Yukawa and Tri-scalar Processes in Electroweak Baryogenesis

Christopher Lee; Michael J. Ramsey-Musolf; Sean Tulin; Vincenzo Cirigliano

REVIEW

Yukawa and Tri-scalar Processes in Electroweak Baryogenesis

Vincenzo Cirigliano, Christopher Lee, Michael J. Ramsey-Musolf, Sean Tulin

High Energy Physics - Phenomenology · Submitted 8 Mar 2006 · 37 references

Pith's verdict: New decay/inverse-decay Yukawa rates and the breakdown of the fast-ΓY approximation are real, but the 20–100% Y_B claims rest on an unclosed transport system and an untested supergauge assumption.

T0 · AI review

How this review was made: An AI referee (deepseek-v4-flash) read the paper on August 28, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 4 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/0603058 (version 2)

Pith IDHR2AQX4X, Pith's permanent record of this paper and its review

CitationChristopher Lee, Michael J. Ramsey-Musolf, Sean Tulin, Vincenzo Cirigliano. "Yukawa and Tri-scalar Processes in Electroweak Baryogenesis." arXiv:hep-ph/0603058 (2006). https://pith.science/paper/HR2AQX4X

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Two things to know. First, the paper earns its keep: it computes the O(alpha_s^0) decay and inverse-decay contributions to the Yukawa transport coefficient ΓY, shows they can exceed the O(alpha_s) scattering terms usually assumed to dominate, and gives a clear argument—backed by an analytic 1/ΓY expansion—that the fast-ΓY approximation breaks down. Second, the quantitative Y_B numbers (20–100% enhancement) rest on a transport system that is not closed, and the paper says so. That makes the numerical claims illustrative rather than final.

What is actually new: the building-block integrals IB and IF, the decay-rate expressions in Eq. (40), the new \tildeΓY term, and the identification in Appendix C of the missed O(1/ΓY) correction to the H density. The derivation from the CTP formalism is explicit and internally consistent; Fig. 4 supports the claim that decay rates dominate over scattering for realistic parameters. Credit where due: the decay-vs-scattering hierarchy is a real result, and the breakdown of the fast-ΓY approximation does not look like an artifact of the approximations—the physical comparison ΓH, ΓM > ΓY in the broken phase is the right one.

Soft spots. (1) The transport system (41) contains h/kh terms through \barΓY, but the authors explicitly defer the equation for ∂μ h^μ. No prescription for fixing h is given, so the printed system is underdetermined. Setting h = 0 would close it, but that is not justified and the paper does not say it was done. The Fig. 5–8 values therefore are not fully determined by the displayed equations. (2) The supergauge equilibrium condition μ_H = μ_\tildeH is assumed, but Appendix B's own source equation contains a μ_h I_F^(-) term; setting that source to zero gives μ_H − μ_\tildeH = − μ_h I_F^(-)/I_F^(+), so the equality requires μ_h = 0 or equal Higgs masses. Neither condition is established. The authors flag this too. These two issues are load-bearing for the numerical central claim, but not for the existence of the new rates or the qualitative breakdown argument. (3) Minor: the study is limited to low tanβ; the \tildeΓY formula is provided but not applied.

The EDM section is standard and not the core. Self-citations to the earlier CTP work are appropriate; those are independent, parameter-free derivations.

Bottom line: This is a serious paper that should be refereed, not desk rejected. A referee should ask the authors to close the h equation or clearly state the approximation, and to test the supergauge assumption or temper the 20–100% language. I would cite it for the decay rates and the breakdown result, and I would bring it to the reading group.

Referee report

Significance

If the results hold, the paper addresses a genuine and important gap in electroweak baryogenesis transport theory: it computes Yukawa-induced transport coefficients at zeroth order in α_s rather than estimating them from O(α_s) scattering, and it shows that the often-used fast-Γ_Y approximation can fail. The analytic derivation of I_B and I_F is explicit and internally consistent, the parameter dependence of Γ_Y and \barΓ_Y is displayed directly in Fig. 4, and the paper makes sharp, falsifiable statements about the dependence of Y_B on MSSM parameters and about the compatibility of EWB with EDM limits. The main strength is the transport-coefficient derivation; the numerical Y_B results, however, rest on a closure assumption that the paper itself acknowledges to be untested.

Major objections (3)

[III.C, Eq. (41)] The reduced transport system is not closed. Equations (41a)-(41c) contain the density h through the terms ∓\barΓ_Y h/k_h, but no equation of motion for h is provided; the text explicitly says that the computation of the CP-violating source for h and its relaxation coefficient Γ_h is left for future work. Since the paper demonstrates that \barΓ_Y is not negligible relative to Γ_Y (|\barΓ_Y/Γ_Y|<1/2, and Fig. 4), the h-dependent terms are not parametrically small. The numerical Y_B values in Figs. 5-8 and the 20-100% finite-Γ_Y enhancement claimed in Section IV.A are therefore not determined by the printed system unless a specific prescription for h is supplied. The authors should either add the missing h dynamics, or state explicitly what assumption on h is used in the numerics and rerun/reframe the quantitative claims.
[Appendix B, Eqs. (B3)-(B8)] The supergauge closure μ_H = μ_{\tilde H}, used to reduce the chemical potentials and to arrive at Eqs. (40) and (41), is not established by the stated fast-gaugino assumption. Setting the source in Eq. (B4) to zero gives μ_H0 − μ_{\tilde H0} = −μ_h0 I_F^{(-)}/I_F^{(+)} (up to sign conventions), not μ_H = μ_{\tilde H}, unless μ_h0 = 0 or m_Hu = m_Hd. Neither condition is shown to hold, and μ_h is precisely the undetermined combination that enters through h/k_h in Eq. (41). Because the reduced transport system and all numerical results use μ_H = μ_{\tilde H}, a quantitative test of this assumption, or at least a bounded estimate of the error it introduces, is needed before the Y_B results can be considered reliable.
[Appendix C, Eq. (C7a)] The claimed breakdown of the 1/Γ_Y expansion relies on the first-order correction δY in Eq. (C7a), which contains the uncomputed source S_{\tilde h}(¯z). Since Section III.C states that the CP-violating contribution to the h source and the relaxation coefficient Γ_h are left for future work, the parametric estimate δ\barS/\barS ∼ (Γ_H/Γ_Y)√(rΓ Γ_M^- L_w √\barD (Γ_M^-+Γ_H)) in Eq. (C10) and the conclusion that δY_B/Y_B ∼ O(1) are not fully grounded unless S_{\tilde h} is specified or bounded. Please state the value or range of S_{\tilde h} used in the estimate and test the sensitivity of the conclusion to this input.

Minor objections (4)

[Title page] The University of Washington affiliation contains the typo 'Se attle'; it should read 'Seattle'.
[III.C] The sentence after Eq. (41), 'we have left for future work the calculation of the CP-violating contribution, SCP/upslope\tilde h to its source', is missing a comma or preposition after 'contribution'; it should read '... contribution, SCP/upslope\tilde h, to its source...'.
[IV.A, Eq. (47)] The square-root expression in Eq. (47) is typeset ambiguously; it should be made explicit that the factor L_w√\barD(Γ_M^-+Γ_H) is inside the square root.
[References] Reference [35] is cited as 'in preparation'; unless it has appeared, it should be marked as such in the reference list or removed from the citations that rely on it.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Decays, not scatterings, dominate the Yukawa transport rate that feeds MSSM electroweak baryogenesis.

The reading

This paper derives the contributions that top-quark Yukawa and tri-scalar interactions make to the quantum transport equations of electroweak baryogenesis in the Minimal Supersymmetric Standard Model (MSSM), the equations that track particle densities as bubbles of broken electroweak symmetry expand through the plasma. It shows that decays and inverse decays of squarks, quarks, Higgs scalars, and Higgsinos contribute to the Yukawa transport coefficient $\Gamma_Y$ — the rate at which Higgs-supermultiplet densities are converted into quark-supermultiplet densities — at zeroth order in the strong coupling, and that these contributions can be substantially larger than the $O(\alpha_s)$ scattering terms that earlier treatments assumed dominate. It further argues that the usual fast-$\Gamma_Y$ approximation breaks down for realistic MSSM parameters, because the chiral relaxation rates in the bubble wall are comparable to or larger than $\Gamma_Y$. Solving the transport equations numerically, it finds that keeping $\Gamma_Y$ finite raises the baryon-to-entropy ratio $Y_B$ by 20% in the resonant regime and up to 100% in the nonresonant regime relative to the $\Gamma_Y \to \infty$ limit. The result matters because a quantitative link between baryogenesis and electric-dipole-moment experiments depends on getting these transport rates right.

What carries the argument

The central object is the Closed Time Path (CTP) Schwinger-Dyson formulation of quantum transport, applied to three-body source terms through the rate functions $I_B$ (tri-scalar decays) and $I_F$ (Yukawa decays). These integrals encode thermally averaged decay, emission, and absorption rates with all mass-threshold and Bose/Fermi distribution structure, and they are what determine whether the $O(\alpha_s^0)$ channels are kinematically open; they enter the transport equations through $\Gamma_Y$ and $\bar{\Gamma}_Y$ in Eqs. (40a)-(40b). The reduction to a closed set of equations uses the chemical-potential equalities enforced by fast gauge and gaugino interactions, including the supergauge equilibrium condition $\mu_H = \mu_{\widetilde H}$ of Eq. (37), which lets Higgs and Higgsino densities be combined into the reduced set $(T,Q,H,h)$.

Extended reading notes

Core claim

On this paper's own terms, the central discovery is a hierarchy reversal in the transport equations: the coefficient $\Gamma_Y$ that couples Higgs-supermultiplet densities to third-generation quark-supermultiplet densities receives its leading contributions from two-body decay and inverse-decay channels---for example $t_R + \tilde t_L \leftrightarrow H_u^0$ and the analogous superpartner processes---at order $\alpha_s^0$, not from the $O(\alpha_s)$ scattering processes such as $t_R + g \to t_L + H_u^0$ on which earlier treatments focused. The paper derives the rate functions $I_B$ and $I_F$ for tri-scalar and Yukawa three-body sources, builds $\Gamma_Y$ and $\bar{\Gamma}_Y$ from them, and shows that for MSSM parameters consistent with a strong first-order phase transition and precision electroweak data the decay contributions are typically several times larger than the scattering contribution. It also derives the new coefficient $\tilde{\Gamma}_Y$ and shows $|\bar{\Gamma}_Y/\Gamma_Y| < 1/2$, the paper's correction to an earlier equality. Because the relaxation rates $\Gamma_H$ and $\Gamma_M$ computed in the same CTP framework are as large as or larger than $\Gamma_Y$ inside the bubble wall, the $1/\Gamma_Y$ expansion fails; numerically, the finite-$\Gamma_Y$ correction to $Y_B$ is 20% in the resonant case and up to 100% in the nonresonant case.

Load-bearing premise

The load-bearing premise is that gaugino-mediated interactions are fast enough during the phase transition to keep the Higgs scalars and their Higgsino partners in chemical equilibrium with a single chemical potential ($\mu_H = \mu_{\widetilde H}$); the paper explicitly defers a test of this assumption, and if it fails, the reduced transport equations and all numerical baryon-asymmetry results derived from them are not correct.

Editorial extensions

If this is right

At MSSM parameter points where the relevant three-body decay channels are kinematically open, previous $O(\alpha_s)$ scattering estimates understate $\Gamma_Y$; when $\Gamma_Y$ is in the realistic few-GeV range, including the decay contributions changes $Y_B$ at the 10\u201320% level.
The fast-$\Gamma_Y$ approximation should not be used: the $1/\Gamma_Y$ expansion misses $O(1)$ corrections to the Higgs density $H$, and therefore to $Q$ and $T$, so the transport equations must be solved numerically with finite $\Gamma_Y$.
The earlier assumption $|\bar{\Gamma}_Y| = |\Gamma_Y|$ is not correct; for the MSSM parameters considered here $|\bar{\Gamma}_Y/\Gamma_Y| < 1/2$, making the $h/k_h$ term in the transport equations weaker than assumed.
In large-$\tan\beta$ scenarios the new coefficient $\tilde{\Gamma}_Y$ and the bottom-quark supermultiplet densities are not suppressed, and the general formulas given in the paper let future calculations include them.

Reading between the lines

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

The same $I_B$ and $I_F$ building blocks should transfer to extensions such as the NMSSM or $U(1)^\prime$ models, where a light stop is not needed for the phase transition; in those settings the tri-scalar $A$-dependent part of $\Gamma_Y$ may be relatively more important than in the MSSM benchmark studied here.
A spectrum measurement has direct transport consequences: if future colliders place the relevant superpartner masses far from the threshold where the largest mass is just above the sum of the other two, the $O(\alpha_s^0)$ decay contribution is Boltzmann-suppressed and the fast-$\Gamma_Y$ approximation becomes more reliable; measuring the spectrum would therefore test which regime governs baryogen
Because finite $\Gamma_Y$ raises $Y_B$ relative to the $\Gamma_Y \to \infty$ limit, the paper's results imply that slightly less CP violation is needed in the Higgs sector to match the observed baryon asymmetry, modestly easing the tension with electron and neutron EDM limits while preserving the conclusion that sleptons must be heavier than about 1 TeV.

Original abstract

We derive the contributions to the quantum transport equations for electroweak baryogenesis due to decays and inverse decays induced by tri-scalar and Yukawa interactions. In the Minimal Supersymmetric Standard Model (MSSM), these contributions give rise to couplings between Higgs and fermion supermultiplet densities, thereby communicating the effects of CP-violation in the Higgs sector to the baryon sector. We show that the decay and inverse decay-induced contributions that arise at zeroth order in the strong coupling, \alpha_s, can be substantially larger than the O(\alpha_s) terms that are generated by scattering processes and that are usually assumed to dominate. We revisit the often-used approximation of fast Yukawa-induced processes and show that for realistic parameter choices it is not justified. We solve the resulting quantum transport equations numerically with special attention on the impact of Yukawa rates and study the dependence of the baryon-to-entropy ratio Y_B on MSSM parameters.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,421 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.43 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We derive the contributions to the quantum transport equations for electroweak baryogenesis due to decays and inverse decays induced by tri-scalar and Yukawa interactions. In the Minimal Supersymmetric Standard Model (MSSM), these contributions give rise to couplings between Higgs and fermion supermultiplet densities, thereby communicating the effects of CP-violation in the Higgs sector to the baryon sector. We show that the decay and inverse decay-induced contributions that arise at zeroth order in the strong coupling, \alpha_s, can be substantially larger than the O(\alpha_s) terms that are generated by scattering processes and that are usually assumed to dominate. We revisit the often-used approximation of fast Yukawa-induced processes and show that for realistic parameter choices it is not justified. We solve the resulting quantum transport equations numerically with special attention on the impact of Yukawa rates and study the dependence of the baryon-to-entropy ratio Y_B on MSSM parameters.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive the contributions to the quantum transport equations for electroweak baryogenesis due to decays and inverse decays induced by tri-scalar and Yukawa interactions.	contribution 0.99	0.96	0.09	asserted 0.99
s1	In the Minimal Supersymmetric Standard Model (MSSM), these contributions give rise to couplings between Higgs and fermion supermultiplet densities, thereby communicating the effects of CP-violation in the Higgs sector to the baryon sector.	interpretation 0.61	0.69	0.12	asserted 1.00
s2	We show that the decay and inverse decay-induced contributions that arise at zeroth order in the strong coupling, \alpha_s, can be substantially larger than the O(\alpha_s) terms that are generated by scattering processes and that are usually assumed to dominate.	result 1.00	0.93	0.63	asserted 0.98
s3	We revisit the often-used approximation of fast Yukawa-induced processes and show that for realistic parameter choices it is not justified.	result 0.70	0.90	0.12	asserted 1.00
s4	We solve the resulting quantum transport equations numerically with special attention on the impact of Yukawa rates and study the dependence of the baryon-to-entropy ratio Y_B on MSSM parameters.	method 0.64	0.97	0.13	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.79 · evidence from simulation or computation 0.74.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Leading contributions to the self-energies Σ

**Figure 2.** FIG. 2: Self energies for scalar and fermion fields induced by

**Figure 5.** illustrate two key points of the Yukawa-induced dynamics: (i) Efficient chargino/neutralino-mediated baryogenesis occurs for ΓY ≫ v 2 w/Dh ∼ 0.0025 GeV, as the Higgs supermultiplet density H injected in the unbroken phase is efficiently converted into LH top-quark density (fueling sphaleron processes) before the bubble catches up. Inclusion of the O(α 0 s ) terms in ΓY affects YB at the 10 − 20% level, as one is already in the plateau region in

**Figure 7.** FIG. 7: Allowed bands in the

Showing 6 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0603058 by the authors.

References

Works cited (37)

[1]

J. Erler and M. J. Ramsey-Musolf, Prog. Part. Nucl. Phys. 54, 351 (2005) [arXiv:hep-ph/0404291]

View on Pith Pith review arXiv 2005
[2]

015 [26]. From the reference values of Table I one can derive typical values for the bubble wall velocity and thickness, for which we use vw = 0. 05 [27] and Lw = 25/T [26]. With this choice of parameters one has F2 ∼ 10−3F1. We now discuss in greater detail the role of Yukawa-induced rates o n the transport equa- tions. A. Revisiting the approximation of...

View on Pith
[3]

A. G. Cohen, D. B. Kaplan and A. E. Nelson, Phys. Lett. B 336, 41 (1994) [arXiv:hep-ph/9406345]

View on Pith Pith review arXiv 1994
[4]

M. Pospelov and A. Ritz, Annals Phys. 318, 119 (2005) [arXiv:hep-ph/0504231]

View on Pith Pith review arXiv 2005
[5]

M. Joyce, T. Prokopec and N. Turok, Phys. Rev. Lett. 75, 1695 (1995) [Erratum-ibid. 75, 3375 (1995)] [arXiv:hep-ph/9408339]

View on Pith Pith review arXiv 1995
[6]

P. Huet and A. E. Nelson, Phys. Rev. D 53, 4578 (1996) [arXiv:hep-ph/9506477]

View on Pith Pith review arXiv 1996
[7]

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

View on Pith Pith review arXiv 1999
[8]

M. Joyce, T. Prokopec and N. Turok, Phys. Rev. D 53, 2930 (1996) [arXiv:hep-ph/9410281]

View on Pith Pith review arXiv 1996
[9]

A. Riotto, Phys. Rev. D 58, 095009 (1998) [arXiv:hep-ph/9803357]

View on Pith Pith review arXiv 1998
[10]

A. Riotto, Phys. Rev. D 53, 5834 (1996) [arXiv:hep-ph/9510271]

View on Pith Pith review arXiv 1996
[11]

M. Carena, M. Quiros, M. Seco and C. E. M. Wagner, Nucl. Ph ys. B 650, 24 (2003) [arXiv:hep-ph/0208043]

View on Pith Pith review arXiv 2003
[12]

M. Carena, J. M. Moreno, M. Quiros, M. Seco and C. E. M. Wag ner, Nucl. Phys. B 599, 158 (2001) [arXiv:hep-ph/0011055]

View on Pith Pith review arXiv 2001
[13]

T. Konstandin, T. Prokopec and M. G. Schmidt, Nucl. Phys . B 679, 246 (2004) [arXiv:hep-ph/0309291]

View on Pith Pith review arXiv 2004
[14]

T. Konstandin, T. Prokopec and M. G. Schmidt, Nucl. Phys . B 716, 373 (2005) [arXiv:hep-ph/0410135]

View on Pith Pith review arXiv 2005
[15]

and references therein) and describe the input MSSM paramet ers which will be used in the subsequent numerical explorations. The baryon-to-entrop y ratio can be expressed as an integral of nL = 5Q + 4T in the unbroken phase: YB = −nF Γ ws 2s 1 Dqλ + ∫ 0 −∞ nL(x)e−λ− xdx . (44) 15 0 200 400 600 800 1000 /VertBar1Μ/VertBar1 /LParen1GeV/RParen1 2 4 6 8 10 12...

View on Pith
[16]

T. Konstandin, T. Prokopec, M. G. Schmidt and M. Seco, Nu cl. Phys. B 738, 1 (2006) [arXiv:hep-ph/0505103]

View on Pith Pith review arXiv 2006
[17]

C. Lee, V. Cirigliano and M. J. Ramsey-Musolf, Phys. Rev . D 71, 075010 (2005) [arXiv:hep-ph/0412354]

View on Pith Pith review arXiv 2005
[18]

M. Carena, M. Quiros, A. Riotto, I. Vilja and C. E. M. Wagn er, Nucl. Phys. B 503, 387 (1997) [arXiv:hep-ph/9702409]

View on Pith Pith review arXiv 1997
[19]

C. Balazs, M. Carena, A. Menon, D. E. Morrissey and C. E. M . Wagner, Phys. Rev. D 71, 075002 (2005) [arXiv:hep-ph/0412264]

View on Pith Pith review arXiv 2005
[20]

M. Laine and K. Rummukainen, Nucl. Phys. B 535, 423 (1998) [arXiv:hep-lat/9804019]; M. Laine and K. Rummukainen, Nucl. Phys. B 597, 23 (2001) [arXiv:hep-lat/0009025]; M. Laine, arXiv:hep-ph/0010275

View on Pith Pith review arXiv 1998
[21]

M. Pietroni, Nucl. Phys. B 402 (1993) 27 [arXiv:hep-ph/9207227], A. T. Davies, C. D. Frogg att and R. G. Moorhouse, Phys. Lett. B 372 (1996) 88 [arXiv:hep-ph/9603388], S. J. Huber and M. G. Schmidt, Nucl. Phys. B 606 (2001) 183 [arXiv:hep-ph/0003122], M. Bastero- 27 Gil, C. Hugonie, S. F. King, D. P. Roy and S. Vempati, Phys. Let t. B 489, 359 (2000) [arX...

View on Pith Pith review arXiv 1993
[22]

J. M. Cline and K. Kainulainen, Phys. Rev. Lett. 85, 5519 (2000) [arXiv:hep-ph/0002272]

View on Pith Pith review arXiv 2000
[23]

J. M. Cline, M. Joyce and K. Kainulainen, JHEP 0007, 018 (2000) [arXiv:hep-ph/0006119] (Erratum, arXiv:hep-ph/0110031)

View on Pith Pith review arXiv 2000
[24]

J. Schwinger, J. Math. Phys. 2, 407 (1961); K. T. Mahanthappa, Phys. Rev. D 126, 329 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; R. A. Craig, J. Math. Phys. 9, 605 (1968); K. c. Chou, Z. b. Su, B. l. Hao and L. Yu, Phys. Rept. 1...

View on Pith 1961
[25]

L. P. Kadanoﬀ and G. Baym, Quantum Statistical Mechanics , Benjamin 1962

View on Pith 1962
[26]

K. Enqvist, A. Riotto and I. Vilja, Phys. Lett. B 438, 273 (1998) [arXiv:hep-ph/9710373]

View on Pith Pith review arXiv 1998
[27]

D. Bodeker, G. D. Moore and K. Rummukainen, Phys. Rev. D 61, 056003 (2000) [arXiv:hep-ph/9907545]; G. D. Moore and K. Rummukainen, Ph ys. Rev. D 61, 105008 (2000) [arXiv:hep-ph/9906259] ; G. D. Moore, Phys. Rev. D 62, 085011 (2000) [arXiv:hep-ph/0001216]

View on Pith Pith review arXiv 2000
[28]

J. M. Moreno, M. Quiros and M. Seco, Nucl. Phys. B 526, 489 (1998) [arXiv:hep-ph/9801272]

View on Pith Pith review arXiv 1998
[29]

P. John and M. G. Schmidt, Nucl. Phys. B 598, 291 (2001) [Erratum-ibid. B 648, 449 (2003)] [arXiv:hep-ph/0002050]

View on Pith Pith review arXiv 2001
[30]

D. N. Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl. 148, 175 (2003) [arXiv:astro-ph/0302209]

View on Pith Pith review arXiv 2003
[31]

B. C. Regan, E. D. Commins, C. J. Schmidt and D. DeMille, P hys. Rev. Lett. 88, 071805 (2002)

View on Pith 2002
[32]

C. A. Baker et al. , arXiv:hep-ex/0602020

View on Pith Pith review arXiv
[33]

M. V. Romalis, W. C. Griﬃth, J. P. Jacobs and E. N. Fortson , Phys. Rev. Lett. 86, 2505 (2001) [arXiv:hep-ex/0012001]

View on Pith Pith review arXiv 2001
[34]

T. Ibrahim and P. Nath, Phys. Rev. D 57, 478 (1998) [Erratum-ibid. D 58, 019901(1998), D 60, 079903 (1999), D 60, 119901 (1999)] [arXiv:hep-ph/9708456]

View on Pith Pith review arXiv 1998
[35]

D. Chang, W. Y. Keung and A. Pilaftsis, Phys. Rev. Lett. 82, 900 (1999) [Erratum-ibid. 83, 3972 (1999)] [arXiv:hep-ph/9811202]; D. Chang, W. F. Chang and W. Y. Keung, Phys. Rev. D 66, 116008 (2002) [arXiv:hep-ph/0205084]; A. Pilaftsis, Nuc l. Phys. B 644, 263 (2002) [arXiv:hep-ph/0207277]

View on Pith Pith review arXiv 1999
[36]

S. Eidelman et al. [Particle Data Group Collaboration], Phys. Lett. B 592, 1 (2004)

View on Pith 2004
[37]

V. Cirigliano, S. Profumo, M. J. Ramsey-Musolf, in prep aration. 28

View on Pith

Forward citations

Cited by 9 Pith papers

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

An Effective Sphaleron Awakens
hep-ph 2025-06 conditional novelty 7.0 of 10

A consistent 3D EFT computation of the Higgs phase sphaleron rate yields universal baryon preservation bounds x ≈ 0.025 (strong) and x ≈ 0.036 (weak), and shows two-loop corrections eliminate strong one-step transitio...
Electroweak baryogenesis from charged current anomalies in $B$ meson decays
hep-ph 2025-02 conditional novelty 6.0 of 10

Complex lepton Yukawa couplings in a two Higgs doublet model that explain the R(D(*)) flavor anomalies can also source electroweak baryogenesis, yielding the observed baryon asymmetry under assumed strong first-order ...
Baryogenesis from Decaying Magnetic Helicity
astro-ph.CO 2016-06 conditional novelty 6.0 of 10

A maximally helical primordial magnetic field with decaying helicity can generate n_B/s up to about 10^-10 through chiral anomalies, without violating (B-L), because the decaying field sources chirality and blocks sph...
Two-Step Electroweak Baryogenesis
hep-ph 2015-08 conditional novelty 6.0 of 10

CP violation in a partially secluded singlet sector can generate the observed baryon asymmetry during the first step of a two-step electroweak phase transition while evading present and projected electric dipole momen...
Electroweak Baryogenesis and the Standard Model Effective Field Theory
hep-ph 2017-10 accept novelty 5.0 of 10

Two effective-field-theory scenarios related by the classical equations of motion produce baryon asymmetries differing by a factor of four, so the Standard Model EFT expansion fails for electroweak baryogenesis.

Show 4 more citing papers

Testing Electroweak Baryogenesis with Future Colliders
hep-ph 2014-08 conditional novelty 5.0 of 10

A minimal hidden-sector singlet scalar that enables electroweak baryogenesis can be fully probed by a 100 TeV hadron collider using Higgs self-coupling and vector-boson-fusion invisible searches, though only under a f...
Excluding Electroweak Baryogenesis in the MSSM
hep-ph 2012-03 conditional novelty 5.0 of 10

The light right-handed stop required by electroweak baryogenesis in the MSSM would raise gluon-fusion Higgs rates and suppress diphoton decays; combining 2012 ATLAS and CMS Higgs searches excludes that correlated patt...
Super-critical primordial black hole formation via delayed first-order electroweak phase transition
hep-ph 2025-01 conditional novelty 4.0 of 10

Delayed first-order electroweak phase transitions can form super-critical primordial black holes, and a timescale ratio t_H/t_V captures the threshold better than the standard density contrast.
Quantum Transport and Electroweak Baryogenesis
hep-ph 2013-02 accept novelty 2.0 of 10

The review consolidates the first-principles derivation of electroweak baryogenesis transport equations and surveys which models remain viable after EDM and LHC constraints.

How the literature uses it

27 arXiv papers cite this in 64 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 36 sentences without a confident label

Contests it 1 paper

In addition, the Boltzmann equations of Refs. [ref] follow from Eqs. ([ref],b,[ref]); they too are no longer valid for $τ_yb,τ_yτ ≲τ_diff$.

Lepton-mediated electroweak baryogenesis · Setting up the Boltzmann equations · contest 0.83

Builds on it 2 papers

The plot is based on our recent computation [ref] of the function $F_μ$ in Eq. ([ref]) that builds on our earlier treatment of the quantum transport during a supersymmetric electroweak phase transition [ref] .

Neutrons and the New Standard Model · EDMs and the Origin of Matter · 0.95
Electroweak baryogenesis utilizing these sources in the MSSM has been extensively analyzed in recent studies (e.g. [ref] ), and we build on these analyses in our study of the accidental SUSY scenario.

Accidental Supersymmetric Dark Matter and Baryogenesis · Introduction · 0.96

Uses its method or tool 10 papers

To obtain $Y_B$ as a function of the MSSM parameters, we rely on the work of Ref. [ref] , which include the parameter dependence of both the CPV source terms in the quantum Boltzmann equations as well as that of the CP-conserving, particle number-changing interactions.

MSSM Baryogenesis and Electric Dipole Moments: An Update on the Phenomenology · MSSM Baryogenesis and EDMs · 0.84
With the above considerations, we calculate the baryon asymmetry following the techniques and assumptions detailed in Refs. [ref] .

Accidental Supersymmetric Dark Matter and Baryogenesis · The Baryon Asymmetry · 1.00
We refer the reader to Ref. [ref] for the general form of $ℐ_F$, which is the form used in our numerical analysis.

Lepton-mediated electroweak baryogenesis · Determination of bottom/tau Yukawa rates · 0.86

Uses its data or values 1 paper

The Yukawa-loop self energy function $I_F$ is taken from Ref. [ref] ,

Electroweak Baryogenesis with Vector-like Leptons and Scalar Singlets · Transport Equation Formulae · 0.89

Compares with it 2 papers

In particular, we find that the EWB resonance found in previous treatments [ref] does persist somewhat in our more exact formalism.

Flavored Quantum Boltzmann Equations · Introduction · 0.93
Modern summaries [ref] present a slightly different convention, writing $Γ_ws= 6 κα_w^5T^4$, while [ref] , even though quoting [ref] , they use the numerical value $Γ_ws= 6.3×10^-6 T$.

Electroweak Baryogenesis with BARYONET: a self-contained review of the WKB approach · Reconciliation with the literature for Gamma_ws · 0.84

Cites it as support 1 paper

Previous studies have shown that the solutions to the Boltzmann equations are insensitive to sub-$𝒪(1)$ variations in the interaction coefficients [ref] .

CP violation Beyond the MSSM: Baryogenesis and Electric Dipole Moments · Baryon Asymmetry Computation · 0.98

Cites it as background 7 papers

Should one allow for additional source terms, such as non-resonant sources (see e.g. [ref] ) or sources associated with left-right stops, sbottoms or staus (see e.g. [ref] ), all of our conclusions would be weakened.

Closing in on Supersymmetric Electroweak Baryogenesis with Dark Matter Searches and the Large Hadron Collider · EWB and Bino-like Dark Matter · 0.81
As discussed in Refs. [ref] , these scales include a decoherence time, $τ_d$, associated with the departure from adiabatic dynamics; a plasma time, $τ_p$, associated with mixing between degenerate states in the plasma; and an intrinsic quasiparticle evolution time, $τ_int$, associated with the time evolution of a state of a given energy.

Supergauge interactions and electroweak baryogenesis · Three-body rates: general formalism · 0.81
The various issues of calculating the baryon asymmetry of the universe (BAU) in a given particle physics model are a subject of active research (see, for example, [ref] ).

Beyond MSSM Baryogenesis · Introduction · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

J. Erler and M. J. Ramsey-Musolf, Prog. Part. Nucl. Phys. 54, 351 (2005) [arXiv:hep-ph/0404291]

View on Pith Pith review arXiv 2005

[2] [2]

015 [26]. From the reference values of Table I one can derive typical values for the bubble wall velocity and thickness, for which we use vw = 0. 05 [27] and Lw = 25/T [26]. With this choice of parameters one has F2 ∼ 10−3F1. We now discuss in greater detail the role of Yukawa-induced rates o n the transport equa- tions. A. Revisiting the approximation of...

View on Pith

[3] [3]

A. G. Cohen, D. B. Kaplan and A. E. Nelson, Phys. Lett. B 336, 41 (1994) [arXiv:hep-ph/9406345]

View on Pith Pith review arXiv 1994

[4] [4]

M. Pospelov and A. Ritz, Annals Phys. 318, 119 (2005) [arXiv:hep-ph/0504231]

View on Pith Pith review arXiv 2005

[5] [5]

M. Joyce, T. Prokopec and N. Turok, Phys. Rev. Lett. 75, 1695 (1995) [Erratum-ibid. 75, 3375 (1995)] [arXiv:hep-ph/9408339]

View on Pith Pith review arXiv 1995

[6] [6]

P. Huet and A. E. Nelson, Phys. Rev. D 53, 4578 (1996) [arXiv:hep-ph/9506477]

View on Pith Pith review arXiv 1996

[7] [7]

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

View on Pith Pith review arXiv 1999

[8] [8]

M. Joyce, T. Prokopec and N. Turok, Phys. Rev. D 53, 2930 (1996) [arXiv:hep-ph/9410281]

View on Pith Pith review arXiv 1996

[9] [9]

A. Riotto, Phys. Rev. D 58, 095009 (1998) [arXiv:hep-ph/9803357]

View on Pith Pith review arXiv 1998

[10] [10]

A. Riotto, Phys. Rev. D 53, 5834 (1996) [arXiv:hep-ph/9510271]

View on Pith Pith review arXiv 1996

[11] [11]

M. Carena, M. Quiros, M. Seco and C. E. M. Wagner, Nucl. Ph ys. B 650, 24 (2003) [arXiv:hep-ph/0208043]

View on Pith Pith review arXiv 2003

[12] [12]

M. Carena, J. M. Moreno, M. Quiros, M. Seco and C. E. M. Wag ner, Nucl. Phys. B 599, 158 (2001) [arXiv:hep-ph/0011055]

View on Pith Pith review arXiv 2001

[13] [13]

T. Konstandin, T. Prokopec and M. G. Schmidt, Nucl. Phys . B 679, 246 (2004) [arXiv:hep-ph/0309291]

View on Pith Pith review arXiv 2004

[14] [14]

T. Konstandin, T. Prokopec and M. G. Schmidt, Nucl. Phys . B 716, 373 (2005) [arXiv:hep-ph/0410135]

View on Pith Pith review arXiv 2005

[15] [15]

and references therein) and describe the input MSSM paramet ers which will be used in the subsequent numerical explorations. The baryon-to-entrop y ratio can be expressed as an integral of nL = 5Q + 4T in the unbroken phase: YB = −nF Γ ws 2s 1 Dqλ + ∫ 0 −∞ nL(x)e−λ− xdx . (44) 15 0 200 400 600 800 1000 /VertBar1Μ/VertBar1 /LParen1GeV/RParen1 2 4 6 8 10 12...

View on Pith

[16] [16]

T. Konstandin, T. Prokopec, M. G. Schmidt and M. Seco, Nu cl. Phys. B 738, 1 (2006) [arXiv:hep-ph/0505103]

View on Pith Pith review arXiv 2006

[17] [17]

C. Lee, V. Cirigliano and M. J. Ramsey-Musolf, Phys. Rev . D 71, 075010 (2005) [arXiv:hep-ph/0412354]

View on Pith Pith review arXiv 2005

[18] [18]

M. Carena, M. Quiros, A. Riotto, I. Vilja and C. E. M. Wagn er, Nucl. Phys. B 503, 387 (1997) [arXiv:hep-ph/9702409]

View on Pith Pith review arXiv 1997

[19] [19]

C. Balazs, M. Carena, A. Menon, D. E. Morrissey and C. E. M . Wagner, Phys. Rev. D 71, 075002 (2005) [arXiv:hep-ph/0412264]

View on Pith Pith review arXiv 2005

[20] [20]

M. Laine and K. Rummukainen, Nucl. Phys. B 535, 423 (1998) [arXiv:hep-lat/9804019]; M. Laine and K. Rummukainen, Nucl. Phys. B 597, 23 (2001) [arXiv:hep-lat/0009025]; M. Laine, arXiv:hep-ph/0010275

View on Pith Pith review arXiv 1998

[21] [21]

M. Pietroni, Nucl. Phys. B 402 (1993) 27 [arXiv:hep-ph/9207227], A. T. Davies, C. D. Frogg att and R. G. Moorhouse, Phys. Lett. B 372 (1996) 88 [arXiv:hep-ph/9603388], S. J. Huber and M. G. Schmidt, Nucl. Phys. B 606 (2001) 183 [arXiv:hep-ph/0003122], M. Bastero- 27 Gil, C. Hugonie, S. F. King, D. P. Roy and S. Vempati, Phys. Let t. B 489, 359 (2000) [arX...

View on Pith Pith review arXiv 1993

[22] [22]

J. M. Cline and K. Kainulainen, Phys. Rev. Lett. 85, 5519 (2000) [arXiv:hep-ph/0002272]

View on Pith Pith review arXiv 2000

[23] [23]

J. M. Cline, M. Joyce and K. Kainulainen, JHEP 0007, 018 (2000) [arXiv:hep-ph/0006119] (Erratum, arXiv:hep-ph/0110031)

View on Pith Pith review arXiv 2000

[24] [24]

J. Schwinger, J. Math. Phys. 2, 407 (1961); K. T. Mahanthappa, Phys. Rev. D 126, 329 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]; R. A. Craig, J. Math. Phys. 9, 605 (1968); K. c. Chou, Z. b. Su, B. l. Hao and L. Yu, Phys. Rept. 1...

View on Pith 1961

[25] [25]

L. P. Kadanoﬀ and G. Baym, Quantum Statistical Mechanics , Benjamin 1962

View on Pith 1962

[26] [26]

K. Enqvist, A. Riotto and I. Vilja, Phys. Lett. B 438, 273 (1998) [arXiv:hep-ph/9710373]

View on Pith Pith review arXiv 1998

[27] [27]

D. Bodeker, G. D. Moore and K. Rummukainen, Phys. Rev. D 61, 056003 (2000) [arXiv:hep-ph/9907545]; G. D. Moore and K. Rummukainen, Ph ys. Rev. D 61, 105008 (2000) [arXiv:hep-ph/9906259] ; G. D. Moore, Phys. Rev. D 62, 085011 (2000) [arXiv:hep-ph/0001216]

View on Pith Pith review arXiv 2000

[28] [28]

J. M. Moreno, M. Quiros and M. Seco, Nucl. Phys. B 526, 489 (1998) [arXiv:hep-ph/9801272]

View on Pith Pith review arXiv 1998

[29] [29]

P. John and M. G. Schmidt, Nucl. Phys. B 598, 291 (2001) [Erratum-ibid. B 648, 449 (2003)] [arXiv:hep-ph/0002050]

View on Pith Pith review arXiv 2001

[30] [30]

D. N. Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl. 148, 175 (2003) [arXiv:astro-ph/0302209]

View on Pith Pith review arXiv 2003

[31] [31]

B. C. Regan, E. D. Commins, C. J. Schmidt and D. DeMille, P hys. Rev. Lett. 88, 071805 (2002)

View on Pith 2002

[32] [32]

C. A. Baker et al. , arXiv:hep-ex/0602020

View on Pith Pith review arXiv

[33] [33]

M. V. Romalis, W. C. Griﬃth, J. P. Jacobs and E. N. Fortson , Phys. Rev. Lett. 86, 2505 (2001) [arXiv:hep-ex/0012001]

View on Pith Pith review arXiv 2001

[34] [34]

T. Ibrahim and P. Nath, Phys. Rev. D 57, 478 (1998) [Erratum-ibid. D 58, 019901(1998), D 60, 079903 (1999), D 60, 119901 (1999)] [arXiv:hep-ph/9708456]

View on Pith Pith review arXiv 1998

[35] [35]

D. Chang, W. Y. Keung and A. Pilaftsis, Phys. Rev. Lett. 82, 900 (1999) [Erratum-ibid. 83, 3972 (1999)] [arXiv:hep-ph/9811202]; D. Chang, W. F. Chang and W. Y. Keung, Phys. Rev. D 66, 116008 (2002) [arXiv:hep-ph/0205084]; A. Pilaftsis, Nuc l. Phys. B 644, 263 (2002) [arXiv:hep-ph/0207277]

View on Pith Pith review arXiv 1999

[36] [36]

S. Eidelman et al. [Particle Data Group Collaboration], Phys. Lett. B 592, 1 (2004)

View on Pith 2004

[37] [37]

V. Cirigliano, S. Profumo, M. J. Ramsey-Musolf, in prep aration. 28

View on Pith