Green and C. Wen, Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values , JHEP 11
Original
1908
Earlier work this paper cites.
C. de Rham and A. J. Tolley, Speed of gravity , Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
G. J. Loges, T. Noumi and G. Shiu, Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture , 1909.01352
Original
1909
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 , 1910.11799
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 , 1912.10018
Original
1912
Earlier work this paper cites.
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation , Phys. Rev. 123
1961
Earlier work this paper cites.
A. Martin, Unitarity and high-energy behavior of scattering amplitudes , Phys. Rev. 129
1963
Earlier work this paper cites.
Y. S. Jin and A. Martin, Number of Subtractions in Fixed-Transfer Dispersion Relations , Phys. Rev. 135
1964
Earlier work this paper cites.
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1. , Nuovo Cim. A42
1965
Earlier work this paper cites.
S. Weinberg, Pion scattering lengths , Phys. Rev. Lett. 17
1966
Earlier work this paper cites.
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop , Annals Phys. 158
1984
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.
M. R. Pennington and J. Portoles, The Chiral Lagrangian parameters, l1, l2, are determined by the rho resonance , Phys. Lett. B344
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.
J. Comellas, J. I. Latorre and J. Taron, Constraints on chiral perturbation theory parameters from QCD inequalities , Phys. Lett. B360
1995
Earlier work this paper cites.
J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. E. Sainio, Elastic pi pi scattering to two loops , Phys. Lett. B374
1996
Earlier work this paper cites.

Similar

L. Girlanda, M. Knecht, B. Moussallam and J. Stern, Comment on the prediction of two loop standard chiral perturbation theory for low-energy π π \pi\pi scattering , Phys. Lett. B409
1997
Cited alongside, same era.
G. R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space , Phys. Lett. B485
2000
Cited alongside, same era.
G. Amoros, J. Bijnens and P. Talavera, K ℓ 4 K_{\ell 4} form-factors and π \pi - π \pi scattering , Nucl. Phys. B585
2000
Cited alongside, same era.
G. Colangelo, J. Gasser and H. Leutwyler, π π \pi\pi scattering , Nucl. Phys. B603
2001
Cited alongside, same era.
M. A. Luty, M. Porrati and R. Rattazzi, Strong interactions and stability in the DGP model , JHEP 09
2003
Cited alongside, same era.