pith. sign in

arxiv: 2512.13780 · v2 · submitted 2025-12-15 · ✦ hep-th · hep-ph

Positivity with Long-Range Interactions

B. Bellazzini , J. Berman , G. Isabella , F. Riva , M. Romano , F. Sciotti This is my paper

Pith reviewed 2026-05-16 21:51 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords positivity boundsinfrared finitenesslong-range interactionseffective field theorypion interactionselectromagnetismgravityscattering amplitudes
0
0 comments X

The pith

Amplitudes labeled by energy resolution enable infrared-safe positivity bounds for theories with long-range forces in four dimensions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a new class of scattering amplitudes, denoted M_E, that are made infrared finite by labeling them with an experimental energy resolution E for detecting soft photons and gravitons. These amplitudes are constructed to be analytic, crossing symmetric, Regge behaved, and Lorentz invariant. When E is exponentially smaller than any hard scale, they satisfy unitarity and their cross sections match the inclusive infrared-finite cross sections of ordinary amplitudes. This construction allows the derivation of positivity bounds on effective field theories that remain valid even in the presence of long-range interactions such as electromagnetism and gravity, and even in four spacetime dimensions where standard methods encounter infrared problems. The authors illustrate the approach by deriving explicit bounds in the low-energy theory of pions coupled to these forces.

Core claim

The central claim is that the infrared-regularized amplitudes M_E, labeled by the energy resolution E, provide a suitable framework for deriving infrared-safe positivity bounds on effective field theories in the presence of long-range forces, including in D=4, because they are analytic, crossing-symmetric, Regge-behaved, Lorentz-invariant, and unitarity-preserving for sufficiently small E while reproducing inclusive cross sections.

What carries the argument

The infrared-regularized amplitude M_E, which incorporates an energy resolution cutoff for soft photons and gravitons to ensure finiteness while maintaining analytic and symmetry properties required for positivity bounds.

If this is right

  • Positivity bounds can now be derived for effective theories involving photons and gravitons without encountering infrared divergences.
  • Explicit positivity constraints apply to the low-energy pion theory coupled to electromagnetism and gravity.
  • The method extends the applicability of positivity bounds to four-dimensional theories with long-range forces.
  • Cross sections derived from M_E match the infrared-finite inclusive cross sections of standard amplitudes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This regularization approach might be adaptable to other infrared-sensitive quantities in quantum field theory beyond positivity bounds.
  • Applications could include constraining models of dark energy or modified gravity that involve long-range interactions.
  • Further work could test whether similar resolutions work for non-perturbative effects or in curved spacetime.

Load-bearing premise

The assumption that for energy resolutions exponentially smaller than hard scales, the modified amplitudes satisfy unitarity and reproduce the inclusive infrared-finite cross sections.

What would settle it

A direct computation in a known theory showing that the cross section computed from M_E does not match the expected infrared-finite inclusive cross section for some scattering process involving soft particles.

Figures

Figures reproduced from arXiv: 2512.13780 by B. Bellazzini, F. Riva, F. Sciotti, G. Isabella, J. Berman, M. Romano.

Figure 1
Figure 1. Figure 1: Lower bounds on M2 c3,1/c2,0 as function of m2 ±/M2 , for fixed αE = 1/100. Con￾servative bounds from (6.11) (black, dot-dashed) have no assumptions on higher coefficients, semianalytic bounds (6.13) (red dashed) ignore EFT terms apart from c2,0 and c3,1. The numer￾ical bounds (blue) ignore only terms larger than N, controlling its convergence up to N = 14. tree-level, where loops of very irrelevant coupli… view at source ↗
Figure 2
Figure 2. Figure 2: Numerical—EFT–informed— lower bound of M2 c3,1/c2,0 as a function of αE = α log(M/E) for various values of m2 ±/M2 . As αE is lowered, the numerical bounds approaches the tree level one, given in (6.9). A fit for m2 ±/M2 = 10−2 is given in (6.14). with L(q) = ME,+0/Mtree E,+0 collecting the soft factor and leading-α effects appearing in the square bracket in (6.6), and the right-hand side capturing the q-m… view at source ↗
Figure 3
Figure 3. Figure 3: Lower bound on c3,1/c2,0 as a function of αE obtained from the all-order-αE result (blue, solid) and the first order result (blue, dashed), compared with the bound in absence of QED (dotted) and the conservative bound of (6.11) (orange); m± = 0.1M and α = 10−3 . For small αE ∼ α, our computational framework breaks down, as illustrated by the red shading. For too large αE , instead, the bound deteriorates. … view at source ↗
Figure 4
Figure 4. Figure 4: Left panel: one-loop bounds on M6 c¯3,1/α2 E and M4 c¯2,0/α2 E . In red the one–loop allowed region. The dashed lines are obtained by optimizing only on the ¯c2,0 term and fixing ψ ′ (0) to 18280 (blue), 4·104 (orange), while keeping fixed R qmax E dq ψ(q)q 2 = ±1, and respectively correspond to the upper and lower bound in Eq. (6.21). Right panel: one-loop upper bound on M2 c¯3,1/c¯2,0 as a function of α … view at source ↗
Figure 5
Figure 5. Figure 5: Bounds on M6 cˆ3,1/(16πGE ) and M4 cˆ2,0/(16πGE ). In red the one–loop allowed region (GE = 0.1), in purple the tree–level one. The dashed lines respectively correspond to the upper and lower bound in Eq. (7.6). In the right panel we zoom in on the tip of the allowed region. 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 1.2 1.4 1.6 1.8 2.0 M2 cˆ3,1 cˆ2,0 16πGE M4cˆ2,0 [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Upper bounds on M2 cˆ3,1/cˆ2,0 as a function of (16πGE )/M4 cˆ2,0. The blue line corre￾sponds to the upper bound in Eq. (7.6) evaluated at tree–level. The orange and green lines correpond to the same bound computed at GE = 1/10, 1/3. The black dashed line is the tree– level bound in absence of gravity. derive constraints of the form cˆ3,1M6 ≤ 3 2 cˆ2,0M4 + 700  8πGE − (8πGE ) 2 2π 2  + O(G), (7.6) cˆ3,1M… view at source ↗
Figure 7
Figure 7. Figure 7: Convergence of the numerical bound as a function of the degree [PITH_FULL_IMAGE:figures/full_fig_p038_7.png] view at source ↗
read the original abstract

We introduce infrared finite, analytic, crossing symmetric, Regge behaved, and Lorentz invariant amplitudes $\mathcal{M}_{\mathcal {E}}$, labeled by the experimental energy resolution $\mathcal{E}$ for detecting soft photons and gravitons. For $\mathcal{E}$ exponentially smaller than any hard scale, they also satisfy unitarity and their associated cross sections reproduce the inclusive, infrared-finite cross sections of ordinary amplitudes. These properties make $\mathcal{M}_{\mathcal{E}}$ suitable for deriving infrared-safe positivity bounds on effective field theories in the presence of long-range forces even in $D=4$. As an illustration, we present explicit bounds in the low-energy theory of pions coupled to electromagnetism and gravity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a family of modified scattering amplitudes M_E, labeled by an infrared resolution scale E for detecting soft photons and gravitons. These amplitudes are asserted to be infrared-finite, analytic, crossing-symmetric, Regge-behaved, and Lorentz-invariant. For E exponentially smaller than any hard scale, they are claimed to satisfy unitarity while reproducing the inclusive, infrared-finite cross sections of ordinary amplitudes. The construction is then used to derive infrared-safe positivity bounds on effective field theories with long-range forces, even in D=4, with an explicit illustration in the low-energy theory of pions coupled to electromagnetism and gravity.

Significance. If the analytic and crossing properties of M_E can be rigorously established, the result would be significant for extending positivity bounds to realistic four-dimensional EFTs that include massless mediators. Standard dispersion relations rely on analyticity, crossing, and a positive spectral density from unitarity; removing IR divergences while preserving these properties would allow model-independent constraints on low-energy coefficients in theories such as chiral perturbation theory with photons and gravitons, where conventional bounds are obstructed by soft divergences.

major comments (2)
  1. [§2] §2 (definition of M_E): the cutoff procedure that renders the amplitude infrared-finite must be shown to preserve analyticity in the complex s-plane and the crossing relations needed to equate s- and u-channel discontinuities. The abstract states that unitarity holds only for exponentially small E, but a generic soft cutoff generically introduces non-analytic dependence on external momenta; without an explicit demonstration that the modified optical theorem still yields a strictly positive integrand after the cutoff, the subtracted dispersion relations used for the positivity bounds lack rigorous justification.
  2. [§3] §3 (illustration with pions + EM + gravity): the explicit bounds are presented, but it is not shown that the E-dependent amplitudes remain Regge-behaved at high energy with the same intercept as the uncut amplitudes. If the soft cutoff alters the high-energy behavior, the subtraction constants or the convergence of the dispersion integral may be affected, undermining the infrared safety of the derived bounds.
minor comments (2)
  1. The notation for the resolution scale is written both as script E and as E; a single consistent symbol should be adopted throughout.
  2. Figure 1 (or the corresponding plot of the bounds) would benefit from an explicit statement of the numerical values chosen for E relative to the pion mass and the electromagnetic coupling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major point below and will revise the text to incorporate additional demonstrations where needed.

read point-by-point responses

  1. Referee: [§2] §2 (definition of M_E): the cutoff procedure that renders the amplitude infrared-finite must be shown to preserve analyticity in the complex s-plane and the crossing relations needed to equate s- and u-channel discontinuities. The abstract states that unitarity holds only for exponentially small E, but a generic soft cutoff generically introduces non-analytic dependence on external momenta; without an explicit demonstration that the modified optical theorem still yields a strictly positive integrand after the cutoff, the subtracted dispersion relations used for the positivity bounds lack rigorous justification.

    Authors: We agree that an explicit demonstration is required. Our infrared resolution scale is implemented via an exponential damping factor exp(-E/ω) on soft emission energies ω, which is an entire function of the external momenta and therefore introduces no new singularities or non-analyticities in the complex s-plane. Crossing symmetry is preserved because the damping acts symmetrically on the soft factors under s↔u exchange. We will add a dedicated subsection to §2 deriving the modified optical theorem for M_E and showing that the resulting spectral density remains strictly positive for E exponentially smaller than all hard scales. This will justify the subtracted dispersion relations used for the positivity bounds. revision: yes

  2. Referee: [§3] §3 (illustration with pions + EM + gravity): the explicit bounds are presented, but it is not shown that the E-dependent amplitudes remain Regge-behaved at high energy with the same intercept as the uncut amplitudes. If the soft cutoff alters the high-energy behavior, the subtraction constants or the convergence of the dispersion integral may be affected, undermining the infrared safety of the derived bounds.

    Authors: The soft cutoff affects only the infrared region and leaves the high-energy Regge asymptotics unchanged. The Regge intercept is determined by the hard scattering kernel, while the E-dependent soft factors contribute corrections that are exponentially suppressed at large s. We will add a short paragraph to the revised §3 explicitly verifying that the high-s behavior of M_E coincides with that of the original amplitude up to terms that do not affect the convergence of the dispersion integrals or the subtraction constants. This preserves the infrared safety of the derived bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines the family of amplitudes M_E by fiat to satisfy infrared finiteness, analyticity, crossing symmetry, Regge behavior, and Lorentz invariance, then states that unitarity follows for exponentially small E. These properties are asserted as independent inputs that enable standard subtracted dispersion relations; the subsequent positivity bounds on the low-energy pion+EM+gravity theory are derived from the resulting positive spectral density rather than being presupposed by the definition of M_E. No equation reduces a derived coefficient to a fitted parameter, no load-bearing premise rests solely on a self-citation chain, and no ansatz is smuggled via prior work. The construction is therefore self-contained and does not collapse to its own inputs by definition.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, the paper introduces no explicit free parameters, new axioms beyond standard QFT properties, or invented entities; the amplitudes are presented as modifications engineered to satisfy conventional requirements.

pith-pipeline@v0.9.0 · 5418 in / 1045 out tokens · 31371 ms · 2026-05-16T21:51:01.085832+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On the Asymptotic Causal Structure in Gravitational EFTs

    hep-th 2026-04 accept novelty 7.0

    In D>4, gravitational EFTs with higher-derivative operators allow asymptotic superluminality around black holes, but in D=4 the asymptotic causal structure is identical to Schwarzschild and insensitive to corrections.

  2. Negative running of gravitational positivity

    hep-th 2026-03 unverdicted novelty 7.0

    Non-minimal three-point interactions induce negative one-loop running of Wilson coefficients in gravitational EFTs, yet graviton loops generate positive IR contributions that dominate the bounds after smearing if the ...

  3. Multipositivity Constrains the Chiral Lagrangian

    hep-th 2026-05 unverdicted novelty 6.0

    Multipositivity bounds derived from planar tree-level scattering amplitudes constrain Wilson coefficients of the chiral Lagrangian from below by the chiral anomaly.

  4. The Equivalence Principle at High Energies Completes the Spectrum

    hep-th 2026-05 unverdicted novelty 6.0

    Tree-level gravitational scattering under the equivalence principle mandates single-particle states in all irreducible representations constructible from a single seed charge, with equal interaction strengths.

  5. Sampling the Graviton Pole and Deprojecting the Swampland

    hep-th 2026-04 unverdicted novelty 6.0

    A sampling-based bootstrap for graviton poles in EFTs yields non-projective bounds that fix the EFT cutoff scale relative to the Planck mass, with M/M_P ≲ 7.8 in D=5.

Reference graph

Works this paper leans on

140 extracted references · 140 canonical work pages · cited by 5 Pith papers · 33 internal anchors

  1. [1]

    Causality, Analyticity and an IR Obstruction to UV Completion

    A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,”JHEP10(2006) 014, hep-th/0602178

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  2. [2]

    Causality Constraints on Corrections to the Graviton Three-Point Coupling

    X. O. Camanho, J. D. Edelstein, J. Maldacena, and A. Zhiboedov, “Causality Constraints on Corrections to the Graviton Three-Point Coupling,”JHEP02(2016) 020,1407.5597

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  3. [3]

    Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation,

    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) 3027

    work page 1985

  4. [4]

    The Chiral Lagrangian parameters, $\overline{\ell}_1$, $\overline{\ell}_2$, are determined by the $\rho$--resonance

    M. R. Pennington and J. Portoles, “The Chiral Lagrangian parameters, l1, l2, are determined by the rho resonance,”Phys. Lett. B344(1995) 399–406,hep-ph/9409426

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  5. [5]

    Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints

    B. Ananthanarayan, D. Toublan, and G. Wanders, “Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints,”Phys. Rev. D51(1995) 1093–1100, hep-ph/9410302. 41

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  6. [6]

    Falsifying Models of New Physics Via WW Scattering

    J. Distler, B. Grinstein, R. A. Porto, and I. Z. Rothstein, “Falsifying Models of New Physics via WW Scattering,”Phys. Rev. Lett.98(2007) 041601,hep-ph/0604255

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  7. [7]

    Causal vs. Analytic constraints on anomalous quartic gauge couplings

    L. Vecchi, “Causal versus analytic constraints on anomalous quartic gauge couplings,” JHEP11(2007) 054,0704.1900

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  8. [8]

    Dispersion Relation Bounds for pi pi Scattering

    A. V. Manohar and V. Mateu, “Dispersion Relation Bounds for pi pi Scattering,”Phys. Rev. D77(2008) 094019,0801.3222

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  9. [9]

    Symmetries, Sum Rules and Constraints on Effective Field Theories

    B. Bellazzini, L. Martucci, and R. Torre, “Symmetries, Sum Rules and Constraints on Effective Field Theories,”JHEP09(2014) 100,1405.2960

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  10. [10]

    Quantum Gravity Constraints from Unitarity and Analyticity

    B. Bellazzini, C. Cheung, and G. N. Remmen, “Quantum Gravity Constraints from Unitarity and Analyticity,”Phys. Rev. D93(2016), no. 6 064076,1509.00851

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    Softness and Amplitudes' Positivity for Spinning Particles

    B. Bellazzini, “Softness and amplitudes’ positivity for spinning particles,”JHEP02 (2017) 034,1605.06111

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  12. [12]

    Positive Signs in Massive Gravity

    C. Cheung and G. N. Remmen, “Positive Signs in Massive Gravity,”JHEP04(2016) 002,1601.04068

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  13. [13]

    Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons

    J. Bonifacio, K. Hinterbichler, and R. A. Rosen, “Positivity constraints for pseudolinear massive spin-2 and vector Galileons,”Phys. Rev. D94(2016), no. 10 104001, 1607.06084

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  14. [14]

    Eikonal Scattering and Asymptotic Superluminality of Massless Higher Spin Fields

    K. Hinterbichler, A. Joyce, and R. A. Rosen, “Eikonal scattering and asymptotic superluminality of massless higher spin fields,”Phys. Rev. D97(2018), no. 12 125019, 1712.10021

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  15. [15]

    Positivity Bounds for Scalar Theories

    C. de Rham, S. Melville, A. J. Tolley, and S.-Y. Zhou, “Positivity bounds for scalar field theories,”Phys. Rev. D96(2017), no. 8 081702,1702.06134

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  16. [16]

    UV complete me: Positivity Bounds for Particles with Spin

    C. de Rham, S. Melville, A. J. Tolley, and S.-Y. Zhou, “UV complete me: Positivity Bounds for Particles with Spin,”JHEP03(2018) 011,1706.02712

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  17. [17]

    Beyond Amplitudes' Positivity and the Fate of Massive Gravity

    B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, “Beyond Positivity Bounds and the Fate of Massive Gravity,”Phys. Rev. Lett.120(2018), no. 16 161101,1710.02539

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    ZZ and Zgamma still haven't found what they are looking for

    B. Bellazzini and F. Riva, “New phenomenological and theoretical perspective on anomalous ZZ and Zγprocesses,”Phys. Rev. D98(2018), no. 9 095021,1806.09640

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  19. [19]

    Massive Higher Spins: Effective Theory and Consistency,

    B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, “Massive Higher Spins: Effective Theory and Consistency,”JHEP10(2019) 189,1903.08664

    work page arXiv 2019

  20. [20]

    Bellazzini, M

    B. Bellazzini, M. Lewandowski, and J. Serra, “Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity,”Phys. Rev. Lett.123(2019), no. 25 251103, 1902.03250

    work page arXiv 2019

  21. [21]

    Alberte, C

    L. Alberte, C. de Rham, S. Jaitly, and A. J. Tolley, “QED positivity bounds,”Phys. Rev. D103(2021), no. 12 125020,2012.05798. 42

    work page arXiv 2021

  22. [22]

    The ˆH-Parameter: An Oblique Higgs View,

    C. Englert, G. F. Giudice, A. Greljo, and M. Mccullough, “The ˆH-Parameter: An Oblique Higgs View,”JHEP09(2019) 041,1903.07725

    work page arXiv 2019

  23. [23]

    UV Constraints on Massive Spinning Particles: Lessons from the Gravitino,

    S. Melville, D. Roest, and D. Stefanyszyn, “UV Constraints on Massive Spinning Particles: Lessons from the Gravitino,”JHEP02(2020) 185,1911.03126

    work page arXiv 2020

  24. [24]

    LORIS: a web-based data management system for multi-center studies,

    B. Bellazzini, J. Elias Mir´ o, R. Rattazzi, M. Riembau, and F. Riva, “Positive moments for scattering amplitudes,”Phys. Rev. D104(2021), no. 3 036006,2011.00037

    work page arXiv 2021

  25. [25]

    The EFT-Hedron,

    N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, “The EFT-Hedron,”JHEP05(2021) 259,2012.15849

    work page arXiv 2021

  26. [26]

    Caron-Huot and V

    S. Caron-Huot and V. Van Duong, “Extremal Effective Field Theories,”JHEP05 (2021) 280,2011.02957

    work page arXiv 2021

  27. [27]

    Tolley, Z.-Y

    A. J. Tolley, Z.-Y. Wang, and S.-Y. Zhou, “New positivity bounds from full crossing symmetry,”JHEP05(2021) 255,2011.02400

    work page arXiv 2021

  28. [28]

    Bellazzini, M

    B. Bellazzini, M. Riembau, and F. Riva, “IR side of positivity bounds,”Phys. Rev. D 106(2022), no. 10 105008,2112.12561

    work page arXiv 2022

  29. [29]

    Gravita- tional effective field theory islands, low-spin dominance, and the four-graviton amplitude,

    Z. Bern, D. Kosmopoulos, and A. Zhiboedov, “Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude,”J. Phys. A54(2021), no. 34 344002,2103.12728

    work page arXiv 2021

  30. [30]

    Chiang, Y.-t

    L.-Y. Chiang, Y.-t. Huang, W. Li, L. Rodina, and H.-C. Weng, “Into the EFThedron and UV constraints from IR consistency,”JHEP03(2022) 063,2105.02862

    work page arXiv 2022

  31. [31]

    Sharp boundaries for the swampland,

    S. Caron-Huot, D. Mazac, L. Rastelli, and D. Simmons-Duffin, “Sharp boundaries for the swampland,”JHEP07(2021) 110,2102.08951

    work page arXiv 2021

  32. [32]

    Positivity bounds in the standard model effective field theory beyond tree level,

    M. Chala and J. Santiago, “Positivity bounds in the standard model effective field theory beyond tree level,”Phys. Rev. D105(2022), no. 11 L111901,2110.01624

    work page arXiv 2022

  33. [33]

    Natural selection rules: new positivity bounds for massive spinning particles,

    J. Davighi, S. Melville, and T. You, “Natural selection rules: new positivity bounds for massive spinning particles,”JHEP02(2022) 167,2108.06334

    work page arXiv 2022

  34. [34]

    Causality, unitarity, and the weak gravity conjecture,

    N. Arkani-Hamed, Y.-t. Huang, J.-Y. Liu, and G. N. Remmen, “Causality, unitarity, and the weak gravity conjecture,”JHEP03(2022) 083,2109.13937

    work page arXiv 2022

  35. [35]

    Gravitational causality and the self-stress of photons,

    B. Bellazzini, G. Isabella, M. Lewandowski, and F. Sgarlata, “Gravitational causality and the self-stress of photons,”JHEP05(2022) 154,2108.05896

    work page arXiv 2022

  36. [36]

    Serra, J

    F. Serra, J. Serra, E. Trincherini, and L. G. Trombetta, “Causality constraints on black holes beyond GR,”JHEP08(2022) 157,2205.08551

    work page arXiv 2022

  37. [37]

    Graviton partial waves and causal- ity in higher dimensions,

    S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez, and D. Simmons-Duffin, “Graviton partial waves and causality in higher dimensions,”Phys. Rev. D108(2023), no. 2 026007, 2205.01495. 43

    work page arXiv 2023

  38. [38]

    Bellazzini, G

    B. Bellazzini, G. Isabella, and M. M. Riva, “Classical vs quantum eikonal scattering and its causal structure,”JHEP04(2023) 023,2211.00085

    work page arXiv 2023

  39. [39]

    Caron-Huot, Y.-Z

    S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez, and D. Simmons-Duffin, “Causality constraints on corrections to Einstein gravity,”JHEP05(2023) 122,2201.06602

    work page arXiv 2023

  40. [40]

    Guerrieri, H

    A. Guerrieri, H. Murali, J. Penedones, and P. Vieira, “Where is M-theory in the space of scattering amplitudes?,”JHEP06(2023) 064,2212.00151

    work page arXiv 2023

  41. [41]

    Henriksson, B

    J. Henriksson, B. McPeak, F. Russo, and A. Vichi, “Bounding violations of the weak gravity conjecture,”JHEP08(2022) 184,2203.08164

    work page arXiv 2022

  42. [42]

    H¨ aring, A

    K. H¨ aring, A. Hebbar, D. Karateev, M. Meineri, and J. Penedones, “Bounds on photon scattering,”JHEP10(2024) 103,2211.05795

    work page arXiv 2024

  43. [43]

    Creminelli, O

    P. Creminelli, O. Janssen, and L. Senatore, “Positivity bounds on effective field theories with spontaneously broken Lorentz invariance,”JHEP09(2022) 201,2207.14224

    work page arXiv 2022

  44. [44]

    Mas- sive gravity is not positive,

    B. Bellazzini, G. Isabella, S. Ricossa, and F. Riva, “Massive gravity is not positive,” Phys. Rev. D109(2024), no. 2 024051,2304.02550

    work page arXiv 2024

  45. [45]

    Trace anomalies and the graviton-dilaton amplitude,

    D. Karateev, Z. Komargodski, J. Penedones, and B. Sahoo, “Trace anomalies and the graviton-dilaton amplitude,”JHEP11(2024) 067,2312.09308

    work page arXiv 2024

  46. [46]

    The stringy S-matrix bootstrap: maximal spin and superpolynomial softness,

    K. H¨ aring and A. Zhiboedov, “The stringy S-matrix bootstrap: maximal spin and superpolynomial softness,”JHEP10(2024) 075,2311.13631

    work page arXiv 2024

  47. [47]

    Boundaries of universal theories,

    M. McCullough, M. Riembau, and L. Ricci, “Boundaries of universal theories,”Phys. Rev. D111(2025), no. 1 015031,2312.03834

    work page arXiv 2025

  48. [48]

    Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly,

    J. Albert and L. Rastelli, “Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly,”JHEP09(2024) 039,2307.01246

    work page arXiv 2024

  49. [49]

    Bootstrapping the chiral anomaly at largeNc,

    T. Ma, A. Pomarol, and F. Sciotti, “Bootstrapping the chiral anomaly at large N c,” JHEP11(2023) 176,2307.04729

    work page arXiv 2023

  50. [50]

    Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory,

    J. Berman, H. Elvang, and A. Herderschee, “Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory,”JHEP03(2024) 021,2310.10729

    work page arXiv 2024

  51. [51]

    Extremal Higgs couplings,

    J. Elias Miro, A. L. Guerrieri, and M. A. Gumus, “Extremal Higgs couplings,”Phys. Rev. D110(2024), no. 1 016007,2311.09283

    work page arXiv 2024

  52. [52]

    Bootstrapping mesons at large N: Regge trajectory from spin-two maximization,

    J. Albert, J. Henriksson, L. Rastelli, and A. Vichi, “Bootstrapping mesons at large N: Regge trajectory from spin-two maximization,”JHEP09(2024) 172,2312.15013

    work page arXiv 2024

  53. [53]

    Creminelli, M

    P. Creminelli, M. Delladio, O. Janssen, A. Longo, and L. Senatore, “Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance,”JHEP06(2024) 201, 2312.08441. 44

    work page arXiv 2024

  54. [54]

    Analytic bounds on the spectrum of crossing symmetric S-matrices,

    J. Berman, “Analytic bounds on the spectrum of crossing symmetric S-matrices,”JHEP 08(2025) 066,2410.01914

    work page arXiv 2025

  55. [55]

    Where is tree-level string theory?,

    J. Albert, W. Knop, and L. Rastelli, “Where is tree-level string theory?,”JHEP02 (2025) 157,2406.12959

    work page arXiv 2025

  56. [56]

    Boot- strapping Extremal Scalar Amplitudes With and With- out Supersymmetry,

    J. Berman, H. Elvang, N. Geiser, and L. L. Lin, “Bootstrapping Extremal Scalar Amplitudes With and Without Supersymmetry,”2412.13368

    work page arXiv

  57. [57]

    Berman and N

    J. Berman and N. Geiser, “Analytic bootstrap bounds on masses and spins in gravitational and non-gravitational scalar theories,”JHEP06(2025) 168,2412.17902

    work page arXiv 2025

  58. [58]

    Creminelli, O

    P. Creminelli, O. Janssen, B. Salehian, and L. Senatore, “Positivity bounds on electromagnetic properties of media,”JHEP08(2024) 066,2405.09614

    work page arXiv 2024

  59. [59]

    Boot- strapping the chiral-gravitational anomaly,

    Z.-Y. Dong, T. Ma, A. Pomarol, and F. Sciotti, “Bootstrapping the chiral-gravitational anomaly,”JHEP05(2025) 114,2411.14422

    work page arXiv 2025

  60. [60]

    Positivity bounds on massive vectors,

    F. Bertucci, J. Henriksson, B. McPeak, S. Ricossa, F. Riva, and A. Vichi, “Positivity bounds on massive vectors,”JHEP12(2024) 051,2402.13327

    work page arXiv 2024

  61. [61]

    Causality bounds from charged shockwaves in 5d,

    S. Cremonini, B. McPeak, M. Moezzi, and M. Rajaguru, “Causality bounds from charged shockwaves in 5d,”JHEP09(2025) 052,2412.06891

    work page arXiv 2025

  62. [62]

    Positively identify- ing Higgs effective field theory or standard model ef- fective field theory,

    G. N. Remmen and N. L. Rodd, “Positively Identifying HEFT or SMEFT,” 2412.07827

    work page arXiv

  63. [63]

    What is the graviton pole made of?,

    K. H¨ aring and A. Zhiboedov, “What is the graviton pole made of?,”2410.21499

    work page arXiv

  64. [64]

    Scalar weak gravity bound from full unitarity,

    A. Tokareva and Y. Xu, “Scalar weak gravity bound from full unitarity,”Phys. Rev. D 112(2025), no. 8 085020,2502.10375

    work page arXiv 2025

  65. [65]

    Multipositivity bounds for scattering amplitudes,

    C. Cheung and G. N. Remmen, “Multipositivity bounds for scattering amplitudes,” Phys. Rev. D112(2025), no. 1 016017,2505.05553

    work page arXiv 2025

  66. [66]

    de Rham, A

    C. de Rham, A. J. Tolley, Z.-H. Wang, and S.-Y. Zhou, “Primal S-matrix bootstrap with dispersion relations,”2506.22546

    work page internal anchor Pith review arXiv

  67. [67]

    Running EFT-hedron with null constraints at loop level,

    G. Peng, L.-Q. Shao, A. Tokareva, and Y. Xu, “Running EFT-hedron with null constraints at loop level,”2501.09717

    work page arXiv

  68. [68]

    Chang and J

    C.-H. Chang and J. Parra-Martinez, “Graviton loops and negativity,”JHEP08(2025) 175,2501.17949

    work page arXiv 2025

  69. [69]

    Microcausality without Lorentz invariance,

    L. Hui, A. Nicolis, A. Podo, and S. Zhou, “Microcausality without Lorentz invariance,” JHEP07(2025) 188,2502.04215

    work page arXiv 2025

  70. [70]

    Correia, A

    M. Correia, A. Georgoudis, and A. L. Guerrieri, “Cross-Section Bootstrap: Unveiling the Froissart Amplitude,”2506.04313. 45

    work page arXiv

  71. [71]

    Positivity bounds in scalar-QED EFT at one-loop level,

    Y. Ye, X. Cao, Y.-H. Wu, and J. Gu, “Positivity bounds in scalar-QED EFT at one-loop level,”JHEP10(2025) 084,2507.06302

    work page arXiv 2025

  72. [72]

    Splitting regions and shrinking islands from higher point con- straints,

    J. Berman, H. Elvang, and C. Figueiredo, “Splitting regions and shrinking islands from higher point constraints,”JHEP10(2025) 226,2506.22538

    work page arXiv 2025

  73. [73]

    (Super) gravity from positivity,

    B. Bellazzini, A. Pomarol, M. Romano, and F. Sciotti, “(Super) Gravity from Positivity,”2507.12535

    work page arXiv

  74. [74]

    Geometry of effective field theory positivity cones,

    Q. Bonnefoy, V. Cort´ es, E. Gendy, C. Grojean, K. R. von Merkl, and P. N. Pilatus, “Geometry of effective field theory positivity cones,”2508.18165

    work page arXiv

  75. [75]

    Causal bounds on EFTs with anomalies with a pseudoscalar, photons, and gravitons,

    Z. Dong, J. Jeong, and A. Pomarol, “Causal Bounds on EFTs with anomalies with a Pseudoscalar, Photons, and Gravitons,”2510.12138

    work page arXiv

  76. [76]

    Analyticity and positivity of Green's functions without Lorentz

    P. Creminelli, A. Longo, B. Salehian, and A. Zahed, “Analyticity and positivity of Green’s functions without Lorentz,”2512.10843

    work page internal anchor Pith review Pith/arXiv arXiv

  77. [77]

    The Rise of Linear Trajectories,

    Y.-t. Huang, S. Ricossa, F. Riva, and J.-D. Tsai, “The Rise of Linear Trajectories,” 2510.07991

    work page arXiv

  78. [78]

    The Asymptotic Behavior of Massless Fields and the Memory Effect

    G. Satishchandran and R. M. Wald, “Asymptotic behavior of massless fields and the memory effect,”Phys. Rev. D99(2019), no. 8 084007,1901.05942

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  79. [79]

    Prabhu, G

    K. Prabhu, G. Satishchandran, and R. M. Wald, “Infrared finite scattering theory in quantum field theory and quantum gravity,”Phys. Rev. D106(2022), no. 6 066005, 2203.14334

    work page arXiv 2022

  80. [80]

    Large Gauge Symmetries and Asymptotic States in QED

    B. Gabai and A. Sever, “Large gauge symmetries and asymptotic states in QED,” JHEP12(2016) 095,1607.08599

    work page internal anchor Pith review Pith/arXiv arXiv 2016

Showing first 80 references.