pith. machine review for the scientific record. sign in

arxiv: 2605.03580 · v1 · submitted 2026-05-05 · ✦ hep-ph

Recognition: unknown

Non-Markovian Electroweak Baryogenesis: Memory Effects on CP-Violating Transport and Gravitational Waves

Arnab Chaudhuri
Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:41 UTC · model grok-4.3

classification ✦ hep-ph
keywords electroweak baryogenesisnon-Markovian transportmemory effectsCP violationbubble wall velocitybaryon asymmetrygravitational wavesKadanoff-Baym hierarchy
0
0 comments X

The pith

Non-Markovian memory effects shift the optimal bubble wall velocity lower and create non-monotonic baryon asymmetry dependence that Markovian models cannot match.

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

The paper extends electroweak baryogenesis to include non-Markovian dynamics when the relaxation time of CP-violating mediators becomes comparable to the time for a bubble wall to pass a given point. Transport equations then acquire memory kernels that correct both the CP-violating source term and the diffusion equations. These corrections move the velocity that maximizes the asymmetry to smaller values, shrink the range of parameters that can produce the observed baryon asymmetry, and generate a non-monotonic dependence on the memory timescale at sub-optimal velocities. The same framework also predicts that memory effects lengthen and strengthen the effective source for stochastic gravitational waves produced by the phase transition.

Core claim

Within the Schwinger-Keldysh real-time effective field theory and the Kadanoff-Baym hierarchy, when the relaxation time of CP-violating mediators becomes comparable to the bubble-wall crossing time, transport dynamics acquire temporal nonlocality. This produces memory-kernel corrections to the CP-violating source and diffusion equations beyond the Markovian approximation. The corrections shift the optimal wall velocity to smaller values, narrow the viable parameter space, and induce a characteristic non-monotonic dependence of the baryon asymmetry on the memory timescale for sub-optimal wall velocities that cannot be reproduced by a consistent Markovian reparameterisation.

What carries the argument

Memory-kernel corrections to the CP-violating source and diffusion equations, derived from the Kadanoff-Baym hierarchy when mediator relaxation times match bubble-wall crossing times.

If this is right

  • The optimal bubble-wall velocity shifts to smaller values.
  • The viable parameter space for generating the observed baryon asymmetry narrows.
  • Baryon asymmetry shows non-monotonic dependence on memory timescale for sub-optimal velocities.
  • Memory effects enhance the duration and amplitude of the effective source for gravitational-wave signals.

Where Pith is reading between the lines

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

  • Measurements of the baryon asymmetry could be used to place direct constraints on the memory timescale of CP-violating mediators.
  • Correlated observations from gravitational-wave detectors and collider searches for CP violation could jointly test whether the non-Markovian regime is realized.
  • Similar memory-kernel effects may appear in transport calculations for other cosmological phase transitions that involve comparable relaxation and crossing timescales.

Load-bearing premise

The relaxation time of CP-violating mediators is comparable to the bubble-wall crossing time so that non-Markovian memory effects become important in the transport dynamics.

What would settle it

A concrete model calculation that produces only monotonic dependence of the baryon asymmetry on the memory timescale, without the predicted non-monotonic feature at sub-optimal wall velocities, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.03580 by Arnab Chaudhuri.

Figure 1
Figure 1. Figure 1: FIG. 1: Constraints in the ( view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Non-Markovian CP-violating source view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Baryon asymmetry view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Baryon asymmetry view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Memory-induced shift of the optimal wall velocity view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Baryon asymmetry view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Baryon asymmetry view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Joint correlation between the baryon asymmetry view at source ↗
read the original abstract

We develop a non-Markovian extension of electroweak baryogenesis within the Schwinger--Keldysh real-time effective field theory framework and the Kadanoff--Baym hierarchy. When the relaxation time of CP-violating mediators becomes comparable to the bubble-wall crossing time, transport dynamics acquire temporal nonlocality, leading to memory-kernel corrections to the CP-violating source and diffusion equations beyond the Markovian approximation. These effects shift the optimal wall velocity to smaller values, narrow the viable parameter space, and induce a characteristic non-monotonic dependence of the baryon asymmetry on the memory timescale for sub-optimal wall velocities, which cannot be reproduced by a consistent Markovian reparameterisation. A systematic parameter analysis identifies regions compatible with the observed baryon asymmetry and constrains the allowed memory timescale from hydrodynamic stability and the physical range of the CP-violating phase. We also assess the correlated impact on the stochastic gravitational-wave signal, finding that memory effects can enhance the effective source duration and amplitude, although much of the viable parameter space remains below near-future detector sensitivities and theoretical uncertainties remain at the order-of-magnitude level. These results establish non-Markovian transport as a well-motivated extension of electroweak baryogenesis and introduce the memory timescale as a parameter testable through baryon asymmetry measurements, collider CP probes, and gravitational-wave observations.

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 manuscript develops a non-Markovian extension of electroweak baryogenesis within the Schwinger-Keldysh real-time effective field theory and Kadanoff-Baym hierarchy. When the relaxation time of CP-violating mediators is comparable to the bubble-wall crossing time, temporal nonlocality induces memory-kernel corrections to the CP-violating source and diffusion equations. These corrections shift the optimal wall velocity to smaller values, narrow the viable parameter space, produce a non-monotonic dependence of the baryon asymmetry on the memory timescale (unreproducible by Markovian reparameterization), and modify the stochastic gravitational-wave signal. A parameter scan constrains the memory timescale via hydrodynamic stability and the physical range of the CP-violating phase while matching the observed baryon asymmetry, with an assessment of GW detectability.

Significance. If the central results hold, the work would introduce the memory timescale as a new, testable parameter in electroweak baryogenesis, constrained by first-principles transport and observable quantities. The systematic exploration of non-Markovian effects, their correlation with gravitational-wave amplitude and duration, and the identification of regions compatible with the baryon asymmetry constitute a clear advance over standard Markovian treatments. The paper ships a concrete, falsifiable signature (non-monotonic baryon asymmetry vs. memory timescale) that could be probed by collider CP measurements and future GW observatories, although GW predictions remain at order-of-magnitude level.

major comments (2)
  1. [§4.1] §4.1 (Kadanoff-Baym hierarchy truncation): the derivation of the memory kernel assumes the quasi-particle and gradient expansions remain controlled when the mediator relaxation time τ_rel becomes comparable to the wall transit time τ_wall. No explicit error estimate, convergence test, or higher-order term assessment is supplied for this marginal regime, which is precisely the regime in which the claimed shifts in wall velocity and non-monotonic baryon asymmetry are generated. This truncation directly underpins the reliability of the numerical results for the asymmetry and GW spectrum.
  2. [§5.3] §5.3 (numerical results): the non-monotonic dependence of the baryon asymmetry on the memory timescale is asserted to be a distinctive non-Markovian signature. However, the manuscript does not present a side-by-side comparison against a Markovian model whose parameters have been re-tuned to reproduce the same integrated source strength, leaving open whether the non-monotonicity is an artifact of the particular truncation or a genuine physical effect.
minor comments (2)
  1. [Abstract] The abstract states that 'theoretical uncertainties remain at the order-of-magnitude level' for the GW signal, yet no quantitative breakdown of these uncertainties (e.g., variation with wall velocity or memory timescale) appears in the text or figures.
  2. [Figures 4-6] Figure captions and axis labels for the baryon asymmetry and GW spectra should explicitly indicate the range of memory timescales scanned and the hydrodynamic stability cut applied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment point by point below, providing clarifications and indicating the revisions we will implement to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§4.1] §4.1 (Kadanoff-Baym hierarchy truncation): the derivation of the memory kernel assumes the quasi-particle and gradient expansions remain controlled when the mediator relaxation time τ_rel becomes comparable to the wall transit time τ_wall. No explicit error estimate, convergence test, or higher-order term assessment is supplied for this marginal regime, which is precisely the regime in which the claimed shifts in wall velocity and non-monotonic baryon asymmetry are generated. This truncation directly underpins the reliability of the numerical results for the asymmetry and GW spectrum.

    Authors: We acknowledge that an explicit error estimate for the quasi-particle and gradient expansions in the regime τ_rel ≈ τ_wall would strengthen the presentation. The manuscript relies on the standard validity conditions of the Kadanoff-Baym hierarchy, where the memory kernel arises as a controlled correction when the relaxation time is comparable to the wall transit time. To address the concern directly, we will revise §4.1 to include a quantitative estimate of higher-order terms, scaling with powers of the ratio τ_rel/τ_wall, together with a numerical convergence test obtained by varying the truncation order. This addition will confirm that the reported shifts in wall velocity and the non-monotonic baryon asymmetry remain robust within the controlled regime. revision: yes

  2. Referee: [§5.3] §5.3 (numerical results): the non-monotonic dependence of the baryon asymmetry on the memory timescale is asserted to be a distinctive non-Markovian signature. However, the manuscript does not present a side-by-side comparison against a Markovian model whose parameters have been re-tuned to reproduce the same integrated source strength, leaving open whether the non-monotonicity is an artifact of the particular truncation or a genuine physical effect.

    Authors: The non-monotonic dependence originates from the nonlocal temporal structure of the memory kernel, which cannot be reproduced by any local Markovian source term even after re-tuning its integrated strength. The manuscript already states that the feature is absent under consistent Markovian reparameterization. To make the distinction explicit, we will add in the revised §5.3 a direct side-by-side comparison: the baryon asymmetry versus memory timescale (or wall velocity) for the non-Markovian case is contrasted with a Markovian model whose CP-violating source is adjusted to match the same integrated strength. This comparison will demonstrate that the non-monotonicity is absent in the re-tuned Markovian case, confirming it as a genuine physical signature of temporal nonlocality. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation introduces memory timescale as independent parameter and constrains it externally

full rationale

The paper's central derivation starts from the Schwinger-Keldysh real-time EFT and Kadanoff-Baym hierarchy (standard frameworks), derives memory-kernel corrections when relaxation time approaches wall-crossing time, and treats the memory timescale as a new free parameter. This parameter is then bounded by hydrodynamic stability and the physical range of the CP-violating phase while the baryon asymmetry is required to match the observed value; the resulting shifts in wall velocity, parameter space, and non-monotonic dependence are computed outputs rather than inputs. No self-citation is invoked to justify the truncation or kernel form, no fitted quantity is relabeled as a prediction, and no ansatz is smuggled via prior work by the same author. The chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the Schwinger-Keldysh and Kadanoff-Baym framework for non-Markovian transport and on the physical comparability of relaxation and wall-crossing timescales; the memory timescale itself functions as a new free parameter.

free parameters (1)
  • memory timescale
    New parameter introduced to quantify non-Markovian effects and constrained by hydrodynamic stability and CP-violating phase range.
axioms (1)
  • domain assumption Schwinger-Keldysh real-time effective field theory and Kadanoff-Baym hierarchy correctly describe CP-violating transport when relaxation time is comparable to bubble-wall crossing time
    Invoked to derive the memory-kernel corrections beyond the Markovian approximation.

pith-pipeline@v0.9.0 · 5542 in / 1652 out tokens · 54929 ms · 2026-05-07T15:41:22.496411+00:00 · methodology

Review history (2 revisions) →

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

90 extracted references · 83 canonical work pages · 2 internal anchors

  1. [1]

    a shift of the peak positionv ∗,NM w toward smaller values, which can bring the peak closer to or further from the chosenv w depending on the initial position

  2. [2]

    The competition between these two effects leads to three qualitatively distinct regimes, which we now analyse in turn

    an overall suppression of the source amplitude by (1 + Γ 0τmem)−1, which reducesY B regardless of the peak alignment. The competition between these two effects leads to three qualitatively distinct regimes, which we now analyse in turn. Sub-peak regime (vw < v ∗ w) In the Markovian limitτ mem →0, the chosenv w liesbelowthe peak positionv ∗ w =L wΓ0, i.e. ...

  3. [2]

    The competition between these two effects leads to three qualitatively distinct regimes, which we now analyse in turn

    an overall suppression of the source amplitude by (1 + Γ 0τmem)−1, which reducesY B regardless of the peak alignment. The competition between these two effects leads to three qualitatively distinct regimes, which we now analyse in turn. Sub-peak regime (vw < v ∗ w) In the Markovian limitτ mem →0, the chosenv w liesbelowthe peak positionv ∗ w =L wΓ0, i.e. ...

  4. [3]

    Increasingτ mem suppresses Γeff and henceS NM CP , reducingY B at fixedv w through the factor (1+Γ0τmem)−1 acting on the source (Eq. (43)). At the benchmarkv w = 0.1> v ∗ w, this suppression is monotonic and uncompensated

  5. [4]

    (81)–(82), amplifying Ω GW by the factor in Eq

    Simultaneously, increasingϵ mem = Γ0τmem enhancesβ −1 mem andκ mem v through Eqs. (81)–(82), amplifying Ω GW by the factor in Eq. (86). These effects operate in opposite directions in the (Y B,Ω GW) plane, producing the anti-correlation visible in Fig. 8: points with largerτ mem (yellow/orange in the colour scale) have lowerYB and higher ΩGW, while smalle...

  6. [5]

    is maximised at Γ 0 =v w/Lw and is monotonically decreasing for Γ 0 > v w/Lw. Any attempt to mimic the non-Markovianτ mem dependence by varying Γ 0 →Γ eff(τmem) would require Γ 0 toincreaseat smallτ mem (to move the Markovian peak towardv w) and thendecreaseat largeτ mem. But Γ 0 is a fixed physical quantity set by the model parameters; it cannot vary wit...

  7. [5]

    is maximised at Γ 0 =v w/Lw and is monotonically decreasing for Γ 0 > v w/Lw. Any attempt to mimic the non-Markovianτ mem dependence by varying Γ 0 →Γ eff(τmem) would require Γ 0 toincreaseat smallτ mem (to move the Markovian peak towardv w) and thendecreaseat largeτ mem. But Γ 0 is a fixed physical quantity set by the model parameters; it cannot vary wit...

  8. [6]

    V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B155(1985), 36 doi:10.1016/0370-2693(85)91028-7

    work page doi:10.1016/0370-2693(85)91028-7 1985

  9. [7]

    P. B. Arnold and L. D. McLerran, Phys. Rev. D36(1987), 581 doi:10.1103/PhysRevD.36.581

    work page doi:10.1103/physrevd.36.581 1987

  10. [8]

    V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk166(1996), 493-537 doi:10.1070/PU1996v039n05ABEH000145 [arXiv:hep-ph/9603208 [hep-ph]]

    work page doi:10.1070/pu1996v039n05abeh000145 1996

  11. [9]

    Trodden, Rev

    M. Trodden, Rev. Mod. Phys.71(1999), 1463-1500 doi:10.1103/RevModPhys.71.1463 [arXiv:hep-ph/9803479 [hep-ph]]

    work page doi:10.1103/revmodphys.71.1463 1999

  12. [10]

    D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys.14(2012), 125003 doi:10.1088/1367-2630/14/12/125003 [arXiv:1206.2942 [hep-ph]]

    work page doi:10.1088/1367-2630/14/12/125003 2012

  13. [11]

    G. A. White, Morgan & Claypool, 2016, ISBN 978-1-68174-456-8, 978-1-68174-457-5 doi:10.1088/978-1-6817-4457-5 32

    work page doi:10.1088/978-1-6817-4457-5 2016

  14. [12]

    A. D. Sakharov, Pisma Zh. Eksp. Teor. Fiz.5(1967), 32-35 doi:10.1070/PU1991v034n05ABEH002497

    work page doi:10.1070/pu1991v034n05abeh002497 1967

  15. [13]

    A. G. Cohen, D. B. Kaplan and A. E. Nelson, Ann. Rev. Nucl. Part. Sci.43(1993), 27-70 doi:10.1146/annurev.ns.43.120193.000331 [arXiv:hep-ph/9302210 [hep-ph]]

    work page doi:10.1146/annurev.ns.43.120193.000331 1993

  16. [14]

    Finite temperature field theory and phase transitions

    M. Quiros, [arXiv:hep-ph/9901312 [hep-ph]]

    work page internal anchor Pith review arXiv

  17. [15]

    Carena, M

    M. Carena, M. Quiros, M. Seco and C. E. M. Wagner, Nucl. Phys. B650(2003), 24-42 doi:10.1016/S0550-3213(02)01065-9 [arXiv:hep-ph/0208043 [hep-ph]]

    work page doi:10.1016/s0550-3213(02)01065-9 2003

  18. [16]

    Prokopec, M

    T. Prokopec, M. G. Schmidt and S. Weinstock, Annals Phys.314(2004), 208-265 doi:10.1016/j.aop.2004.06.002 [arXiv:hep- ph/0312110 [hep-ph]]

    work page doi:10.1016/j.aop.2004.06.002 2004

  19. [17]

    Konstandin, T

    T. Konstandin, T. Prokopec and M. G. Schmidt, Nucl. Phys. B716(2005), 373-400 doi:10.1016/j.nuclphysb.2005.03.013 [arXiv:hep-ph/0410135 [hep-ph]]

    work page doi:10.1016/j.nuclphysb.2005.03.013 2005

  20. [18]

    G. W. Anderson and L. J. Hall, Phys. Rev. D45(1992), 2685-2698 doi:10.1103/PhysRevD.45.2685

    work page doi:10.1103/physrevd.45.2685 1992

  21. [19]

    A. E. Nelson, D. B. Kaplan and A. G. Cohen, Nucl. Phys. B373(1992), 453-478 doi:10.1016/0550-3213(92)90440-M

    work page doi:10.1016/0550-3213(92)90440-m 1992

  22. [20]

    Huet and A

    P. Huet and A. E. Nelson, Phys. Rev. D53(1996), 4578-4597 doi:10.1103/PhysRevD.53.4578 [arXiv:hep-ph/9506477 [hep-ph]]

    work page doi:10.1103/physrevd.53.4578 1996

  23. [21]

    Joyce, T

    M. Joyce, T. Prokopec and N. Turok, Phys. Rev. D53(1996), 2958-2980 doi:10.1103/PhysRevD.53.2958 [arXiv:hep- ph/9410282 [hep-ph]]

    work page doi:10.1103/physrevd.53.2958 1996

  24. [22]

    J. M. Cline, M. Joyce and K. Kainulainen, JHEP07(2000), 018 doi:10.1088/1126-6708/2000/07/018 [arXiv:hep- ph/0006119 [hep-ph]]

    work page doi:10.1088/1126-6708/2000/07/018 2000

  25. [23]

    J. M. Cline, A. Friedlander, D. M. He, K. Kainulainen, B. Laurent and D. Tucker-Smith, Phys. Rev. D103(2021) no.12, 123529 doi:10.1103/PhysRevD.103.123529 [arXiv:2102.12490 [hep-ph]]

    work page doi:10.1103/physrevd.103.123529 2021

  26. [24]

    J. M. Cline, M. Joyce and K. Kainulainen, [arXiv:hep-ph/0110031 [hep-ph]]

    work page internal anchor Pith review arXiv

  27. [25]

    Kainulainen, JCAP11(2021) no.11, 042 doi:10.1088/1475-7516/2021/11/042 [arXiv:2108.08336 [hep-ph]]

    K. Kainulainen, JCAP11(2021) no.11, 042 doi:10.1088/1475-7516/2021/11/042 [arXiv:2108.08336 [hep-ph]]

    work page doi:10.1088/1475-7516/2021/11/042 2021

  28. [26]

    Laurent and J

    B. Laurent and J. M. Cline, Phys. Rev. D106(2022) no.2, 023501 doi:10.1103/PhysRevD.106.023501 [arXiv:2204.13120 [hep-ph]]

    work page doi:10.1103/physrevd.106.023501 2022

  29. [27]

    Carena, G

    M. Carena, G. Nardini, M. Quiros and C. E. M. Wagner, Nucl. Phys. B812(2009), 243-263 doi:10.1016/j.nuclphysb.2008.12.014 [arXiv:0809.3760 [hep-ph]]

    work page doi:10.1016/j.nuclphysb.2008.12.014 2009

  30. [28]

    J. M. Cline and K. Kainulainen, JCAP01(2013), 012 doi:10.1088/1475-7516/2013/01/012 [arXiv:1210.4196 [hep-ph]]

    work page doi:10.1088/1475-7516/2013/01/012 2013

  31. [29]

    Postma and J

    M. Postma and J. van de Vis, JHEP02(2020), 090 doi:10.1007/JHEP02(2020)090 [arXiv:1910.11794 [hep-ph]]

    work page doi:10.1007/jhep02(2020)090 2020

  32. [30]

    J. R. Espinosa, T. Konstandin, J. M. No and G. Servant, JCAP06(2010), 028 doi:10.1088/1475-7516/2010/06/028 [arXiv:1004.4187 [hep-ph]]

    work page doi:10.1088/1475-7516/2010/06/028 2010

  33. [31]

    Fromme, S

    L. Fromme, S. J. Huber and M. Seniuch, JHEP11(2006), 038 doi:10.1088/1126-6708/2006/11/038 [arXiv:hep-ph/0605242 [hep-ph]]

    work page doi:10.1088/1126-6708/2006/11/038 2006

  34. [32]

    Chaudhuri, [arXiv:2509.22293 [hep-ph]]

    A. Chaudhuri, [arXiv:2509.22293 [hep-ph]]

    work page arXiv

  35. [33]

    J. S. Schwinger, J. Math. Phys.2(1961), 407-432 doi:10.1063/1.1703727

    work page doi:10.1063/1.1703727 1961

  36. [34]

    L. V. Keldysh, Sov. Phys. JETP20(1965), 1018-1026 doi:10.1142/9789811279461 0007

    work page doi:10.1142/9789811279461 1965

  37. [35]

    Calzetta, B

    E. Calzetta and B. L. Hu, Phys. Rev. D37(1988), 2878 doi:10.1103/PhysRevD.37.2878

    work page doi:10.1103/physrevd.37.2878 1988

  38. [36]

    Berges, AIP Conf

    J. Berges, AIP Conf. Proc.739(2004) no.1, 3-62 doi:10.1063/1.1843591 [arXiv:hep-ph/0409233 [hep-ph]]

    work page doi:10.1063/1.1843591 2004

  39. [37]

    Danielewicz, Annals Phys.152(1984), 239-304 doi:10.1016/0003-4916(84)90092-7

    P. Danielewicz, Annals Phys.152(1984), 239-304 doi:10.1016/0003-4916(84)90092-7

    work page doi:10.1016/0003-4916(84)90092-7 1984

  40. [38]

    E. P. Wigner, Phys. Rev.40(1932), 749-760 doi:10.1103/PhysRev.40.749

    work page doi:10.1103/physrev.40.749 1932

  41. [39]

    J. E. Moyal, Proc. Cambridge Phil. Soc.45(1949), 99-124 doi:10.1017/S0305004100000487

    work page doi:10.1017/s0305004100000487 1949

  42. [40]

    Planck 2018 Results

    N. Aghanimet al.[Planck], Astron. Astrophys.641(2020), A6 [erratum: Astron. Astrophys.652(2021), C4] doi:10.1051/0004-6361/201833910 [arXiv:1807.06209 [astro-ph.CO]]

    work page doi:10.1051/0004-6361/201833910 2020

  43. [41]

    Caprini, M

    C. Caprini, M. Hindmarsh, S. Huber, T. Konstandin, J. Kozaczuk, G. Nardini, J. M. No, A. Petiteau, P. Schwaller and G. Servant,et al.JCAP04(2016), 001 doi:10.1088/1475-7516/2016/04/001 [arXiv:1512.06239 [astro-ph.CO]]

    work page doi:10.1088/1475-7516/2016/04/001 2016

  44. [42]

    Caprini, et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, JCAP 03 (2020) 024.arXiv:1910.13125,doi:10.1088/1475-7516/2020/03/024

    C. Caprini, M. Chala, G. C. Dorsch, M. Hindmarsh, S. J. Huber, T. Konstandin, J. Kozaczuk, G. Nardini, J. M. No and K. Rummukainen,et al.JCAP03(2020), 024 doi:10.1088/1475-7516/2020/03/024 [arXiv:1910.13125 [astro-ph.CO]]

    work page doi:10.1088/1475-7516/2020/03/024 2020

  45. [43]

    Grojean and G

    C. Grojean and G. Servant, Phys. Rev. D75(2007), 043507 doi:10.1103/PhysRevD.75.043507 [arXiv:hep-ph/0607107 [hep-ph]]

    work page doi:10.1103/physrevd.75.043507 2007

  46. [44]

    , keywords =

    M. Hindmarsh, S. J. Huber, K. Rummukainen and D. J. Weir, Phys. Rev. D92(2015) no.12, 123009 doi:10.1103/PhysRevD.92.123009 [arXiv:1504.03291 [astro-ph.CO]]

    work page doi:10.1103/physrevd.92.123009 2015

  47. [45]

    J. R. Espinosa, Nucl. Phys. B475(1996), 273-292 doi:10.1016/0550-3213(96)00297-0 [arXiv:hep-ph/9604320 [hep-ph]]

    work page doi:10.1016/0550-3213(96)00297-0 1996

  48. [46]

    J. R. Espinosa and M. Quiros, Phys. Rev. D76(2007), 076004 doi:10.1103/PhysRevD.76.076004 [arXiv:hep-ph/0701145 [hep-ph]]

    work page doi:10.1103/physrevd.76.076004 2007

  49. [47]

    Curtin, P

    D. Curtin, P. Meade and C. T. Yu, JHEP11(2014), 127 doi:10.1007/JHEP11(2014)127 [arXiv:1409.0005 [hep-ph]]

    work page doi:10.1007/jhep11(2014)127 2014

  50. [48]

    Kurup and M

    G. Kurup and M. Perelstein, Phys. Rev. D96(2017) no.1, 015036 doi:10.1103/PhysRevD.96.015036 [arXiv:1704.03381 [hep-ph]]

    work page doi:10.1103/physrevd.96.015036 2017

  51. [49]

    Chaudhuri and K

    A. Chaudhuri and K. Kohri, Nucl. Phys. B1018(2025), 117098 doi:10.1016/j.nuclphysb.2025.117098 [arXiv:2404.10288 [hep-ph]]

    work page doi:10.1016/j.nuclphysb.2025.117098 2025

  52. [50]

    Chaudhuri, Nucl

    A. Chaudhuri, Nucl. Phys. B1024(2026), 117357 doi:10.1016/j.nuclphysb.2026.117357 [arXiv:2507.13135 [astro-ph.CO]]

    work page doi:10.1016/j.nuclphysb.2026.117357 2026

  53. [51]

    Aadet al.[ATLAS], Eur

    G. Aadet al.[ATLAS], Eur. Phys. J. C83(2023) no.9, 774 doi:10.1140/epjc/s10052-023-11873-5 [arXiv:2301.06822 [hep- ex]]

    work page doi:10.1140/epjc/s10052-023-11873-5 2023

  54. [52]

    Carniani, K

    A. Tumasyanet al.[CMS], Nature607(2022) no.7917, 60-68 [erratum: Nature623(2023) no.7985, E4] doi:10.1038/s41586- 022-04892-x [arXiv:2207.00043 [hep-ex]]. 33

    work page doi:10.1038/s41586- 2022

  55. [53]

    Search for the Standard Model Higgs boson at LEP

    R. Barateet al.[LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3 and OPAL], Phys. Lett. B565 (2003), 61-75 doi:10.1016/S0370-2693(03)00614-2 [arXiv:hep-ex/0306033 [hep-ex]]

    work page doi:10.1016/s0370-2693(03)00614-2 2003

  56. [54]

    G. D. Moore and T. Prokopec, Phys. Rev. Lett.75(1995), 777-780 doi:10.1103/PhysRevLett.75.777 [arXiv:hep-ph/9503296 [hep-ph]]

    work page doi:10.1103/physrevlett.75.777 1995

  57. [55]

    John and M

    P. John and M. G. Schmidt, Nucl. Phys. B598(2001), 291-305 [erratum: Nucl. Phys. B648(2003), 449-452] doi:10.1016/S0550-3213(00)00768-9 [arXiv:hep-ph/0002050 [hep-ph]]

    work page doi:10.1016/s0550-3213(00)00768-9 2001

  58. [56]

    H. A. Weldon, Phys. Rev. D28(1983), 2007 doi:10.1103/PhysRevD.28.2007

    work page doi:10.1103/physrevd.28.2007 1983

  59. [57]

    P. B. Arnold, G. D. Moore and L. G. Yaffe, JHEP01(2003), 030 doi:10.1088/1126-6708/2003/01/030 [arXiv:hep- ph/0209353 [hep-ph]]

    work page doi:10.1088/1126-6708/2003/01/030 2003

  60. [58]

    Ghiglieri, O

    J. Ghiglieri, O. Kaczmarek, M. Laine and F. Meyer, Phys. Rev. D94(2016) no.1, 016005 doi:10.1103/PhysRevD.94.016005 [arXiv:1604.07544 [hep-lat]]

    work page doi:10.1103/physrevd.94.016005 2016

  61. [59]

    J. P. Blaizot and E. Iancu, Phys. Rept.359(2002), 355-528 doi:10.1016/S0370-1573(01)00061-8 [arXiv:hep-ph/0101103 [hep-ph]]

    work page doi:10.1016/s0370-1573(01)00061-8 2002

  62. [60]

    G. D. Moore, Phys. Rev. D62(2000), 085011 doi:10.1103/PhysRevD.62.085011 [arXiv:hep-ph/0001216 [hep-ph]]

    work page doi:10.1103/physrevd.62.085011 2000

  63. [61]

    P. B. Arnold, G. D. Moore and L. G. Yaffe, JHEP11(2000), 001 doi:10.1088/1126-6708/2000/11/001 [arXiv:hep- ph/0010177 [hep-ph]]

    work page doi:10.1088/1126-6708/2000/11/001 2000

  64. [62]

    G. D. Moore, C. r. Hu and B. Muller, Phys. Rev. D58(1998), 045001 doi:10.1103/PhysRevD.58.045001 [arXiv:hep- ph/9710436 [hep-ph]]

    work page doi:10.1103/physrevd.58.045001 1998

  65. [63]

    D’Onofrio, K

    M. D’Onofrio, K. Rummukainen and A. Tranberg, Phys. Rev. Lett.113(2014) no.14, 141602 doi:10.1103/PhysRevLett.113.141602 [arXiv:1404.3565 [hep-ph]]

    work page doi:10.1103/physrevlett.113.141602 2014

  66. [64]

    P. B. Arnold, D. Son and L. G. Yaffe, Phys. Rev. D55(1997), 6264-6273 doi:10.1103/PhysRevD.55.6264 [arXiv:hep- ph/9609481 [hep-ph]]

    work page doi:10.1103/physrevd.55.6264 1997

  67. [65]

    E. W. Kolb and M. S. Turner, Front. Phys.69(1990), 1-547 Taylor and Francis, 2019, ISBN 978-0-429-49286-0, 978-0- 201-62674-2 doi:10.1201/9780429492860

    work page doi:10.1201/9780429492860 1990

  68. [66]

    Engel, M

    J. Engel, M. J. Ramsey-Musolf and U. van Kolck, Prog. Part. Nucl. Phys.71(2013), 21-74 doi:10.1016/j.ppnp.2013.03.003 [arXiv:1303.2371 [nucl-th]]

    work page doi:10.1016/j.ppnp.2013.03.003 2013

  69. [67]

    & Reece, M

    C. Cesarotti, Q. Lu, Y. Nakai, A. Parikh and M. Reece, JHEP05(2019), 059 doi:10.1007/JHEP05(2019)059 [arXiv:1810.07736 [hep-ph]]

    work page doi:10.1007/jhep05(2019)059 2019

  70. [68]

    Andreevet al.Improved limit on the electric dipole moment of the electron.Nature562, 355–360, DOI: 10.1038/s41586-018-0599-8 (2018)

    V. Andreevet al.[ACME], Nature562(2018) no.7727, 355-360 doi:10.1038/s41586-018-0599-8

    work page doi:10.1038/s41586-018-0599-8 2018

  71. [69]

    Fuchs, M

    E. Fuchs, M. Losada, Y. Nir and Y. Viernik, JHEP05(2020), 056 doi:10.1007/JHEP05(2020)056 [arXiv:2003.00099 [hep-ph]]

    work page doi:10.1007/jhep05(2020)056 2020

  72. [70]

    Chaudhuri and J

    A. Chaudhuri and J. Das, Phys. Rev. D106(2022) no.9, 095016 doi:10.1103/PhysRevD.106.095016 [arXiv:2206.08699 [hep-ph]]

    work page doi:10.1103/physrevd.106.095016 2022

  73. [71]

    Srivastava, J

    T. Srivastava, J. Das, A. Ghosh and A. Chaudhuri, JCAP02(2026), 032 doi:10.1088/1475-7516/2026/02/032 [arXiv:2507.05917 [hep-ph]]

    work page doi:10.1088/1475-7516/2026/02/032 2026

  74. [72]

    Chaudhuri, P

    A. Chaudhuri, P. Mishra and R. Mohanta, [arXiv:2508.09835 [hep-ph]]

    work page arXiv

  75. [73]

    Chaudhuri, [arXiv:2602.20760 [hep-ph]]

    A. Chaudhuri, [arXiv:2602.20760 [hep-ph]]

    work page arXiv

  76. [74]

    J. Das, S. Niyogi and T. Srivastava, [arXiv:2601.13147 [hep-ph]]

    work page arXiv

  77. [75]

    Athron, C

    P. Athron, C. Bal´ azs, A. Fowlie, L. Morris and L. Wu, Prog. Part. Nucl. Phys.135(2024), 104094 doi:10.1016/j.ppnp.2023.104094 [arXiv:2305.02357 [hep-ph]]

    work page doi:10.1016/j.ppnp.2023.104094 2024

  78. [76]

    Borah, P

    P. Borah, P. Ghosh, S. Roy and A. K. Saha, JHEP08(2023), 029 doi:10.1007/JHEP08(2023)029 [arXiv:2301.05061 [hep-ph]]

    work page doi:10.1007/jhep08(2023)029 2023

  79. [77]

    Hindmarsh, S

    M. Hindmarsh, S. J. Huber, K. Rummukainen and D. J. Weir, Phys. Rev. D96(2017) no.10, 103520 [erratum: Phys. Rev. D101(2020) no.8, 089902] doi:10.1103/PhysRevD.96.103520 [arXiv:1704.05871 [astro-ph.CO]]

    work page doi:10.1103/physrevd.96.103520 2017

  80. [78]

    , keywords =

    C. Caprini, R. Durrer and G. Servant, JCAP12(2009), 024 doi:10.1088/1475-7516/2009/12/024 [arXiv:0909.0622 [astro- ph.CO]]

    work page doi:10.1088/1475-7516/2009/12/024 2009

Showing first 80 references.