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arxiv: 2604.03033 · v1 · submitted 2026-04-03 · ✦ hep-ph · hep-th

Recognition: 2 theorem links

· Lean Theorem

Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow

Daniele Rizzo, Dario Zappala, Enrico Maria Sessolo, Gabriele Giacometti, Kamila Kowalska

Authors on Pith no claims yet

Pith reviewed 2026-05-13 18:02 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords quantum gravitybeta functionsgauge couplingsYukawa couplingsproper-time flowEinstein-Hilbert truncationfunctional renormalization groupasymptotic safety
0
0 comments X

The pith

Quantum gravity contributions to gauge and Yukawa beta functions are derived via the Schwinger proper-time flow equation in the Einstein-Hilbert truncation.

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

The paper computes how quantum gravity alters the energy-scale dependence of gauge and Yukawa couplings by applying the Schwinger proper-time flow equation to a matter theory coupled to gravity. Working inside the Einstein-Hilbert truncation, it tracks the dependence of these corrections on gauge-fixing choices and regulator functions, then evaluates them at gravity's interacting fixed point. A sympathetic reader would care because the size of these corrections determines whether they can produce measurable shifts in Standard Model running or generate testable predictions in extensions with new physics. The work also compares the results to those obtained in other renormalization schemes to assess robustness.

Core claim

Using the Schwinger proper-time flow equation in the Einstein-Hilbert truncation, we obtain quantum gravity corrections to the renormalization group beta functions for the gauge and Yukawa couplings in a matter theory. The dependence on the gauge-fixing parameter and the regulator function is investigated, and the gravitational contribution is evaluated at the non-Gaussian fixed point of the gravitational sector. Results are compared with those from other renormalization group schemes, and the magnitude of the corrections is assessed against the values required to generate observable effects in the Standard Model and various new physics scenarios.

What carries the argument

The Schwinger proper-time flow equation, which integrates the renormalization group flow over proper-time scales, applied to the Einstein-Hilbert truncation of gravity coupled to matter fields.

Load-bearing premise

The Einstein-Hilbert truncation together with the chosen proper-time regulator and gauge fixing is sufficient to capture the leading quantum-gravity effects on the matter beta functions.

What would settle it

A calculation of the gravitational corrections to the same beta functions performed in an extended truncation that includes higher-curvature terms such as R squared, yielding substantially different numerical values, would show that the leading-order truncation is insufficient.

Figures

Figures reproduced from arXiv: 2604.03033 by Daniele Rizzo, Dario Zappala, Enrico Maria Sessolo, Gabriele Giacometti, Kamila Kowalska.

Figure 1
Figure 1. Figure 1: fy as a function of the regulator m for G˜ = 1. Solid blue: α = 1, Λ = 0; dashed ˜ blue: α = 1, Λ =˜ −4; dotted red: α = 0, Λ = 0; dot-dashed red: ˜ α = 0, Λ =˜ −4. where we have used the fact that Λ is a constant with respect to both momenta and fields and therefore commutes with both of them. After expanding Eq. (46) we retain the linear order in the Yukawa operator and perform the heat kernel integral, … view at source ↗
Figure 2
Figure 2. Figure 2: Dependence on the gauge-fixing parameter [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dependence on the gauge-fixing parameter [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Isocontour lines of (a) fg and (b) fy in the (Λ˜ ∗ , G˜∗ ) plane, computed in the sharp￾regulator limit of the proper time flow with gauge-fixing parameter α = 1. The markers indicate the gravitational UV fixed points for the SM, B − L, SU(5), and SU(6) matter content. Isocontour lines of (a) fg and (b) fy in the (Λ˜ ∗ , G˜∗ ) plane, computed in the sharp￾regulator limit of the proper time flow with gauge-… view at source ↗
Figure 5
Figure 5. Figure 5: Regulator dependence of the fixed-point values of the Einstein-Hilbert action, [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
read the original abstract

We derive quantum gravity contributions to the beta functions of the gauge and Yukawa couplings of a matter theory using the Schwinger proper-time flow equation. Working in the Einstein-Hilbert truncation, we investigate the gauge-fixing and regulator dependence of the corresponding renormalization group equations. We quantify the sensitivity of our results on unphysical parameters by evaluating the gravitational correction to the running matter couplings at the interactive fixed point of gravity and we compare our findings with existing determinations in alternative schemes. We finally confront the derived contributions with the typical size they should assume to generate observable low-scale predictions in the Standard Model and in several scenarios of new physics.

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.

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The derivation obtains the gravitational corrections to gauge and Yukawa beta functions directly from the Schwinger proper-time flow equation inside the Einstein-Hilbert truncation. Fixed-point values are imported from prior literature as an external input (standard in asymptotic-safety calculations) rather than being fitted or redefined inside the present work. The paper explicitly checks regulator and gauge-fixing dependence within the truncation and compares results against independent schemes, so the central claim does not reduce to its own inputs by construction. No self-definitional, fitted-prediction, or load-bearing self-citation steps are present.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the Einstein-Hilbert truncation for gravity and the validity of the functional renormalization-group flow in the proper-time scheme; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Einstein-Hilbert truncation captures the dominant quantum-gravity effects on matter couplings
    Invoked when the flow equations are written and when results are evaluated at the gravity fixed point.

pith-pipeline@v0.9.0 · 5410 in / 1248 out tokens · 53661 ms · 2026-05-13T18:02:59.465078+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

108 extracted references · 108 canonical work pages

  1. [1]

    Weinberg,General Relativity, pp

    S. Weinberg,General Relativity, pp. 790–831. S.W.Hawking, W.Israel (Eds.), Cam- bridge Univ. Press, 1980

    work page 1980

  2. [2]

    Exact evolution equation for the effective potential,

    C. Wetterich, “Exact evolution equation for the effective potential,”Physics Letters B 301no. 1, (1993) 90 – 94

    work page 1993

  3. [3]

    The Exact renormalization group and approximate solutions,

    T. R. Morris, “The Exact renormalization group and approximate solutions,”Int. J. Mod. Phys. A9(1994) 2411–2450,arXiv:hep-ph/9308265

    work page arXiv 1994

  4. [4]

    Nonperturbative evolution equation for quantum gravity,

    M. Reuter, “Nonperturbative evolution equation for quantum gravity,”Phys. Rev. D 57(1998) 971–985,arXiv:hep-th/9605030

    work page arXiv 1998

  5. [5]

    Ultraviolet fixed point and generalized flow equation of quantum gravity,

    O. Lauscher and M. Reuter, “Ultraviolet fixed point and generalized flow equation of quantum gravity,”Phys. Rev. D65(2002) 025013,arXiv:hep-th/0108040

    work page arXiv 2002

  6. [6]

    Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation,

    M. Reuter and F. Saueressig, “Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation,”Phys. Rev. D65(2002) 065016,arXiv:hep-th/0110054 22

    work page arXiv 2002

  7. [7]

    Flow equation of quantum Einstein gravity in a higher derivative truncation,

    O. Lauscher and M. Reuter, “Flow equation of quantum Einstein gravity in a higher derivative truncation,”Phys. Rev. D66(2002) 025026,arXiv:hep-th/0205062

    work page arXiv 2002

  8. [8]

    Fixed points of quantum gravity,

    D. F. Litim, “Fixed points of quantum gravity,”Phys. Rev. Lett.92(2004) 201301, arXiv:hep-th/0312114

    work page arXiv 2004

  9. [9]

    Fixed points of higher derivative gravity,

    A. Codello and R. Percacci, “Fixed points of higher derivative gravity,”Phys. Rev. Lett.97(2006) 221301,arXiv:hep-th/0607128

    work page arXiv 2006

  10. [10]

    On the renormalization group flow of f(R)-gravity,

    P. F. Machado and F. Saueressig, “On the renormalization group flow of f(R)-gravity,” Phys. Rev. D77(2008) 124045,arXiv:0712.0445 [hep-th]

    work page arXiv 2008

  11. [11]

    Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation,

    A. Codello, R. Percacci, and C. Rahmede, “Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation,”Annals Phys.324(2009) 414–469,arXiv:0805.2909 [hep-th]

    work page arXiv 2009

  12. [12]

    Asymptotic safety in higher- derivative gravity,

    D. Benedetti, P. F. Machado, and F. Saueressig, “Asymptotic safety in higher- derivative gravity,”Mod. Phys. Lett. A24(2009) 2233–2241,arXiv:0901.2984 [hep-th]

    work page arXiv 2009

  13. [13]

    Asymptotic safety in the f(R) approximation,

    J. A. Dietz and T. R. Morris, “Asymptotic safety in the f(R) approximation,”JHEP 01(2013) 108,arXiv:1211.0955 [hep-th]

    work page arXiv 2013

  14. [14]

    A bootstrap towards asymp- totic safety,

    K. Falls, D. Litim, K. Nikolakopoulos, and C. Rahmede, “A bootstrap towards asymp- totic safety,”arXiv:1301.4191 [hep-th]

    work page arXiv

  15. [15]

    Further evidence for asymptotic safety of quantum gravity,

    K. Falls, D. F. Litim, K. Nikolakopoulos, and C. Rahmede, “Further evidence for asymptotic safety of quantum gravity,”Phys. Rev. D93no. 10, (2016) 104022, arXiv:1410.4815 [hep-th]

    work page arXiv 2016

  16. [16]

    Constraints on matter from asymptotic safety,

    R. Percacci and D. Perini, “Constraints on matter from asymptotic safety,”Phys. Rev. D67(2003) 081503,arXiv:hep-th/0207033

    work page arXiv 2003

  17. [17]

    Asymptotic safety of gravity coupled to matter,

    R. Percacci and D. Perini, “Asymptotic safety of gravity coupled to matter,”Phys. Rev. D68(2003) 044018,arXiv:hep-th/0304222

    work page arXiv 2003

  18. [18]

    Gravitational corrections to Yukawa systems,

    O. Zanusso, L. Zambelli, G. Vacca, and R. Percacci, “Gravitational corrections to Yukawa systems,”Phys. Lett. B689(2010) 90–94,arXiv:0904.0938 [hep-th]

    work page arXiv 2010

  19. [19]

    Running Gauge Coupling in Asymptotically Safe Quantum Gravity,

    J.-E. Daum, U. Harst, and M. Reuter, “Running Gauge Coupling in Asymptotically Safe Quantum Gravity,”JHEP01(2010) 084,arXiv:0910.4938 [hep-th]

    work page arXiv 2010

  20. [20]

    Non-perturbative QEG Corrections to the Yang-Mills Beta Function,

    J.-E. Daum, U. Harst, and M. Reuter, “Non-perturbative QEG Corrections to the Yang-Mills Beta Function,”Gen. Rel. Grav.43(2011) 2393,arXiv:1005.1488 [hep-th]

    work page arXiv 2011

  21. [21]

    Asymptotic freedom of Yang-Mills theory with gravity,

    S. Folkerts, D. F. Litim, and J. M. Pawlowski, “Asymptotic freedom of Yang-Mills theory with gravity,”Phys. Lett. B709(2012) 234–241,arXiv:1101.5552 [hep-th] 23

    work page arXiv 2012

  22. [22]

    Matter matters in asymptotically safe quan- tum gravity,

    P. Don` a, A. Eichhorn, and R. Percacci, “Matter matters in asymptotically safe quan- tum gravity,”Phys. Rev. D89no. 8, (2014) 084035,arXiv:1311.2898 [hep-th]

    work page arXiv 2014

  23. [23]

    Asymptotic safety of gravity-matter systems,

    J. Meibohm, J. M. Pawlowski, and M. Reichert, “Asymptotic safety of gravity-matter systems,”Phys. Rev. D93no. 8, (2016) 084035,arXiv:1510.07018 [hep-th]

    work page arXiv 2016

  24. [24]

    Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity,

    K.-y. Oda and M. Yamada, “Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity,”Class. Quant. Grav.33no. 12, (2016) 125011, arXiv:1510.03734 [hep-th]

    work page arXiv 2016

  25. [25]

    Quantum-gravity effects on a Higgs- Yukawa model,

    A. Eichhorn, A. Held, and J. M. Pawlowski, “Quantum-gravity effects on a Higgs- Yukawa model,”Phys. Rev. D94no. 10, (2016) 104027,arXiv:1604.02041 [hep-th]

    work page arXiv 2016

  26. [26]

    Asymptotic safety of gravity with matter,

    N. Christiansen, D. F. Litim, J. M. Pawlowski, and M. Reichert, “Asymptotic safety of gravity with matter,”Phys. Rev. D97no. 10, (2018) 106012,arXiv:1710.04669 [hep-th]

    work page arXiv 2018

  27. [27]

    Viability of quantum-gravity induced ultraviolet comple- tions for matter,

    A. Eichhorn and A. Held, “Viability of quantum-gravity induced ultraviolet comple- tions for matter,”Phys. Rev. D96no. 8, (2017) 086025,arXiv:1705.02342 [gr-qc]

    work page arXiv 2017

  28. [28]

    Quantum Gravity: A Fluctuating Point of View,

    J. M. Pawlowski and M. Reichert, “Quantum Gravity: A Fluctuating Point of View,” Front. in Phys.8(2021) 551848,arXiv:2007.10353 [hep-th]

    work page arXiv 2021

  29. [29]

    Asymptotic safety of gravity with matter,

    A. Eichhorn and M. Schiffer, “Asymptotic safety of gravity with matter,” arXiv:2212.07456 [hep-th]

    work page arXiv

  30. [30]

    Ultraviolet properties of f(R)-gravity,

    A. Codello, R. Percacci, and C. Rahmede, “Ultraviolet properties of f(R)-gravity,”Int. J. Mod. Phys. A23(2008) 143–150,arXiv:0705.1769 [hep-th]

    work page arXiv 2008

  31. [31]

    On the scheme dependence of gravitational beta func- tions,

    G. Narain and R. Percacci, “On the scheme dependence of gravitational beta func- tions,”Acta Phys. Polon. B40(2009) 3439–3457,arXiv:0910.5390 [hep-th]

    work page arXiv 2009

  32. [32]

    QED coupled to QEG,

    U. Harst and M. Reuter, “QED coupled to QEG,”JHEP05(2011) 119, arXiv:1101.6007 [hep-th]

    work page arXiv 2011

  33. [33]

    An asymptotically safe solution to the U(1) triviality problem,

    N. Christiansen and A. Eichhorn, “An asymptotically safe solution to the U(1) triviality problem,”Phys. Lett. B770(2017) 154–160,arXiv:1702.07724 [hep-th]

    work page arXiv 2017

  34. [34]

    Upper bound on the Abelian gauge coupling from asymptotic safety,

    A. Eichhorn and F. Versteegen, “Upper bound on the Abelian gauge coupling from asymptotic safety,”JHEP01(2018) 030,arXiv:1709.07252 [hep-th]

    work page arXiv 2018

  35. [35]

    Asymptotic safety of quantum gravity beyond Ricci scalars,

    K. Falls, C. R. King, D. F. Litim, K. Nikolakopoulos, and C. Rahmede, “Asymptotic safety of quantum gravity beyond Ricci scalars,”Phys. Rev. D97no. 8, (2018) 086006, arXiv:1801.00162 [hep-th]

    work page arXiv 2018

  36. [36]

    Aspects of asymptotic safety for quantum gravity,

    K. G. Falls, D. F. Litim, and J. Schr ˜A¶der, “Aspects of asymptotic safety for quantum gravity,”Phys. Rev. D99no. 12, (2019) 126015,arXiv:1810.08550 [gr-qc] 24

    work page arXiv 2019

  37. [37]

    Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators,

    G. P. de Brito and A. Eichhorn, “Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators,”Eur. Phys. J. C83no. 2, (2023) 161,arXiv:2201.11402 [hep-th]

    work page arXiv 2023

  38. [38]

    The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking,

    A. Pastor-Guti´ errez, J. M. Pawlowski, and M. Reichert, “The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking,” SciPost Phys.15no. 3, (2023) 105,arXiv:2207.09817 [hep-th]

    work page arXiv 2023

  39. [39]

    Regulator and gauge dependence of the Abelian gauge coupling in asymptotically safe quantum gravity,

    M. Riabokon, M. Schiffer, and F. Wagner, “Regulator and gauge dependence of the Abelian gauge coupling in asymptotically safe quantum gravity,”Phys. Rev. D112 no. 10, (2025) 106003,arXiv:2508.03563 [hep-th]

    work page arXiv 2025

  40. [40]

    Cosmological constant and quantum gravitational corrections to the run- ning fine structure constant,

    D. J. Toms, “Cosmological constant and quantum gravitational corrections to the run- ning fine structure constant,”Phys. Rev. Lett.101(2008) 131301,arXiv:0809.3897 [hep-th]

    work page arXiv 2008

  41. [41]

    Quantum gravity, gauge coupling constants, and the cosmological con- stant,

    D. J. Toms, “Quantum gravity, gauge coupling constants, and the cosmological con- stant,”Phys. Rev. D80(2009) 064040,arXiv:0908.3100 [hep-th]

    work page arXiv 2009

  42. [42]

    Gravitational correction to running of gauge cou- plings,

    S. P. Robinson and F. Wilczek, “Gravitational correction to running of gauge cou- plings,”Phys. Rev. Lett.96(2006) 231601,arXiv:hep-th/0509050

    work page arXiv 2006

  43. [43]

    Gauge dependence of gravitational correction to running of gauge couplings,

    A. R. Pietrykowski, “Gauge dependence of gravitational correction to running of gauge couplings,”Phys. Rev. Lett.98(2007) 061801,arXiv:hep-th/0606208

    work page arXiv 2007

  44. [44]

    Quantum gravity and charge renormalization,

    D. J. Toms, “Quantum gravity and charge renormalization,”Phys. Rev. D76(2007) 045015,arXiv:0708.2990 [hep-th]

    work page arXiv 2007

  45. [45]

    Absence of gravitational contributions to the running Yang-Mills coupling,

    D. Ebert, J. Plefka, and A. Rodigast, “Absence of gravitational contributions to the running Yang-Mills coupling,”Phys. Lett. B660(2008) 579–582,arXiv:0710.1002 [hep-th]

    work page arXiv 2008

  46. [46]

    Gauge-Invariant Quantum Gravity Correc- tions to Gauge Couplings via Vilkovisky-DeWitt Method and Gravity Assisted Gauge Unification,

    H.-J. He, X.-F. Wang, and Z.-Z. Xianyu, “Gauge-Invariant Quantum Gravity Correc- tions to Gauge Couplings via Vilkovisky-DeWitt Method and Gravity Assisted Gauge Unification,”Phys. Rev. D83(2011) 125014,arXiv:1008.1839 [hep-th]

    work page arXiv 2011

  47. [47]

    Gravitational Contributions to Gauge Green’s Functions and Asymptotic Free Power-Law Running of Gauge Coupling,

    Y. Tang and Y.-L. Wu, “Gravitational Contributions to Gauge Green’s Functions and Asymptotic Free Power-Law Running of Gauge Coupling,”JHEP11(2011) 073, arXiv:1109.4001 [hep-ph]

    work page arXiv 2011

  48. [48]

    Ambi- guities in the gravitational correction of quantum electrodynamics running coupling,

    J. C. C. Felipe, L. A. Cabral, L. C. T. Brito, M. Sampaio, and M. C. Nemes, “Ambi- guities in the gravitational correction of quantum electrodynamics running coupling,” Mod. Phys. Lett. A28(2013) 1350078,arXiv:1205.6779 [hep-th]

    work page arXiv 2013

  49. [49]

    Charge Renormalization due to Graviton Loops,

    G. Narain and R. Anishetty, “Charge Renormalization due to Graviton Loops,”JHEP 07(2013) 106,arXiv:1211.5040 [hep-th]

    work page arXiv 2013

  50. [50]

    Running Couplings in Quantum Theory of Gravity Coupled with Gauge Fields,

    G. Narain and R. Anishetty, “Running Couplings in Quantum Theory of Gravity Coupled with Gauge Fields,”JHEP10(2013) 203,arXiv:1309.0473 [hep-th] 25

    work page arXiv 2013

  51. [51]

    Gravitational Corrections to Yukawa and phi**4 Inter- actions,

    A. Rodigast and T. Schuster, “Gravitational Corrections to Yukawa and phi**4 Inter- actions,”Phys. Rev. Lett.104(2010) 081301,arXiv:0908.2422 [hep-th]

    work page arXiv 2010

  52. [52]

    Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system,

    Y. Hamada and M. Yamada, “Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system,”JHEP08(2017) 070, arXiv:1703.09033 [hep-th]

    work page arXiv 2017

  53. [53]

    Yukawa interactions in Quantum Grav- ity,

    G. P. de Brito, M. Reichert, and M. Schiffer, “Yukawa interactions in Quantum Grav- ity,”arXiv:2510.09572 [hep-th]

    work page arXiv

  54. [54]

    Asymptotic safety of gravity and the Higgs boson mass,

    M. Shaposhnikov and C. Wetterich, “Asymptotic safety of gravity and the Higgs boson mass,”Phys. Lett. B683(2010) 196–200,arXiv:0912.0208 [hep-th]

    work page arXiv 2010

  55. [55]

    Quantum gravity fluctua- tions flatten the Planck-scale Higgs potential,

    A. Eichhorn, Y. Hamada, J. Lumma, and M. Yamada, “Quantum gravity fluctua- tions flatten the Planck-scale Higgs potential,”Phys. Rev. D97no. 8, (2018) 086004, arXiv:1712.00319 [hep-th]

    work page arXiv 2018

  56. [56]

    Asymptotic safety, the Higgs boson mass, and beyond the stan- dard model physics,

    J. H. Kwapisz, “Asymptotic safety, the Higgs boson mass, and beyond the stan- dard model physics,”Phys. Rev. D100no. 11, (2019) 115001,arXiv:1907.12521 [hep-ph]

    work page arXiv 2019

  57. [57]

    Towards a Higgs mass determination in asymp- totically safe gravity with a dark portal,

    A. Eichhorn, M. Pauly, and S. Ray, “Towards a Higgs mass determination in asymp- totically safe gravity with a dark portal,”JHEP10(2021) 100,arXiv:2107.07949 [hep-ph]

    work page arXiv 2021

  58. [58]

    Top mass from asymptotic safety,

    A. Eichhorn and A. Held, “Top mass from asymptotic safety,”Phys. Lett. B777 (2018) 217–221,arXiv:1707.01107 [hep-th]

    work page arXiv 2018

  59. [59]

    Mass difference for charged quarks from asymptotically safe quantum gravity,

    A. Eichhorn and A. Held, “Mass difference for charged quarks from asymptotically safe quantum gravity,”Phys. Rev. Lett.121no. 15, (2018) 151302,arXiv:1803.04027 [hep-th]

    work page arXiv 2018

  60. [60]

    Quark masses and mixings in minimally parameterized UV completions of the Standard Model,

    R. Alkofer, A. Eichhorn, A. Held, C. M. Nieto, R. Percacci, and M. Schr¨ ofl, “Quark masses and mixings in minimally parameterized UV completions of the Standard Model,”Annals Phys.421(2020) 168282,arXiv:2003.08401 [hep-ph]

    work page arXiv 2020

  61. [61]

    Naturally small Yukawa couplings from trans-Planckian asymptotic safety,

    K. Kowalska, S. Pramanick, and E. M. Sessolo, “Naturally small Yukawa couplings from trans-Planckian asymptotic safety,”JHEP08(2022) 262,arXiv:2204.00866 [hep-ph]

    work page arXiv 2022

  62. [62]

    Quark and lepton mixing in the asymp- totically safe Standard Model,

    A. Eichhorn, Z. Gyftopoulos, and A. Held, “Quark and lepton mixing in the asymp- totically safe Standard Model,”arXiv:2507.18304 [hep-ph]

    work page arXiv

  63. [63]

    Asymptotic safety and Confor- mal Standard Model,

    F. Grabowski, J. H. Kwapisz, and K. A. Meissner, “Asymptotic safety and Confor- mal Standard Model,”Phys. Rev. D99no. 11, (2019) 115029,arXiv:1810.08461 [hep-ph]

    work page arXiv 2019

  64. [64]

    Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures,

    A. Chikkaballi, K. Kowalska, and E. M. Sessolo, “Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures,”JHEP11(2023) 224, arXiv:2308.06114 [hep-ph] 26

    work page arXiv 2023

  65. [65]

    Neutrino mass gen- eration in asymptotically safe gravity,

    G. P. de Brito, A. Eichhorn, A. D. Pereira, and M. Yamada, “Neutrino mass gen- eration in asymptotically safe gravity,”Phys. Rev. D112no. 6, (2025) 066004, arXiv:2505.01422 [hep-ph]

    work page arXiv 2025

  66. [66]

    Flavor anomalies from asymptotically safe gravity,

    K. Kowalska, E. M. Sessolo, and Y. Yamamoto, “Flavor anomalies from asymptotically safe gravity,”Eur. Phys. J. C81no. 4, (2021) 272,arXiv:2007.03567 [hep-ph]

    work page arXiv 2021

  67. [67]

    Constraints on Z’ solutions to the flavor anomalies with trans-Planckian asymptotic safety,

    A. Chikkaballi, W. Kotlarski, K. Kowalska, D. Rizzo, and E. M. Sessolo, “Constraints on Z’ solutions to the flavor anomalies with trans-Planckian asymptotic safety,”JHEP 01(2023) 164,arXiv:2209.07971 [hep-ph]

    work page arXiv 2023

  68. [68]

    Minimal models for g-2 and dark matter confront asymptotic safety,

    K. Kowalska and E. M. Sessolo, “Minimal models for g-2 and dark matter confront asymptotic safety,”Phys. Rev. D103no. 11, (2021) 115032,arXiv:2012.15200 [hep-ph]

    work page arXiv 2021

  69. [69]

    Asymptotic safety and gauged baryon number,

    J. Boos, C. D. Carone, N. L. Donald, and M. R. Musser, “Asymptotic safety and gauged baryon number,”Phys. Rev. D106no. 3, (2022) 035015,arXiv:2206.02686 [hep-ph]

    work page arXiv 2022

  70. [70]

    Asymptotically safe dark matter with gauged baryon number,

    J. Boos, C. D. Carone, N. L. Donald, and M. R. Musser, “Asymptotically safe dark matter with gauged baryon number,”Phys. Rev. D107no. 3, (2023) 035018, arXiv:2209.14268 [hep-ph]

    work page arXiv 2023

  71. [71]

    Stabilizing dark matter with quantum scale symmetry,

    A. Chikkaballi, K. Kowalska, R. R. Lino dos Santos, and E. M. Sessolo, “Stabilizing dark matter with quantum scale symmetry,”Phys. Rev. D112no. 11, (2025) 115024, arXiv:2505.02803 [hep-ph]

    work page arXiv 2025

  72. [72]

    A Symmetry preserving cutoff regularization,

    M. Oleszczuk, “A Symmetry preserving cutoff regularization,”Z. Phys. C64(1994) 533–538

    work page 1994

  73. [73]

    The Heat kernel and the average effective potential,

    R. Floreanini and R. Percacci, “The Heat kernel and the average effective potential,” Phys. Lett. B356(1995) 205–210,arXiv:hep-th/9505172

    work page arXiv 1995

  74. [74]

    On connection between momentum cutoff and the proper time regulariza- tions,

    S.-B. Liao, “On connection between momentum cutoff and the proper time regulariza- tions,”Phys. Rev. D53(1996) 2020–2036,arXiv:hep-th/9501124

    work page arXiv 1996

  75. [75]

    Renormalization group flow equations and the phase transition in O(N) models,

    O. Bohr, B. J. Schaefer, and J. Wambach, “Renormalization group flow equations and the phase transition in O(N) models,”Int. J. Mod. Phys. A16(2001) 3823–3852, arXiv:hep-ph/0007098

    work page arXiv 2001

  76. [76]

    Exact RG Flow Equations and Quantum Gravity,

    S. P. de Alwis, “Exact RG Flow Equations and Quantum Gravity,”JHEP03(2018) 118,arXiv:1707.09298 [hep-th]

    work page arXiv 2018

  77. [77]

    On Exact Proper Time Wilso- nian RG Flows,

    A. Bonanno, S. Lippoldt, R. Percacci, and G. P. Vacca, “On Exact Proper Time Wilso- nian RG Flows,”Eur. Phys. J. C80no. 3, (2020) 249,arXiv:1912.08135 [hep-th]

    work page arXiv 2020

  78. [78]

    Simplified functional flow equation,

    C. Wetterich, “Simplified functional flow equation,”Phys. Lett. B864(2025) 139435, arXiv:2403.17523 [hep-th] 27

    work page arXiv 2025

  79. [79]

    Spontaneous symmetry breaking and proper time flow equations,

    A. Bonanno and G. Lacagnina, “Spontaneous symmetry breaking and proper time flow equations,”Nucl. Phys. B693(2004) 36–50,arXiv:hep-th/0403176

    work page arXiv 2004

  80. [80]

    Towards an accurate determination of the critical ex- ponents with the renormalization group flow equations,

    A. Bonanno and D. Zappala, “Towards an accurate determination of the critical ex- ponents with the renormalization group flow equations,”Phys. Lett. B504(2001) 181–187,arXiv:hep-th/0010095

    work page arXiv 2001

Showing first 80 references.