Built on

B. Bellazzini, M. Lewandowski and J. Serra, Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity , Phys. Rev. Lett. 123
Original
1902
Earlier work this paper cites.
L. Cordova, Y. He, M. Kruczenski and P. Vieira, The O(N) S-matrix Monolith , JHEP 04
Original
1909
Earlier work this paper cites.
S.D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices , JHEP 02
Original
1910
Earlier work this paper cites.
J. Penedones, J.A. Silva and A. Zhiboedov, Nonperturbative Mellin Amplitudes: Existence, Properties, Applications , JHEP 08
Original
1912
Earlier work this paper cites.
S.M. Chester, W. Landry, J. Liu, D. Poland, D. Simmons-Duffin, N. Su et al., Carving out OPE space and precise O ⁡ ( 2 ) O(2) model critical exponents , JHEP 06
Original
1912
Earlier work this paper cites.
M. Gell-Mann, M. Goldberger and W.E. Thirring, Use of causality conditions in quantum theory , Phys. Rev. 95
1954
Earlier work this paper cites.
Y. Jin and A. Martin, Number of Subtractions in Fixed-Transfer Dispersion Relations , Phys. Rev. 135
1964
Earlier work this paper cites.
J. Bros, H. Epstein and V. Glaser, A proof of the crossing property for two-particle amplitudes in general quantum field theory , Commun. Math. Phys. 1
1965
Earlier work this paper cites.
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1. , Nuovo Cim. A 42
1965
Earlier work this paper cites.
R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix , Cambridge Univ. Press, Cambridge (1966)
1966
Earlier work this paper cites.
A. Martin, Scattering Theory: Unitarity, Analyticity and Crossing , vol. 3 (1969), 10.1007/BFb0101043
1969
Earlier work this paper cites.
S.M. Roy, Exact integral equation for pion pion scattering involving only physical region partial waves , Phys. Lett. B 36
1971
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. D 31
1985
Earlier work this paper cites.

Similar

B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints , Phys. Rev. D 51
1995
Cited alongside, same era.
G. Colangelo, J. Gasser and H. Leutwyler, π π \pi\pi scattering , Nucl. Phys. B 603
2001
Cited alongside, same era.
I. Caprini, G. Colangelo, J. Gasser and H. Leutwyler, On the precision of the theoretical predictions for pi pi scattering , Phys. Rev. D 68
2003
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. Correia, A. Sever and A. Zhiboedov, An Analytical Toolkit for the S-matrix Bootstrap , 2006.08221
Original
2006
Cited alongside, same era.

Then

D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap , JHEP 06
Original
2015
Later among the works it cites.
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling , JHEP 02
Original
2016
Later among the works it cites.
C. Cheung and G.N. Remmen, Positive Signs in Massive Gravity , JHEP 04
Original
2016
Later among the works it cites.
N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Einstein gravity 3-point functions from conformal field theory , JHEP 12
Original
2017
Later among the works it cites.
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories , Phys. Rev. D 96

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2020

Extremal Effective Field Theories

Caron-Huot, Simon, Van Duong, Vincent

Understand

Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known.

It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity are satisfied at all scales.
We explore those constraints from the perspective of 2 to 2 scattering amplitudes of a light real scalar field, using semi-definite programming to carve out the space of allowed EFT coefficients for a given mass threshold M.
We point out that all EFT parameters are bounded both below and above, effectively showing that dimensional analysis scaling is a consequence of causality.

Built on

B. Bellazzini, M. Lewandowski and J. Serra, Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity , Phys. Rev. Lett. 123
Original
1902
Earlier work this paper cites.
L. Cordova, Y. He, M. Kruczenski and P. Vieira, The O(N) S-matrix Monolith , JHEP 04
Original
1909
Earlier work this paper cites.
S.D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices , JHEP 02
Original
1910
Earlier work this paper cites.
J. Penedones, J.A. Silva and A. Zhiboedov, Nonperturbative Mellin Amplitudes: Existence, Properties, Applications , JHEP 08
Original
1912
Earlier work this paper cites.
S.M. Chester, W. Landry, J. Liu, D. Poland, D. Simmons-Duffin, N. Su et al., Carving out OPE space and precise O ⁡ ( 2 ) O(2) model critical exponents , JHEP 06
Original
1912
Earlier work this paper cites.
M. Gell-Mann, M. Goldberger and W.E. Thirring, Use of causality conditions in quantum theory , Phys. Rev. 95
1954
Earlier work this paper cites.
Y. Jin and A. Martin, Number of Subtractions in Fixed-Transfer Dispersion Relations , Phys. Rev. 135
1964
Earlier work this paper cites.
J. Bros, H. Epstein and V. Glaser, A proof of the crossing property for two-particle amplitudes in general quantum field theory , Commun. Math. Phys. 1
1965
Earlier work this paper cites.
A. Martin, Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1. , Nuovo Cim. A 42
1965
Earlier work this paper cites.
R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix , Cambridge Univ. Press, Cambridge (1966)
1966
Earlier work this paper cites.
A. Martin, Scattering Theory: Unitarity, Analyticity and Crossing , vol. 3 (1969), 10.1007/BFb0101043
1969
Earlier work this paper cites.
S.M. Roy, Exact integral equation for pion pion scattering involving only physical region partial waves , Phys. Lett. B 36
1971
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. D 31
1985
Earlier work this paper cites.

Similar

B. Ananthanarayan, D. Toublan and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints , Phys. Rev. D 51
1995
Cited alongside, same era.
G. Colangelo, J. Gasser and H. Leutwyler, π π \pi\pi scattering , Nucl. Phys. B 603
2001
Cited alongside, same era.
I. Caprini, G. Colangelo, J. Gasser and H. Leutwyler, On the precision of the theoretical predictions for pi pi scattering , Phys. Rev. D 68
2003
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. Correia, A. Sever and A. Zhiboedov, An Analytical Toolkit for the S-matrix Bootstrap , 2006.08221
Original
2006
Cited alongside, same era.

Then

D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap , JHEP 06
Original
2015
Later among the works it cites.
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling , JHEP 02
Original
2016
Later among the works it cites.
C. Cheung and G.N. Remmen, Positive Signs in Massive Gravity , JHEP 04
Original
2016
Later among the works it cites.
N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Einstein gravity 3-point functions from conformal field theory , JHEP 12
Original
2017
Later among the works it cites.
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories , Phys. Rev. D 96

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

J. Tokuda, K. Aoki and S. Hirano, Gravitational positivity bounds , 2007.15009

Original

2007

Cited alongside, same era.

L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, Positivity Bounds and the Massless Spin-2 Pole , 2007.12667

Original

2007

Cited alongside, same era.

S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Dispersive CFT Sum Rules , 2008.04931

Original

2008

Cited alongside, same era.

A.L. Guerrieri, A. Homrich and P. Vieira, Dual S-matrix Bootstrap I: 2D Theory , 2008.02770

Original

2008

Cited alongside, same era.

B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive Moments for Scattering Amplitudes , 2011.00037

Original

2011

Cited alongside, same era.

A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry , 2011.02400

Original

2011

Cited alongside, same era.

Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions , JHEP 12

Original

2011

Cited alongside, same era.

Original

2017

Later among the works it cites.

N. Arkani-Hamed and Y.-T. Huang, Positive geometry of effective field theory, lectures at the CERN winter school on supergravity, strings and gauge theory (2019); New positivity bounds from the EFT hedron, talk at the 24th rencontres Itzykson of the IPHT of CEA-Saclay (2019)

2019

Later among the works it cites.

I. Brivio and M. Trott, The Standard Model as an Effective Field Theory , Phys. Rept. 793

Original

2019

Later among the works it cites.

M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part III: higher dimensional amplitudes , JHEP 12

Original

2019

Later among the works it cites.

A.L. Guerrieri, J. Penedones and P. Vieira, Bootstrapping QCD Using Pion Scattering Amplitudes , Phys. Rev. Lett. 122

Original