UV completions of scalar-tensor EFTs

Adam Falkowski; Edoardo Alviani; Panagiotis Marinellis

REVIEW 1 major objections 3 minor 2 cited by

UV completions of scalar-tensor EFTs

T0 review · 1 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper argues that shift-symmetric scalar Gauss-Bonnet gravity has no UV completion among weakly coupled one-loop models with massive spin-0, 1/2, and 1 matter, whereas dynamical Chern-Simons gravity is UV-completable, uniquely via a…

desk verdict Careful one-loop matching paper that scopes a no-go: shift-symmetric SGB is not generated by these simple UV completions, while DCS is via the PQ model; the 'unique' wording is the only real blemish. read the letter →

arxiv 2507.11426 v1 pith:XWJ22VP7 submitted 2025-07-15 hep-th hep-ph

Edoardo Alviani , Adam Falkowski , Panagiotis Marinellis This is my paper

classification hep-thhep-ph

keywords scalar-tensorEFTscalarGauss-BonnetgravitydynamicalChern-Simonsone-loopmatchingon-shellamplitudesspinor-helicityformalismshiftsymmetryPeccei-Quinn

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks which ultraviolet (UV) completions can produce low-energy scalar-tensor theories of gravity in which a massless scalar couples to the Gauss-Bonnet invariant (SGB) or to the Chern-Simons invariant (DCS). Working with one-loop matching between a UV theory of massive spin-0, spin-1/2, and spin-1 particles and the low-energy effective field theory, it derives explicit formulas for the SGB and DCS Wilson coefficients in terms of UV masses and couplings. The central qualitative result is an asymmetry: a shift-symmetric SGB theory cannot be obtained from any of these UV setups, because shift-symmetry-breaking operators such as $\phi R^3$ and $\phi^2 R_{\rm GB}^2$ are generated along with $C_{\phi GB}$; the shift-symmetric DCS theory, by contrast, has a unique UV completion, a fermion plus complex scalar with a Peccei-Quinn symmetry. The results matter because SGB and DCS are widely studied gravity extensions that predict black-hole scalar hair and gravitational-wave signatures, and knowing which ones have sensible UV completions tells theorists which effective theories to take seriously.

What carries the argument

The load-bearing machinery is the on-shell matching of one-loop four-point amplitudes in the spinor-helicity formalism. For each heavy species the paper builds tree-level three- and four-point amplitudes from minimal gravitational couplings and cubic scalar couplings, computes the $s$-channel discontinuity of the one-loop amplitude as a two-body phase-space integral over an intermediate heavy pair, and reconstructs the full amplitude in a basis of scalar integrals (tadpole, bubble, triangle, box). Expanding in the ratio of external energy to heavy mass and comparing with the EFT amplitude fixes the Wilson coefficients, with the decisive convention that rational terms growing as the heavy mass goes to zero are forbidden; this is what makes the coefficients predictive. The same calculation applied to the two-graviton-two-scalar amplitude fixes the dimension-six coefficients $C_{\phi^2 GB}$ and $C_{\phi^2 CS}$.

What would settle it

Repeat the one-loop matching with an independent off-shell method, or with a non-minimal gravitational coupling such as an anomalous quadrupole term for the vector; if a minimal-coupling model within this class is found with $C_{\phi GB}\neq 0$ and all shift-symmetry-violating coefficients vanishing without tuned contact terms, the central claim is false.

Watch

Extended reading notes

Core claim

At one loop, integrating out massive spin-0, spin-1/2, and spin-1 particles that are minimally coupled to gravity and coupled to a massless scalar gives the dimension-five Wilson coefficients in Eq. (4.15): $$C_{\phi GB} = -\frac{y_0}{1440\$pi^{2}$ m_\Phi} - \frac{7 y_s}{2880\$pi^{2}$ m_\Psi} - \frac{11 y_d - 2 y_m}{240\$pi^{2}$ M_*}, \qquad C_{\phi CS} = -\frac{y_p}{192\$pi^{2}$ m_\Psi} - \frac{y_a}{24\$pi^{2}$ M_*},$$ up to $O(M_*^{-1})$ corrections. The qualitative discovery is the asymmetry summarized in Sec. 4.3: for every UV setup considered, either the SGB coupling $C_{\phi GB}$ is absent or it is accompanied by shift-symmetry-breaking operators such as $\phi R^3$ and $\phi^2 R_{\rm GB}^2$. Consequently, within this class of models the shift-symmetric scalar Gauss-Bonnet theory is not UV-completable, while the dynamical Chern-Simons coupling has a unique shift-symmetric completion: the scalar is the Goldstone boson of a spontaneously broken $U(1)_{\rm PQ}$ acting chirally on a heavy fermion.

Load-bearing premise

The conclusions rest on the assumptions that heavy particles couple to gravity only through the standard minimal coupling and that unphysical rational pieces of the one-loop amplitudes are fixed by demanding a smooth limit as the heavy mass goes to zero; if either assumption is relaxed, the predicted operator pattern, including the SGB no-go, can change.

Editorial extensions

If this is right

A shift-symmetric scalar Gauss-Bonnet theory cannot be embedded as a low-energy limit of any of the considered weakly coupled UV completions without also generating shift-symmetry-violating operators like $\phi R^3$ and $\phi^2 R_{\rm GB}^2$.
The dynamical Chern-Simons coupling can be generated shift-symmetrically, and the only predictive option found in this class is a heavy fermion with a complex scalar endowed with a Peccei-Quinn symmetry, whose anomaly matches the DCS coupling.
For heavy vector matter the SGB and DCS coefficients are suppressed by the UV cutoff $M_*$ and are of the same order as uncontrolled rational terms, so spin-1 completions are not predictive for these couplings; the authors expect this to persist for higher spins.
In the predictive spin-0 and spin-1/2 completions, lower-dimensional operators such as $\phi^3$ and $\phi^4$ are generically generated, so phenomenological studies should include the full tower of operators rather than only the shift-symmetric terms.
The matching reproduces the known $R^3$ Wilson coefficients as a cross-check, supporting the reliability of the on-shell method for the new coefficients.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implication the authors leave implicit is that any parity-even shift-symmetric gravitational scalar coupling faces the same obstacle: without a parity-odd partner enforcing the symmetry, loop effects from minimal matter will always produce shift-breaking companions.
If the smooth-$m\to 0$ rational-term convention were wrong, the spin-0 and spin-1/2 SGB coefficients could be shifted by scheme-dependent rational terms, so an independent off-shell effective-action computation of the same coefficients would settle the robustness of the matching.
A direct extension would be to repeat the matching with non-minimal gravitational couplings for the heavy fields; the paper notes this could generate $\widetilde{C}_{R^3}$ and change the operator pattern, so the SGB no-go may weaken in that larger class.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Punchline: this paper earns a serious referee. It is a careful one-loop matching calculation that answers a concrete question: which simple QFT completions can generate the SGB and DCS couplings probed by gravitational-wave experiments. The answer, within the class of models considered, is that SGB always comes with shift-symmetry breaking operators, while DCS can be generated shift-symmetrically by the U(1)_PQ fermion model of Refs [41,42]. That is a useful and honest result.

What's new: the systematic scan over spin-0, 1/2, 1 matter, the explicit Wilson coefficients for C_phiGB, C_phi2GB, C_phiR3, C'_4, and the no-go statement for SGB. The matching method is taken from Refs [45,46] but applied to a new sector. The paper is well documented: discontinuities from tree-level amplitudes in Appendix B, rational-term ambiguity isolated in delta_R, and C_R3 agrees with Refs [45,46]. The DCS anomaly consistency check with Ref [41] is a nice cross-check. The exposition is transparent about where matching fails (dimension-four and lower coefficients, spin-1 non-predictivity).

Soft spots: the rational-term fixing is a physical assumption, not a theorem. The paper states 'we are not allowed to introduce rational terms scaling with inverse powers of m_Phi' — without that, the m to 0 limit fails, but one could imagine a different regulator. This is acknowledged, but it means the no-go is conditional on this smoothness premise. Similarly, minimal gravitational coupling (Eq. 3.1) is assumed; non-minimal couplings would change C_phiR3 and possibly the operator pattern. The spin-1 results are non-predictive, as the authors say. The 'unique' in the abstract for the DCS completion is a mild overstatement; the body correctly says 'within the considered class of models' and 'within our setup'. I'd soften that in revision. The one-loop integrals were not independently checked by the reader; I didn't redo them either, but the R3 cross-check and internal consistency give reasonable confidence. No fatal flaw found.

Bottom line: the central claim holds up for the stated model class. The paper is for hep-th/gr-qc readers interested in EFT matching and scalar-tensor gravity. It deserves a serious referee and likely publication in JHEP after minor wording fixes. I would cite it for the Wilson coefficients and the no-go result. Probably bring to reading group if you care about gravitational EFTs.

Referee Report

1 major / 3 minor

Summary. The paper performs a one-loop matching between a UV theory containing massive spin-0, spin-1/2, and spin-1 particles minimally coupled to gravity, and a low-energy scalar-tensor EFT of a massless scalar and the graviton. Using on-shell amplitude methods and unitarity cuts, the authors derive Wilson coefficients for the scalar Gauss-Bonnet (SGB), dynamical Chern-Simons (DCS), and related operators in terms of UV masses and couplings. The central results are Eqs. (4.15) and (4.16) for the dimension-5 and dimension-6 coefficients, Eq. (4.17) for the R3 coefficients, and the qualitative conclusion in Sec. 4.3 that shift-symmetric SGB is not generated within the considered class, while DCS can be generated shift-symmetrically only via a U(1)_PQ model with a heavy fermion.

Significance. If the results hold, this is a valuable contribution to scalar-tensor EFTs, mapping out which weakly coupled UV completions can produce SGB and DCS interactions. The paper is unusually transparent: the rational-term ambiguity is isolated in δR, the R3 coefficients reproduce Refs. [45,46], the DCS coefficient is consistent with anomaly matching in Ref. [41], and the spin-1 non-predictivity and minimal-coupling assumptions are explicitly disclosed. These features, together with the explicit formulas for the Wilson coefficients, give the central claims a high degree of credibility and make the paper useful for follow-up work on scalar-tensor phenomenology and UV-completion constraints.

major comments (1)

[Sec. 4.3, after Eq. (4.22)] The contact-term assignment for the U(1)_PQ model is misstated. The text sets cΨ = M∗/mΨ, but consistency with Eq. (4.16) requires cΨ = y_p^2 M∗/mΨ: substituting cΨ = M∗/mΨ into C_phi2GB for ys = 0 gives 7(1 - y_p^2)/(2880π^2 mΨ^2), which vanishes only for y_p^2 = 1. Since y_p is a free Yukawa coupling and is not set to unity anywhere in the model, the claimed cancellation of the shift-symmetry-violating coefficient is not demonstrated for general y_p. The qualitative conclusion is recoverable once the factor y_p^2 is restored, so this is a correctable error, but it affects a load-bearing step of the DCS shift-symmetry argument.

minor comments (3)

[Sec. 4.3, positivity remark] The statement that C'_4 > 0 is 'easily shown to be satisfied' in the entire parameter space is not immediate for the spin-1 contribution in Eq. (4.19), where the log(μ^2/m_V^2) term is negative for μ < m_V; the authors should justify the sign or qualify the claim to the stated matching scale.
[Sec. 4.3] The expression 'cΨ = M∗/m' has a typo (missing subscript on the mass); the corrected relation is cΨ = y_p^2 M∗/mΨ as noted in the major comment.
[Sec. 4.1] The sentence 'we are not allowed to introduce rational terms scaling with inverse powers of mΦ' could usefully include a footnote clarifying that the physical C_phiGB ~ 1/m term arises from the cut integrals and is not part of the rational-term ambiguity, which affects only terms with non-negative powers of m.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Wilson coefficients are obtained by genuine one-loop matching to independent EFT amplitudes, and the no-go is explicitly scoped to the stated UV model class.

full rationale

The central results, Eqs. (4.15) and (4.16), are derived by computing one-loop UV amplitudes via unitarity cuts, expanding in E/m, and matching the resulting pole and contact terms to the independent EFT amplitude formulas in Eqs. (2.11)–(2.13). The coefficients C_phiGB and C_phiCS are read off from the coefficients of the (1/s + 1/t + 1/u) terms in the matched amplitude, e.g. from Eq. (4.8) to Eq. (4.9); they are not tuned to reproduce a desired SGB or DCS result. The rational-term fixing is an explicitly stated physical requirement: 'we are not allowed to introduce rational terms scaling with inverse powers of m_Phi', and the paper acknowledges that dimension-four and lower coefficients are consequently ambiguous. That is a premise about the UV theory having a smooth massless limit, not a fit to the target coefficients. The R3 result is cross-checked against Refs. [45,46], where [45] is an independent calculation and [46] supplies the matching method; the agreement provides external support for the method. The DCS consistency check uses an independent anomaly equation from Ref. [41], whose authors do not overlap with the present paper. The 'unique' PQ claim is explicitly restricted to the considered model class ('within our setup' in the abstract; 'within the considered class of models' in Sec. 5), and the paper itself flags that non-minimal gravitational couplings could change the pattern after Eq. (4.17). No load-bearing step reduces by construction to its own input, and no central claim depends on an unverified self-citation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper performs a matching calculation, not a fit: UV masses and couplings are inputs, and the EFT coefficients are derived functions of them. There are no data-fitted free parameters. The main extra assumptions are the minimal gravitational coupling of heavy matter (Eq. 3.1), the rational-term fixing via smooth m -> 0 limit (Sec. 4.1), and the standard EFT basis and regularization choices. No new particles or forces are introduced; the UV fields Phi, Psi, and V are standard massive fields, and the PQ complex-scalar and fermion model is taken from Refs. [41,42].

free parameters (3)

Heavy matter masses m_Phi, m_Psi, m_V = input spectrum (not fitted)
Set the EFT cutoff and appear as 1/m in the matched Wilson coefficients (Eqs. 4.15 to 4.19); the paper does not predict them.
Cubic scalar-matter couplings y0, ys, yp, yd, ya, ym = input couplings (not fitted)
These UV couplings determine the sign and size of C_phiGB and C_phiCS (Eq. 4.15) and the higher-dimension coefficients; no data are used to fix them.
UV contact-term coefficients c_Phi, c_Psi, ec_Psi, c_V, ec_V, chat_V = arbitrary (not determined)
Enter the 4-point UV amplitudes (Eqs. 3.6, B.3, B.6); c_Phi controls C_phi2GB = (y0^2 - c_Phi)/(1440 pi^2 m_Phi^2), so the SGB shift-symmetry-breaking conclusion is generic rather than unconditional.

assumptions (5)

domain assumption Heavy matter is minimally coupled to gravity; only the scalar-matter cubic couplings in Eq. (3.2) are considered.
This defines the model class and is the condition under which the SGB no-go and DCS uniqueness hold; non-minimal gravitational couplings such as anomalous quadrupole terms would alter the generated operator pattern, as the authors acknowledge after Eq. (4.17).
ad hoc to paper The one-loop rational-term ambiguity is fixed by requiring a smooth m -> 0 limit, so rational terms cannot scale as inverse powers of m.
Used in Sec. 4.1 around Eq. (4.7) to extract coefficients that scale as 1/m; without this assumption the Wilson coefficients of dimension-four and lower operators are ambiguous and spin-1 contributions are nonpredictive.
domain assumption The UV theory is weakly coupled and the heavy masses m satisfy m << M* <= M_Pl, so one-loop matching and E/m expansions are valid.
Assumed in Section 3 and used to expand amplitudes in powers of E/m throughout Section 4; it also underlies the statement that spin-1 contributions are suppressed by 1/M*.
standard math The EFT operator basis in Section 2 is complete up to dimension 8 after discarding total derivatives and field-redefinition-removable terms such as phi R, R^2, and phi^2 R.
Basis choice explained below Eq. (2.2); matching to this basis defines the extracted Wilson coefficients.
standard math Dimensional regularization with d = 4 - 2 epsilon and tadpole adjustment c1 removes non-local UV divergences.
Used in Appendix A.2 and Sec. 4.1; standard in on-shell matching and needed to reconstruct the full one-loop amplitudes from discontinuities.

how reviews work

0 comments

Cite this review

Pith. "Pith review of UV completions of scalar-tensor EFTs." pith.science (2026). https://pith.science/paper/XWJ22VP7

@misc{pith2026250711426,
  author       = {Pith},
  title        = {Pith review of: UV completions of scalar-tensor EFTs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XWJ22VP7}},
  note         = {Machine review of arXiv:2507.11426}
}

abstract

We study models that give rise to scalar-tensor effective field theories (EFTs) at low energies. Our framework involves massive particles of spin $S=0, 1/2, 1$ coupled to gravity and to a real massless scalar in the UV. Integrating out the massive states leads to a scalar-tensor EFT describing the massless graviton and scalar degrees of freedom. Using the on-shell amplitude methods and the spinor-helicity formalism, we match the two frameworks at one loop, so as to express the EFT Wilson coefficients in terms of the UV masses and coupling. We explore the space of the operators generated in the EFT, including the ones related to the scalar Gauss-Bonnet (SGB) and dynamical Chern-Simons (DCS) gravity theories. We demonstrate that, within our setup, the SGB interactions are always generated with shift-symmetry breaking operators. This is in contrast to the DCS case, where there is a unique choice that preserves the shift symmetry in the IR, corresponding to a theory of spin 1/2 fermions and a complex scalar with a Peccei-Quinn global symmetry.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

Negative running of gravitational positivity
hep-th 2026-03 unverdicted novelty 7.0 of 10

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 ...
Heterotic Footprints in Classical Gravity: PM dynamics from On-Shell soft amplitudes at one loop
hep-th 2025-10 unverdicted novelty 6.0 of 10

Derives conservative potential and scattering angle for charged black holes in EMD theory via one-loop soft amplitudes, showing IR finiteness after Lippmann-Schwinger treatment and smooth reduction to GR.

Reference graph

Works this paper leans on

56 extracted references · 1 canonical work pages · cited by 2 Pith papers

[41]

Alexander and C

S. Alexander and C. Creque-Sarbinowski,UV completions of Chern-Simons gravity, Phys. Rev. D 108 (2023) 104046 [2207.05094]

arXiv 2023
[1]

Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [1807.06209]

arXiv 2020
[2]

Donoghue,General relativity as an effective field theory: The leading quantum corrections, Phys

J.F. Donoghue,General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D50 (1994) 3874 [gr-qc/9405057]

arXiv 1994
[3]

Burgess,Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev

C.P. Burgess,Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev. Rel.7 (2004) 5 [gr-qc/0311082]

arXiv 2004
[4]

Ruhdorfer, J

M. Ruhdorfer, J. Serra and A. Weiler,Effective Field Theory of Gravity to All Orders, JHEP 05 (2020) 083 [1908.08050]

arXiv 2020
[5]

Sotiriou and S.-Y

T.P. Sotiriou and S.-Y. Zhou,Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112 (2014) 251102 [1312.3622]

arXiv 2014
[6]

Sotiriou and S.-Y

T.P. Sotiriou and S.-Y. Zhou,Black hole hair in generalized scalar-tensor gravity: An explicit example, Phys. Rev. D90 (2014) 124063 [1408.1698]

arXiv 2014
[7]

Alexander and N

S. Alexander and N. Yunes,Chern-Simons Modified General Relativity, Phys. Rept. 480 (2009) 1 [0907.2562]

arXiv 2009

Show all 56 references

[8]

Yunes and F

N. Yunes and F. Pretorius,Dynamical Chern-Simons Modified Gravity. I. Spinning Black Holes in the Slow-Rotation Approximation, Phys. Rev. D79 (2009) 084043 [0902.4669]

2009 arXiv
[9]

Serra, J

F. Serra, J. Serra, E. Trincherini and L.G. Trombetta,Causality constraints on black holes beyond GR, JHEP 08 (2022) 157 [2205.08551]

2022 arXiv
[10]

Hong, Z.-H

D.-Y. Hong, Z.-H. Wang and S.-Y. Zhou,Causality bounds on scalar-tensor EFTs, JHEP 10 (2023) 135 [2304.01259]

2023 arXiv
[11]

Alexander and J

S. Alexander and J. Martin,Birefringent gravitational waves and the consistency check of inflation, Phys. Rev. D71 (2005) 063526 [hep-th/0410230]

2005 arXiv
[12]

Okounkova, W.M

M. Okounkova, W.M. Farr, M. Isi and L.C. Stein,Constraining gravitational wave amplitude birefringence and Chern-Simons gravity with GWTC-2, Phys. Rev. D106 (2022) 044067 [2101.11153]

2022 arXiv
[13]

Yunes, R

N. Yunes, R. O’Shaughnessy, B.J. Owen and S. Alexander,Testing gravitational parity violation with coincident gravitational waves and short gamma-ray bursts, Phys. Rev. D82 (2010) 064017 [1005.3310]

2010 arXiv
[14]

Yagi and H

K. Yagi and H. Yang,Probing Gravitational Parity Violation with Gravitational Waves from Stellar-mass Black Hole Binaries, Phys. Rev. D97 (2018) 104018 [1712.00682]

2018 arXiv
[15]

Alexander and N

S.H. Alexander and N. Yunes,Gravitational wave probes of parity violation in compact binary coalescences, Phys. Rev. D97 (2018) 064033 [1712.01853]

2018 arXiv
[16]

D.H. Lyth, C. Quimbay and Y. Rodriguez,Leptogenesis and tensor polarisation from a gravitational Chern-Simons term, JHEP 03 (2005) 016 [hep-th/0501153]

2005 arXiv
[17]

Satoh,Slow-roll Inflation with the Gauss-Bonnet and Chern-Simons Corrections, JCAP 11 (2010) 024 [1008.2724]

M. Satoh,Slow-roll Inflation with the Gauss-Bonnet and Chern-Simons Corrections, JCAP 11 (2010) 024 [1008.2724]

2010 arXiv
[18]

Yagi,A New constraint on scalar Gauss-Bonnet gravity and a possible explanation for the excess of the orbital decay rate in a low-mass X-ray binary, Phys

K. Yagi,A New constraint on scalar Gauss-Bonnet gravity and a possible explanation for the excess of the orbital decay rate in a low-mass X-ray binary, Phys. Rev. D86 (2012) 081504 [1204.4524]. – 26 –

2012 arXiv
[19]

Silva, A.M

H.O. Silva, A.M. Holgado, A. Cárdenas-Avendaño and N. Yunes,Astrophysical and theoretical physics implications from multimessenger neutron star observations, Phys. Rev. Lett. 126 (2021) 181101 [2004.01253]

2021 arXiv
[20]

Saffer and K

A. Saffer and K. Yagi,Tidal deformabilities of neutron stars in scalar-Gauss-Bonnet gravity and their applications to multimessenger tests of gravity, Phys. Rev. D104 (2021) 124052 [2110.02997]

2021 arXiv
[21]

Kanti, N.E

P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis and E. Winstanley,Dilatonic black holes in higher curvature string gravity, Phys. Rev. D54 (1996) 5049 [hep-th/9511071]

1996 arXiv
[22]

Maeda, N

K.-i. Maeda, N. Ohta and Y. Sasagawa,Black Hole Solutions in String Theory with Gauss-Bonnet Curvature Correction, Phys. Rev. D80 (2009) 104032 [0908.4151]

2009 arXiv
[23]

Yagi, L.C

K. Yagi, L.C. Stein, N. Yunes and T. Tanaka,Post-Newtonian, Quasi-Circular Binary Inspirals in Quadratic Modified Gravity, Phys. Rev. D85 (2012) 064022 [1110.5950]

2012 arXiv
[24]

Grumiller and N

D. Grumiller and N. Yunes,How do Black Holes Spin in Chern-Simons Modified Gravity?, Phys. Rev. D77 (2008) 044015 [0711.1868]

2008 arXiv
[25]

K. Yagi, N. Yunes and T. Tanaka,Slowly Rotating Black Holes in Dynamical Chern-Simons Gravity: Deformation Quadratic in the Spin, Phys. Rev. D86 (2012) 044037 [1206.6130]

2012 arXiv
[26]

K. Yagi, N. Yunes and T. Tanaka,Gravitational Waves from Quasi-Circular Black Hole Binaries in Dynamical Chern-Simons Gravity, Phys. Rev. Lett.109 (2012) 251105 [1208.5102]

2012 arXiv
[27]

Yagi, L.C

K. Yagi, L.C. Stein, N. Yunes and T. Tanaka,Isolated and Binary Neutron Stars in Dynamical Chern-Simons Gravity, Phys. Rev. D87 (2013) 084058 [1302.1918]

2013 arXiv
[28]

Witek, L

H. Witek, L. Gualtieri, P. Pani and T.P. Sotiriou,Black holes and binary mergers in scalar Gauss-Bonnet gravity: scalar field dynamics, Phys. Rev. D99 (2019) 064035 [1810.05177]

2019 arXiv
[29]

Loutrel, T

N. Loutrel, T. Tanaka and N. Yunes,Spin-Precessing Black Hole Binaries in Dynamical Chern-Simons Gravity, Phys. Rev. D98 (2018) 064020 [1806.07431]

2018 arXiv
[30]

Julié and E

F.-L. Julié and E. Berti,Post-Newtonian dynamics and black hole thermodynamics in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D100 (2019) 104061 [1909.05258]

2019 arXiv
[31]

Shiralilou, T

B. Shiralilou, T. Hinderer, S.M. Nissanke, N. Ortiz and H. Witek,Post-Newtonian gravitational and scalar waves in scalar-Gauss–Bonnet gravity, Class. Quant. Grav.39 (2022) 035002 [2105.13972]

2022 arXiv
[32]

Julié, L

F.-L. Julié, L. Pompili and A. Buonanno,Inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity within the effective-one-body formalism, Phys. Rev. D 111 (2025) 024016 [2406.13654]

2025 arXiv
[33]

Bhattacharyya, D

A. Bhattacharyya, D. Ghosh, S. Ghosh and S. Pal,Bootstrapping the spinning two body problem in dynamical Chern-Simons gravity using worldline QFT, JHEP 04 (2025) 175 [2407.07195]

2025 arXiv
[34]

Falkowski and P

A. Falkowski and P. Marinellis,Spinning waveforms of scalar radiation in quadratic modified gravity, Eur. Phys. J. C85 (2025) 74 [2407.16457]

2025 arXiv
[35]

Falkowski and P

A. Falkowski and P. Marinellis,On-shell approach to scalar hair in spinning binaries, JHEP 05 (2025) 045 [2411.12909]

2025 arXiv
[36]

Wilson-Gerow,Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity, 2503.02867

J. Wilson-Gerow,Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity, 2503.02867. – 27 –

arXiv
[37]

KAGRA, LIGO Scientific, VIRGO collaboration, All-sky search for continuous gravitational waves from isolated neutron stars using Advanced LIGO and Advanced Virgo O3 data, Phys. Rev. D106 (2022) 102008 [2201.00697]

2022 arXiv
[38]

LISA collaboration, Laser Interferometer Space Antenna, 1702.00786

arXiv
[39]

ET collaboration, Science Case for the Einstein Telescope, JCAP 03 (2020) 050 [1912.02622]

2020 arXiv
[40]

Evans et al.,A Horizon Study for Cosmic Explorer: Science, Observatories, and Community, 2109.09882

M. Evans et al.,A Horizon Study for Cosmic Explorer: Science, Observatories, and Community, 2109.09882

arXiv
[42]

Alexander, H

S. Alexander, H. Bernardo and C. Creque-Sarbinowski,Nontriviality of dynamical Chern-Simons gravity and the standard model, Phys. Rev. D110 (2024) 025015 [2403.15657]

2024 arXiv
[43]

Dreiner, H.E

H.K. Dreiner, H.E. Haber and S.P. Martin,Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys.Rept. 494 (2010) 1 [0812.1594]

2010 arXiv
[44]

Arkani-Hamed, T.-C

N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang,Scattering amplitudes for all masses and spins, JHEP 11 (2021) 070 [1709.04891]

2021 arXiv
[45]

Z. Bern, D. Kosmopoulos and A. Zhiboedov,Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude, J. Phys. A54 (2021) 344002 [2103.12728]

2021 arXiv
[46]

Alviani and A

E. Alviani and A. Falkowski,Matching and positivity beyond minimal coupling in effective theories of photons and gravitons, Eur. Phys. J. C85 (2025) 154 [2408.03439]

2025 arXiv
[47]

Goon,Heavy Fields and Gravity, JHEP 01 (2017) 045 [1611.02705]

G. Goon,Heavy Fields and Gravity, JHEP 01 (2017) 045 [1611.02705]

2017 arXiv
[48]

Bonnefoy, L

Q. Bonnefoy, L. Di Luzio, C. Grojean, A. Paul and A.N. Rossia,The anomalous case of axion EFTs and massive chiral gauge fields, JHEP 07 (2021) 189 [2011.10025]

2021 arXiv
[49]

Adams, N

A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi,Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178]

2006 arXiv
[50]

Camanho, J.D

X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov,Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [1407.5597]

2016 arXiv
[51]

Xu, D.-Y

H. Xu, D.-Y. Hong, Z.-H. Wang and S.-Y. Zhou,Positivity bounds on parity-violating scalar-tensor EFTs, JCAP 01 (2025) 102 [2410.09794]

2025 arXiv
[52]

Nie, L.-T

W.-K. Nie, L.-T. Tan, J. Zhang and S.-Y. Zhou,Scalar-Gauss-Bonnet gravity: Infrared causality and detectability of GW observations, 2410.10973

arXiv
[53]

Doneva and S.S

D.D. Doneva and S.S. Yazadjiev,New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories, Phys. Rev. Lett.120 (2018) 131103 [1711.01187]

2018 arXiv
[54]

Silva, J

H.O. Silva, J. Sakstein, L. Gualtieri, T.P. Sotiriou and E. Berti,Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling, Phys. Rev. Lett.120 (2018) 131104 [1711.02080]

2018 arXiv
[55]

Zwiebel,From Scattering Amplitudes to the Dilatation Generator in N=4 SYM, J

B.I. Zwiebel,From Scattering Amplitudes to the Dilatation Generator in N=4 SYM, J. Phys. A 45 (2012) 115401 [1111.0083]. – 28 –

2012 arXiv
[56]

Caron-Huot and M

S. Caron-Huot and M. Wilhelm,Renormalization group coefficients and the S-matrix, JHEP 12 (2016) 010 [1607.06448]. – 29 –

2016 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [41]

Alexander and C

S. Alexander and C. Creque-Sarbinowski,UV completions of Chern-Simons gravity, Phys. Rev. D 108 (2023) 104046 [2207.05094]

arXiv 2023

[2] [1]

Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [1807.06209]

arXiv 2020

[3] [2]

Donoghue,General relativity as an effective field theory: The leading quantum corrections, Phys

J.F. Donoghue,General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D50 (1994) 3874 [gr-qc/9405057]

arXiv 1994

[4] [3]

Burgess,Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev

C.P. Burgess,Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev. Rel.7 (2004) 5 [gr-qc/0311082]

arXiv 2004

[5] [4]

Ruhdorfer, J

M. Ruhdorfer, J. Serra and A. Weiler,Effective Field Theory of Gravity to All Orders, JHEP 05 (2020) 083 [1908.08050]

arXiv 2020

[6] [5]

Sotiriou and S.-Y

T.P. Sotiriou and S.-Y. Zhou,Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112 (2014) 251102 [1312.3622]

arXiv 2014

[7] [6]

Sotiriou and S.-Y

T.P. Sotiriou and S.-Y. Zhou,Black hole hair in generalized scalar-tensor gravity: An explicit example, Phys. Rev. D90 (2014) 124063 [1408.1698]

arXiv 2014

[8] [7]

Alexander and N

S. Alexander and N. Yunes,Chern-Simons Modified General Relativity, Phys. Rept. 480 (2009) 1 [0907.2562]

arXiv 2009