pith. sign in

arxiv: 2606.28423 · v1 · pith:F5EKPZXQnew · submitted 2026-06-25 · 🌀 gr-qc · astro-ph.CO· hep-th

Quantum corrections to symmetron fifth forces for planar sources

Peter Millington , Michael Udemba This is my paper

Pith reviewed 2026-06-30 00:48 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords symmetronfifth forcequantum correctionsplanar sourcescreened scalar-tensorCANNEXscalar field profile
0
0 comments X

The pith

Quantum corrections suppress symmetron fifth forces near planar sources by order 10 percent.

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

The paper computes the leading quantum corrections to the symmetron-mediated fifth force exerted by a planar source of finite thickness. It finds that the force is suppressed relative to the classical result inside a Compton wavelength of the source and enhanced at greater distances. The size of the near-source suppression reaches about 10 percent in the parameter range relevant to experiments such as CANNEX. A reader would care because the altered force profile can affect the design and interpretation of laboratory and astrophysical tests of screened scalar-tensor gravity.

Core claim

We provide a semi-analytic calculation of the first quantum corrections to the symmetron fifth force around a planar source with nonzero thickness. We find a suppression of the fifth force compared with the classical prediction within a Compton wavelength of the source, which is of order 10% in the parameter region relevant to experiments like CANNEX, while the fifth force is enhanced at larger distances from the source. The resulting change in the spatial profile of the fifth force may be relevant to current and near future terrestrial and astrophysical tests of force laws, and has implications for the optimisation of experimental geometries, including atom interferometers.

What carries the argument

Semi-analytic evaluation of one-loop quantum corrections to the symmetron scalar profile and the derived fifth force for a thick planar source.

If this is right

  • The modified force profile affects the interpretation of current and near-future tests of force laws.
  • Optimisation of experimental geometries, including atom interferometers, must account for the altered spatial dependence.
  • The calculation supplies a benchmark for future numerical studies of quantum-corrected fifth forces in screened scalar-tensor theories.
  • The distance-dependent change from suppression to enhancement can shift the effective range probed by different detector placements.

Where Pith is reading between the lines

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

  • The same semi-analytic method could be applied to spherical or cylindrical sources to check whether the 10 percent scale persists.
  • Higher-order loop corrections or different source densities might be checked numerically to confirm the leading term dominates.
  • The enhancement at large distances could alter bounds extracted from astrophysical systems where the source-observer separation exceeds the Compton wavelength.

Load-bearing premise

The semi-analytic approximation used to compute the leading quantum corrections remains valid for the chosen planar source thickness and does not miss dominant higher-order contributions.

What would settle it

A precision measurement of the fifth-force profile around a planar source that shows no suppression of order 10 percent inside one Compton wavelength would falsify the reported quantum correction.

read the original abstract

We provide a semi-analytic calculation of the first quantum corrections to the symmetron fifth force around a planar source with nonzero thickness. We find a suppression of the fifth force compared with the classical prediction within a Compton wavelength of the source, which is of order 10% in the parameter region relevant to experiments like CANNEX, while the fifth force is enhanced at larger distances from the source. The resulting change in the spatial profile of the fifth force may be relevant to current and near future terrestrial and astrophysical tests of force laws, and has implications for the optimisation of experimental geometries, including atom interferometers. This work provides a key benchmark for future numerical studies of quantum-corrected fifth forces in screened scalar-tensor theories of 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

3 major / 3 minor

Summary. The manuscript presents a semi-analytic calculation of the leading quantum corrections to the symmetron fifth force for a planar source of finite thickness. It reports an approximately 10% suppression of the fifth force relative to the classical prediction within one Compton wavelength of the source (in the parameter regime relevant to CANNEX), together with an enhancement at larger distances, and discusses implications for experimental tests of modified gravity and optimization of geometries such as atom interferometers. The work is positioned as a benchmark for future numerical studies of quantum-corrected fifth forces in screened scalar-tensor theories.

Significance. If the quantitative result is reliable, the paper supplies a concrete benchmark for quantum effects in symmetron models that could affect the interpretation of near-future fifth-force searches; the explicit semi-analytic treatment of the first corrections and the identification of a sign change in the correction across the Compton scale are useful reference points even if higher-order terms ultimately modify the 10% figure.

major comments (3)
  1. [Calculation of quantum corrections / Results] The semi-analytic approximation employed for the leading quantum corrections (detailed in the calculation of the symmetron profile) supplies no explicit error bound on the neglected higher-order contributions nor a direct comparison against a fully numerical solution of the same effective theory; because the headline 10% suppression is extracted from this truncation, the absence of such validation is load-bearing for the central quantitative claim.
  2. [Setup and source model] The choice of planar source thickness is stated to be representative, yet no sensitivity analysis or demonstration is given that the reported suppression/enhancement profile remains stable under modest variations in thickness; this is required to confirm that the geometry does not introduce uncontrolled artifacts in the semi-analytic step.
  3. [Discussion / Implications] The abstract and introduction frame the result as directly relevant to CANNEX, but the parameter region in which the 10% figure is obtained is not cross-checked against the precise experimental constraints or screening lengths used in that experiment; a short table or explicit mapping would strengthen the claim.
minor comments (3)
  1. [Introduction] Notation for the Compton wavelength and the symmetron vacuum expectation value should be introduced once with a clear equation reference rather than assumed from prior literature.
  2. [Figures] Figure captions would benefit from explicit statements of the parameter values (e.g., λ, eta, source thickness) used to generate each curve, to allow immediate reproduction of the plotted profiles.
  3. [Methods] A brief statement on the range of validity of the semi-analytic expansion (e.g., in terms of the coupling strength or source density) would improve clarity without altering the technical content.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive suggestions. We address each of the major comments below.

read point-by-point responses

  1. Referee: [Calculation of quantum corrections / Results] The semi-analytic approximation employed for the leading quantum corrections (detailed in the calculation of the symmetron profile) supplies no explicit error bound on the neglected higher-order contributions nor a direct comparison against a fully numerical solution of the same effective theory; because the headline 10% suppression is extracted from this truncation, the absence of such validation is load-bearing for the central quantitative claim.

    Authors: We agree that an explicit error bound would strengthen the presentation. However, deriving rigorous bounds on the truncation error in this semi-analytic approach is technically involved and beyond the scope of the current work, which focuses on the leading correction. We have added a paragraph in the discussion section explaining the perturbative nature of the expansion and estimating the size of higher-order terms based on the small parameter in the regime considered. A full numerical validation is left for future work, as stated in the manuscript's positioning as a benchmark. revision: partial

  2. Referee: [Setup and source model] The choice of planar source thickness is stated to be representative, yet no sensitivity analysis or demonstration is given that the reported suppression/enhancement profile remains stable under modest variations in thickness; this is required to confirm that the geometry does not introduce uncontrolled artifacts in the semi-analytic step.

    Authors: The thickness was chosen to be representative of experimental setups like CANNEX. To address this, we will include in the revised manuscript a sensitivity analysis demonstrating that the qualitative features (suppression within one Compton wavelength and enhancement beyond) persist under variations of the thickness by factors of order 1 within the screened regime. revision: yes

  3. Referee: [Discussion / Implications] The abstract and introduction frame the result as directly relevant to CANNEX, but the parameter region in which the 10% figure is obtained is not cross-checked against the precise experimental constraints or screening lengths used in that experiment; a short table or explicit mapping would strengthen the claim.

    Authors: We will add a short table in the revised version mapping the parameters used in our calculation to the experimental constraints and screening lengths relevant to CANNEX, to make the connection explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents a direct semi-analytic computation of leading quantum corrections to the symmetron profile and fifth force for a finite-thickness planar source. The reported suppression (order 10% within one Compton wavelength) and enhancement at larger distances are framed as outputs of this calculation applied to the symmetron effective theory, not as quantities fitted to data or defined in terms of themselves. No load-bearing self-citations, ansatzes smuggled via prior work, or self-definitional steps are described in the abstract or context; the result is positioned as a benchmark for future numerics rather than a tautological renaming or forced prediction. The derivation chain is therefore self-contained against the model equations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, axioms, or invented entities used in the calculation.

pith-pipeline@v0.9.1-grok · 5646 in / 994 out tokens · 44455 ms · 2026-06-30T00:48:26.716497+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

52 extracted references · 5 canonical work pages

  1. [1]

    Mehta, P

    K. Mehta, P. Kumar and A. Beesham,Thermodynamics and energy conditions of accelerating brans–dicke universe,International Journal of Geometric Methods in Modern Physics(2026)

    2026

  2. [2]

    Kepuladze,Radiative dark energy in a seesaw framework,Physics Letters B876(2026) 140422

    Z. Kepuladze,Radiative dark energy in a seesaw framework,Physics Letters B876(2026) 140422

    2026

  3. [3]

    Beesham, A.M

    A. Beesham, A.M. Msomi and S.C. Gumede,Scalar field dark energy model via observational constraints,Gravitation and Cosmology32(2026) 70–86

    2026

  4. [4]

    Almurr and J.C

    E. Almurr and J.C. Assaf,Finite-range scalar–tensor gravity: Constraints from cosmology and galaxy dynamics,Galaxies14(2026) 7

    2026

  5. [5]

    Zaregonbadi, N

    R. Zaregonbadi, N. Saba and M. Farhoudi,Chameleon gravity as an alternative to dark matter, The European Physical Journal C85(2025)

    2025

  6. [6]

    Dabbaghsaz and A

    E. Dabbaghsaz and A. Mohebalhojeh,Integrated collective dynamics: A purely theoretical scalar-tensor framework for gravitational dynamics without dark components,Nuclear Physics B1018(2025) 117029

    2025

  7. [7]

    Feleppa, W.M

    F. Feleppa, W.M. de Graaf, P. Brax and G. Lambiase,Bounds on screened dark energy from near-earth space-based measurements,Physical Review Letters136(2026)

    2026

  8. [8]

    Gallardo, K

    P. Gallardo, K. Pardo, O. Philcox, N. Battaglia, E. Battistelli, R. Bean et al.,Test of the gravitational force law on cosmological scales using the kinematic sunyaev-zeldovich effect, Physical Review Letters136(2026) . – 24 –

    2026

  9. [9]

    Will,The confrontation between general relativity and experiment,Living Reviews in Relativity4(2001)

    C.M. Will,The confrontation between general relativity and experiment,Living Reviews in Relativity4(2001)

    2001

  10. [10]

    Clifton, P.G

    T. Clifton, P.G. Ferreira, A. Padilla and C. Skordis,Modified gravity and cosmology,Physics Reports513(2012) 1–189

    2012

  11. [11]

    Amendola, C

    L. Amendola, C. Bernal and R. Gannouji,Nonlinear dynamics in horndeski gravity: A renormalized approach to effective gravitational coupling,Physical Review D112(2025)

    2025

  12. [12]

    Hinterbichler, J

    K. Hinterbichler, J. Khoury, A. Levy and A. Matas,Symmetron Cosmology,Phys. Rev. D84 (2011) 103521 [1107.2112]

    Pith/arXiv arXiv 2011

  13. [13]

    K¨ ading,Lensing with Generalized Symmetrons,Astronomy2(2023) 128 [2304.05875]

    C. K¨ ading,Lensing with Generalized Symmetrons,Astronomy2(2023) 128 [2304.05875]

    arXiv 2023

  14. [14]

    Bachs-Esteban, I

    J. Bachs-Esteban, I. Lopes and J. Rubio,Screening mechanisms on white dwarfs: Symmetron and dilaton,Universe11(2025) 158

    2025

  15. [15]

    Burrage, A

    C. Burrage, A. Kuribayashi-Coleman, J. Stevenson and B. Thrussell,Constraining symmetron fields with atom interferometry,J. Cosmol. Astropart. Phys.2016(2016) 041

    2016

  16. [16]

    Brax, A.-C

    P. Brax, A.-C. Davis and B. Elder,(g-2)µand screened modified gravity,Phys. Rev. D106 (2022) 044040 [2111.01188]

    arXiv 2022

  17. [17]

    Sun, B.J.J

    L. Sun, B.J.J. Slagmolen and J. Qin,Differential torsion sensor for direct detection of ultralight vector dark matter,Phys. Rev. D111(2025) 063064 [2402.08935]

    arXiv 2025

  18. [18]

    Krishak and S

    A. Krishak and S. Desai,Model comparison tests of modified gravity from the e¨ ot-wash experiment,JCAP07(2020) 006 [2003.10127]

    arXiv 2020

  19. [19]

    Wagner, S

    T.A. Wagner, S. Schlamminger, J.H. Gundlach and E.G. Adelberger,Torsion-balance tests of the weak equivalence principle,Class. Quant. Grav.29(2012) 184002 [1207.2442]

    Pith/arXiv arXiv 2012

  20. [20]

    Sedmik and M

    R.I.P. Sedmik and M. Pitschmann,Next generation design and prospects for cannex,Universe 7(2021) 234

    2021

  21. [21]

    Fischer, C

    H. Fischer, C. K¨ ading and M. Pitschmann,Quantum and thermal pressures from light scalar fields,Phys. Dark Univ.47(2025) 101756 [2407.20658]

    arXiv 2025

  22. [22]

    Brax, A.-C

    P. Brax, A.-C. Davis and B. Elder,Screened scalar fields in hydrogen and muonium,Phys. Rev. D107(2023) 044008

    2023

  23. [23]

    Dvorak, K

    A. Dvorak, K. Obigane, H. Lemmel, T. Jenke and S. Sponar,Experimental test of symmetron-field based dark energy model using neutron interferometry,2606.03440

    Pith/arXiv arXiv

  24. [24]

    Fischer, C

    H. Fischer, C. K¨ ading, H. Lemmel, S. Sponar and M. Pitschmann,Search for dark energy with neutron interferometry,PTEP2024(2024) 023E02 [2310.18109]

    arXiv 2024

  25. [25]

    Jenke, J

    T. Jenke, J. Bosina, J. Micko, M. Pitschmann, R. Sedmik and H. Abele,Gravity resonance spectroscopy and dark energy symmetron fields: qbounce experiments performed with rabi and ramsey spectroscopy,Eur. Phys. J. ST230(2021) 1131 [2012.07472]

    arXiv 2021

  26. [26]

    Jenke et al.,Testing gravity at short distances: Gravity resonance spectroscopy with qbounce, EPJ Web Conf.219(2019) 05003

    T. Jenke et al.,Testing gravity at short distances: Gravity resonance spectroscopy with qbounce, EPJ Web Conf.219(2019) 05003

    2019

  27. [27]

    Yin et al.,Experimental constraints on the symmetron field with a magnetically levitated force sensor,Nature Astron.9(2025) 598

    P. Yin et al.,Experimental constraints on the symmetron field with a magnetically levitated force sensor,Nature Astron.9(2025) 598

    2025

  28. [28]

    Li and K.-d

    J. Li and K.-d. Zhu,Constraining symmetron fields with a levitated optomechanical system, JCAP04(2025) 036 [2411.17744]

    arXiv 2025

  29. [29]

    Brax and S

    P. Brax and S. Fichet,Quantum chameleons,Physical Review D99(2019)

    2019

  30. [30]

    Brax and S

    P. Brax and S. Fichet,Scalar-mediated quantum forces between macroscopic bodies and interferometry,Physics of the Dark Universe42(2023) 101294. – 25 –

    2023

  31. [31]

    Millington and M

    P. Millington and M. Udemba,Quantum corrections to symmetron fifth-force profiles,Journal of Cosmology and Astroparticle Physics2026(2026) 087

    2026

  32. [32]

    Coleman,Fate of the false vacuum: Semiclassical theory,Physical Review D15(1977) 2929

    S. Coleman,Fate of the false vacuum: Semiclassical theory,Physical Review D15(1977) 2929

    1977

  33. [33]

    Coleman,Erratum: Fate of the false vacuum: semiclassical theory,Physical Review D16 (1977) 1248

    S. Coleman,Erratum: Fate of the false vacuum: semiclassical theory,Physical Review D16 (1977) 1248

    1977

  34. [34]

    Callan and S

    C.G. Callan and S. Coleman,Fate of the false vacuum. ii. first quantum corrections,Physical Review D16(1977) 1762

    1977

  35. [35]

    Garbrecht and P

    B. Garbrecht and P. Millington,Green’s function method for handling radiative effects on false vacuum decay,Phys. Rev. D91(2015) 105021 [1501.07466]

    Pith/arXiv arXiv 2015

  36. [36]

    Burrage, B

    C. Burrage, B. Elder and P. Millington,Particle level screening of scalar forces in1 + 1 dimensions,Phys. Rev. D99(2019) 024045

    2019

  37. [37]

    Brax and M

    P. Brax and M. Pitschmann,Exact solutions to nonlinear symmetron theory: One- and two-mirror systems,Phys. Rev. D97(2018) 064015

    2018

  38. [38]

    Pitschmann,Exact solutions to nonlinear symmetron theory: One- and two-mirror systems

    M. Pitschmann,Exact solutions to nonlinear symmetron theory: One- and two-mirror systems. ii.,Phys. Rev. D103(2021) 084013

    2021

  39. [39]

    Hinterbichler and J

    K. Hinterbichler and J. Khoury,Screening long-range forces through local symmetry restoration, Physical Review Letters104(2010)

    2010

  40. [40]

    Burrage, B

    C. Burrage, B. Elder, P. Millington, D. Saadeh and B. Thrussell,Fifth-force screening around extremely compact sources,Journal of Cosmology and Astroparticle Physics2021(2021) 052

    2021

  41. [41]

    Nishimori,Statistical Physics of Spin Glasses and In- formation Processing, Oxford University Press (2001)

    A. Almasi, P. Brax, D. Iannuzzi and R.I. Sedmik,Force sensor for chameleon and casimir force experiments with parallel-plate configuration,Physical Review D91(2015) . [42]Heun’s Differential Equations, Oxford University PressOxford (1995), 10.1093/oso/9780198596950.001.0001

    work page doi:10.1093/oso/9780198596950.001.0001 2015

  42. [42]

    Millington and M

    P. Millington and M. Udemba,Quantum corrections to symmetron fifth-force profiles,JCAP 02(2026) 087 [2508.16726]

    Pith/arXiv arXiv 2026

  43. [43]

    Garbrecht and P

    B. Garbrecht and P. Millington,Self-consistent solitons for vacuum decay in radiatively generated potentials,Phys. Rev. D92(2015) 125022

    2015

  44. [44]

    Birkandan, P.-L

    T. Birkandan, P.-L. Giscard and A. Tamar,Computations of general heun functions from their integral series representations, in2021 Days on Diffraction (DD), p. 12–18, IEEE, May, 2021, DOI

    2021

  45. [45]

    Udemba,mudemba/heun path sum, 2026

    M. Udemba,mudemba/heun path sum, 2026. 10.5281/zenodo.20732181

    work page doi:10.5281/zenodo.20732181 2026

  46. [46]

    Banks, J

    H. Banks, J. Carlton, B. Elder, T. Hird and C. McCabe,Searching for screened scalar forces with long-baseline atom interferometers,Phys. Rev. D113(2026) 084047 [2511.09750]

    arXiv 2026

  47. [47]

    Briddon, C

    C. Briddon, C. Burrage, A. Moss and A. Tamosiunas,Using machine learning to optimise chameleon fifth force experiments,JCAP02(2024) 011 [2308.00844]

    arXiv 2024

  48. [48]

    Andrews, R

    G.E. Andrews, R. Askey and R. Roy,Special Functions, Cambridge University Press (Jan., 1999), 10.1017/cbo9781107325937

    work page doi:10.1017/cbo9781107325937 1999

  49. [49]

    Ruby and M

    V.C. Ruby and M. Lakshmanan,A quantum approach to the continuum heisenberg spin-chain model: Position-dependent mass formalism and pre-canonical quantization,Journal of Mathematical Physics66(2025)

    2025

  50. [50]

    L.-B. Wu, L. Xie, L.-M. Cao, M.-F. Ji and Y.-S. Zhou,Quasinormal modes of schwarzschild-de sitter black holes in semi-open systems,Science China Physics, Mechanics and Astronomy69 (2026)

    2026

  51. [51]

    Whittaker and G.N

    E.T. Whittaker and G.N. Watson,A Course of Modern Analysis, Cambridge University Press (Sept., 1996), 10.1017/cbo9780511608759. – 26 –

    work page doi:10.1017/cbo9780511608759 1996

  52. [52]

    Arscott,Periodic Differential Equations, Elsevier (1964), 10.1016/c2013-0-01721-5

    F.M. Arscott,Periodic Differential Equations, Elsevier (1964), 10.1016/c2013-0-01721-5. – 27 –

    work page doi:10.1016/c2013-0-01721-5 1964