REVIEW 3 major objections 4 minor 38 references
Systematic derivation of the Boltzmann equation for electroweak baryogenesis
T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read Deriving the Boltzmann equation for electroweak baryogenesis from the Kadanoff–Baym equations with self-energy corrections retained, this paper shows that fermions acquire a CP-odd shift of the quasiparticle shell at first order in the…
desk verdict Serious KB derivation with a new fermionic CP-odd shell shift, but the shift rests on an unverified narrow-width hierarchy. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing machinery is the algebraic solution of the Kadanoff–Baym equations in a derivative expansion. Writing $\alpha_\pm = D^{[0]} - (M + g^H \pm i g^A)$, the zeroth-order retarded/advanced propagators are $\alpha_\mp^{-1}$ and the first-order pieces are $\alpha_\mp^{-1} i\diamond(\alpha_\mp,\alpha_\mp^{-1})$, with $\diamond$ the Wigner-space gradient bracket that organizes the derivative expansion. The derivation then applies four controlled approximations: the local mass basis that diagonalizes the spacetime-dependent mass and removes diagonal connection terms; the flavor-universal approximation for the self-energy; the quasiparticle approximation, in which Breit–Wigner spectral peaks are replaced by $\operatorname{sign}(k^0)\delta(\Omega^2)$ in the narrow-width limit; and a decomposition of the Wightman self-energy $g^\lambda = \frac{2\eta}{i} n^\lambda g^A + \delta g_{\rm coll}$ that separates on-shell statistical information from collision terms. The first-order fermionic spectral function acquires a $\delta'(\Omega^2)$ term whose coefficient $N^{[1]}_{s,i}$ carries derivatives of the effective mass, and inserting the resulting on-shell Wightman function into the kinetic (Hermitian) equation yields the Boltzmann equation with a shifted Liouville operator.
What would settle it
Compute the absorptive fermionic self-energy components $a_{1,A}$, $a_{2,A}$, and $a_{3,A}$ relative to $a_{0,A}$ in a representative electroweak plasma at the bubble wall. If any of these is comparable to $a_{0,A}$, or if momentum derivatives spoil the assumed hierarchy, the spectral function is not $\operatorname{sign}(\tilde k^0)\delta(\Omega_{s,i}^2)$ in each spin sector, and the shell shift in Eq. (5.43) is not the complete first-order transport correction; the full Kadanoff–Baym solution would then disagree with the derived Boltzmann equation.
Extended reading notes
Core claim
The paper's central claim is that retaining self-energy corrections changes the quasiparticle on-shell condition in a way that matters for CP-violating transport. Solving the Kadanoff–Baym equations to first order in the derivative expansion gives a fermionic spectral function whose first-order piece is proportional to $\delta'(\Omega_{s,i}^2)$, i.e., a shift of the quasiparticle shell. In the wall frame the effective shell is $\Omega_{s,i,\mathrm{eff}}^2 = \Omega_{s,i}^2 + \delta\Omega_{s,i}^2$ with $\delta\Omega_{s,i}^2 = -\frac{1}{\tilde K^0}\bigl[m'_{Ii}(K_z\partial_{k_z}M_{Ri}-M_{Ri}\partial_{k_z}K_z)-m'_{Ri}(K_z\partial_{k_z}M_{Ii}-M_{Ii}\partial_{k_z}K_z)\bigr]$, where $M_{Ri}=m_{Ri}+a_{1s,H}$ and $M_{Ii}=m_{Ii}+a_{2s,H}$. Because the phase of the spacetime-dependent complex mass is CP odd, this shift changes sign for antiparticles and produces particle--antiparticle differences in group velocity and semiclassical force. For bosons the first-order flavor-diagonal shell correction vanishes identically, so no such CP-odd force appears at this order. In the limit of vanishing self-energy, the equations reduce to the known semiclassical Boltzmann equations.
Load-bearing premise
The load-bearing premise is that plasma damping of each fermion behaves almost identically for spin-up and spin-down and acts like a plain scalar, so that each spin mode has a sharp, single-peaked spectral function; if damping has a large spin-dependent or chiral component, the narrow-width delta-function picture and the derived Boltzmann equations break down.
Editorial extensions
If this is right
- Fermionic transport in electroweak baryogenesis should be computed with the dressed shell $\Omega_{s,i,\mathrm{eff}}^2$, so the Hermitian self-energy components $a_{1,H}$ and $a_{2,H}$ enter the CP-odd velocity and force even though they are not themselves CP odd.
- Particle and antiparticle distribution functions obey different Liouville operators, so a CP asymmetry is generated already at the level of free streaming through the wall.
- For bosons, the first-order flavor-diagonal shell correction vanishes, so no CP-violating semiclassical force appears at this order; any bosonic baryogenesis source must enter through collision terms or higher orders.
- When all self-energy corrections are neglected, the derived Boltzmann equations reduce to the conventional semiclassical Boltzmann equations, so previous results are contained as a special case.
- The split of the Wightman self-energy into an on-shell statistical part and a collision remainder gives a controlled recipe for constructing collision terms with dressed on-shell internal states.
Reading between the lines
- A direct extension the paper does not pursue is to feed the off-diagonal flavor-coherence components back into the diagonal transport; for nearly degenerate masses these could alter the on-shell shells at second order.
- One concrete test of the framework would be to take a model self-energy with sizable $a_{2,A}$ and compare the Boltzmann solution with a numerical solution of the full Kadanoff–Baym equations; the comparison quantifies how much the narrow-width assumption controls the CP-odd source.
- The result suggests that electroweak baryogenesis codes generating CP-odd bosonic sources through a first-order classical force are not supported by this derivation; bosonic CP violation would have to enter through collision terms or higher-order shell corrections.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript derives Boltzmann equations for electroweak baryogenesis from the Kadanoff–Baym equations while retaining self-energy corrections. The authors solve the Kadanoff–Baym equations algebraically to first order in the derivative expansion, apply a quasiparticle narrow-width approximation, a local mass basis, a flavor-universal treatment of the self-energy, and a decomposition of the Wightman self-energy into an on-shell statistical part and a collision remainder. They obtain a bosonic Boltzmann equation with a self-energy-corrected quasiparticle shell and no first-order CP-odd shell correction, and a fermionic Boltzmann equation with a first-order CP-odd shell shift, Eq. (5.43), which produces particle–antiparticle differences in group velocities and semiclassical forces. The results are shown to reproduce the conventional semiclassical equations of refs. [8–10] when self-energy corrections are dropped, and to be consistent with the thermally corrected fermionic result of ref. [14] in the appropriate limit.
Significance. If the stated assumptions hold, this is a valuable systematization of the field-theoretic derivation of EWBG transport equations. Its strengths are the explicit algebraic solution of the Kadanoff–Baym equations, the clear inventory of approximations, the reproduction of known limits, and the clarification of the VIA cancellation of ref. [27] from the perspective of the order-by-order solution. The CP-odd fermionic shell shift is a concrete, model-dependent prediction that can be tested numerically once self-energies are specified. The main caveat is that the fermionic result is conditional on a quasiparticle spectral-function hierarchy whose validity in a realistic EWBG plasma is not demonstrated.
major comments (3)
- [Sec. 3.3 and Eqs. (5.15)–(5.17)] The central fermionic result depends on the assumption that the absorptive part of the self-energy is spin-independent and scalar-dominated, a_{0,A} >> a_{m,A}. The manuscript explicitly flags this condition but does not test it for the fermions relevant to electroweak baryogenesis, such as the top quark, whose thermal width from gauge interactions has vector and spatial components. If this hierarchy fails, the spectral function does not reduce to the simple sign(k0) delta(Omega_s^2) form, and the shell shift in Eq. (5.43) and the Boltzmann equation (5.51) are not established. This is a load-bearing limitation rather than a peripheral one; please add a quantitative estimate of a_{0,A} and a_{m,A} in a representative EWBG background, or explicitly restrict the claimed domain of applicability.
- [Footnotes 9 and 10, Eqs. (5.25)–(5.32)] The manuscript asserts that apparently singular O(1/Gamma) contributions to the Wightman functions are removed once the kinetic equation is imposed at the same order, leaving finite terms in the weak-coupling limit. This cancellation is not shown. These terms are precisely the ones that are discarded when defining the on-shell Wightman functions, so the validity of the subsequent Boltzmann equation depends on this step. Please provide the full derivation or a detailed reference for the cancellation.
- [Sec. 5.3.2, Eq. (5.42)] The fermionic Liouville term is presented as the result of a 'straightforward calculation' from Eq. (5.32). This step is the core of the paper's main physical claim, and the intermediate algebra is not shown. In particular, it is not transparent how the N_{s,i}^{[1]} delta-prime term in the Wightman function is converted into the effective shell shift delta Omega^2_{s,i}, and how the Poisson-bracket contribution is handled. Please include the derivation or an appendix with the essential intermediate steps.
minor comments (4)
- [Sec. 5.3.2, Eq. (5.43)] The notation for delta Omega^2_{s,i} would be clearer if the spin label appeared explicitly on the right-hand side rather than only through M_{Ri}, M_{Ii}, K_z, and tilde K_0.
- [Appendix A.2, footnote 15] The discussion of the overall normalization difference by a factor of four in ref. [27] is relegated to a footnote; since the authors say the cancellation is unaffected, this is acceptable, but a brief sentence in the main text would help readers assess the comparison.
- [Sec. 3.2] The boost in Eq. (3.3) uses sign(k0) in defining tilde k_0; the branch choice for negative k_0 is not discussed, and the subsequent integration over k_0 > 0 in Sec. 5.3 would benefit from an explicit statement about which branch is retained.
- [Sec. 5.3.1, Eq. (5.39)] The canonical relations z_dot_i = partial_{k_z} omega_i and p_dot_{z,i} = -partial_z omega_i are stated without derivation; a brief comment that they follow from Hamilton's equations for the quasiparticle dispersion relation would be helpful.
Circularity Check
No significant circularity: the fermionic shell shift is derived from the derivative expansion rather than imposed, and the statistical-function decomposition is an explicit prescription, not a fitted input.
full rationale
Walking the derivation chain, the load-bearing steps are: (i) the algebraic solution of the Kadanoff-Baym equations in the derivative expansion with finite absorptive self-energy (Sec. 4); (ii) the narrow-width reduction of the Breit-Wigner spectral functions under the stated scalar-dominated hierarchy a0,A >> am,A (Secs. 3.3 and 5.1); (iii) the decomposition g^lambda = g^lambda_stat + delta g_coll with g^lambda_stat = (2 eta / i) n^lambda g^A (Eqs. 3.16-3.17), used to identify the on-shell Wightman functions; and (iv) projection of the Hermitian part of the Kadanoff-Baym equations onto the on-shell branch (Sec. 5.3). None of these is circular. The decomposition in (iii) is explicitly labeled a prescription rather than a derivation, and it does not determine the Boltzmann equation: the equation obtained in Sec. 5.3 governs the evolution of n^lambda, which remains the unknown distribution function. The central new result, the fermionic first-order shell shift delta Omega^2_s,i in Eq. (5.43), is produced by the first-order retarded/advanced propagator structure in Eqs. (5.20)-(5.22), not by the statistical ansatz; it is a genuine derivation from the equations of motion. Consistency with the earlier results of refs. [8-10] and [14] is checked by taking limits, not by importing those results as inputs. The paper contains no fitting of data and no load-bearing self-citation by the present authors. The self-flagged limitation concerning the spin-independence and scalar dominance of the absorptive self-energy (Sec. 3.3) is a domain-of-validity assumption and is explicitly acknowledged; if that hierarchy fails, the simple quasiparticle form is said to be insufficient. This is a correctness or applicability risk, not a circular step. The apparent singular 1/Gamma terms are addressed by consistency with the kinetic equation in footnotes 9 and 10. Overall, the derivation is self-contained and no circular reduction is exhibited.
Assumptions & free parameters
assumptions (8)
- domain assumption Derivative expansion k >> partial_x truncates the Wigner-space equations at first order.
- domain assumption Planar-wall and steady-wall: mass depends only on z and is static in the wall frame, with conserved k_parallel.
- domain assumption Quasiparticle approximation: spectral functions have Breit-Wigner form and in the narrow-width limit become sign(k0) delta(Omega^2).
- domain assumption For fermions, absorptive self-energy is spin-independent and scalar-dominated: Gamma_s = O(a_{0,A}) with a_{0,A} >> a_{m,A}, and momentum differentiation does not alter the hierarchy.
- domain assumption Self-energy spin projection along z is conserved in the boosted frame; S_z commutes with kinetic, mass, and self-energy operators.
- domain assumption Flavor-universal approximation: flavor-dependent self-energy delta g is neglected; quasiparticle shells are set by diagonal mass and flavor-universal self-energy.
- domain assumption Gradients acting on self-energy functions are neglected in solving the KB equations; x-dependence enters only through the spacetime-dependent mass term.
- domain assumption Zeroth-order local thermal equilibrium with z-independent temperature and plasma velocity; Wightman self-energy satisfies local KMS relation.
Cite this review
Pith. "Pith review of Systematic derivation of the Boltzmann equation for electroweak baryogenesis." pith.science (2026). https://pith.science/paper/TZ4Z5SIJ
@misc{pith2026260728321,
author = {Pith},
title = {Pith review of: Systematic derivation of the Boltzmann equation for electroweak baryogenesis},
year = {2026},
howpublished = {\url{https://pith.science/paper/TZ4Z5SIJ}},
note = {Machine review of arXiv:2607.28321}
}
read the original abstract
We derive the Boltzmann equation for electroweak baryogenesis within a field-theoretical framework. We first algebraically solve the Kadanoff--Baym equations by incorporating the effects of gradients of the CP-violating bubble-wall background order by order. We then apply approximations and assumptions appropriate for electroweak baryogenesis and identify the on-shell parts of the solutions, which describe quasiparticle states propagating in a plasma. Using these on-shell solutions, we derive the Boltzmann equations for flavor-diagonal quasiparticle modes, while neglecting the off-diagonal components describing quantum coherence between different flavor modes. Our derivation generalizes previous field-theoretical treatments by retaining self-energy corrections, and our results are consistent with the known Boltzmann equations when these corrections are neglected. This framework provides a systematic and transparent derivation applicable to multi-flavor bosonic and fermionic systems.
Reference graph
Works this paper leans on
-
[27]
Resummation and cancellation of the VIA source in electroweak baryogenesis,
M. Postma, J. van de Vis, and G. White, “Resummation and cancellation of the VIA source in electroweak baryogenesis,” JHEP12(2022) 121[arXiv:2206.01120]
arXiv 2022
-
[14]
CP-violating transport theory for electroweak baryogenesis with thermal corrections,
K. Kainulainen, “CP-violating transport theory for electroweak baryogenesis with thermal corrections,” JCAP11(2021) 042[arXiv:2108.08336]
arXiv 2021
-
[1]
On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe,
V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, “On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe,” Phys. Lett. B155(1985) 36
work page 1985
-
[2]
Diffusion enhances spontaneous electroweak baryogenesis,
A. G. Cohen, D. B. Kaplan, and A. E. Nelson, “Diffusion enhances spontaneous electroweak baryogenesis,” Phys. Lett. B336(1994) 41–47[hep-ph/9406345]. – 38 –
arXiv 1994
-
[3]
Electroweak baryogenesis from a classical force,
M. Joyce, T. Prokopec, and N. Turok, “Electroweak baryogenesis from a classical force,” Phys. Rev. Lett.75(1995) 1695–1698[hep-ph/9408339]. [Erratum: Phys.Rev.Lett. 75, 3375 (1995)]
arXiv 1995
-
[4]
Nonlocal electroweak baryogenesis. Part 2: The Classical regime,
M. Joyce, T. Prokopec, and N. Turok, “Nonlocal electroweak baryogenesis. Part 2: The Classical regime,” Phys. Rev. D53(1996) 2958–2980[hep-ph/9410282]
arXiv 1996
-
[5]
Electroweak baryogenesis in supersymmetric models,
P. Huet and A. E. Nelson, “Electroweak baryogenesis in supersymmetric models,” Phys. Rev. D53(1996) 4578–4597[hep-ph/9506477]
arXiv 1996
-
[6]
Supersymmetric electroweak baryogenesis in the WKB approximation,
J. M. Cline, M. Joyce, and K. Kainulainen, “Supersymmetric electroweak baryogenesis in the WKB approximation,” Phys. Lett. B417(1998) 79–86[hep-ph/9708393]. [Erratum: Phys.Lett.B 448, 321–321 (1999)]
arXiv 1998
Show all 38 references
-
[7]
Supersymmetric electroweak baryogenesis,
J. M. Cline, M. Joyce, and K. Kainulainen, “Supersymmetric electroweak baryogenesis,” JHEP07(2000) 018[hep-ph/0006119]
2000 arXiv
-
[8]
First principle derivation of semiclassical force for electroweak baryogenesis,
K. Kainulainen, T. Prokopec, M. G. Schmidt, and S. Weinstock, “First principle derivation of semiclassical force for electroweak baryogenesis,” JHEP06(2001) 031[hep-ph/0105295]
2001 arXiv
-
[9]
Semiclassical force for electroweak baryogenesis: Three-dimensional derivation,
K. Kainulainen, T. Prokopec, M. G. Schmidt, and S. Weinstock, “Semiclassical force for electroweak baryogenesis: Three-dimensional derivation,” Phys. Rev. D66(2002) 043502 [hep-ph/0202177]
2002 arXiv
-
[10]
Transport equations for chiral fermions to orderℏand electroweak baryogenesis. Part 1,
T. Prokopec, M. G. Schmidt, and S. Weinstock, “Transport equations for chiral fermions to orderℏand electroweak baryogenesis. Part 1,” Annals Phys.314(2004) 208–265 [hep-ph/0312110]
2004 arXiv
-
[11]
Transport equations for chiral fermions to orderℏand electroweak baryogenesis. Part II,
T. Prokopec, M. G. Schmidt, and S. Weinstock, “Transport equations for chiral fermions to orderℏand electroweak baryogenesis. Part II,” Annals Phys.314(2004) 267–320 [hep-ph/0406140]
2004 arXiv
-
[12]
Top transport in electroweak baryogenesis,
L. Fromme and S. J. Huber, “Top transport in electroweak baryogenesis,” JHEP03(2007) 049[hep-ph/0604159]
2007 arXiv
-
[13]
Electroweak baryogenesis at high bubble wall velocities,
J. M. Cline and K. Kainulainen, “Electroweak baryogenesis at high bubble wall velocities,” Phys. Rev. D101(2020) 063525[arXiv:2001.00568]
2020 arXiv
-
[15]
Systematic moment expansion for electroweak baryogenesis,
K. Kainulainen and N. Venkatesan, “Systematic moment expansion for electroweak baryogenesis,” JCAP08(2024) 058[arXiv:2407.13639]
2024 arXiv
-
[16]
Brownian motion of a quantum oscillator,
J. S. Schwinger, “Brownian motion of a quantum oscillator,” J. Math. Phys.2(1961) 407–432
1961
-
[17]
Diagram Technique for Nonequilibrium Processes,
L. V. Keldysh, “Diagram Technique for Nonequilibrium Processes,” Sov. Phys. JETP20 (1965) 1018–1026
1965
-
[18]
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. W. A. Benjamin, New York, 1962
1962
-
[19]
Kinetic description of fermion flavor mixing and CP-violating sources for baryogenesis,
T. Konstandin, T. Prokopec, and M. G. Schmidt, “Kinetic description of fermion flavor mixing and CP-violating sources for baryogenesis,” Nucl. Phys. B716(2005) 373–400 [hep-ph/0410135]
2005 arXiv
-
[20]
MSSM electroweak baryogenesis – 39 – and flavor mixing in transport equations,
T. Konstandin, T. Prokopec, M. G. Schmidt, and M. Seco, “MSSM electroweak baryogenesis – 39 – and flavor mixing in transport equations,” Nucl. Phys. B738(2006) 1–22 [hep-ph/0505103]
2006 arXiv
-
[21]
Towards a kinetic theory for fermions with quantum coherence,
M. Herranen, K. Kainulainen, and P. M. Rahkila, “Towards a kinetic theory for fermions with quantum coherence,” Nucl. Phys. B810(2009) 389–426[arXiv:0807.1415]
2009 arXiv
-
[22]
Flavored Quantum Boltzmann Equations,
V. Cirigliano, C. Lee, M. J. Ramsey-Musolf, and S. Tulin, “Flavored Quantum Boltzmann Equations,” Phys. Rev. D81(2010) 103503[arXiv:0912.3523]
2010 arXiv
-
[23]
Resonant Flavor Oscillations in Electroweak Baryogenesis,
V. Cirigliano, C. Lee, and S. Tulin, “Resonant Flavor Oscillations in Electroweak Baryogenesis,” Phys. Rev. D84(2011) 056006[arXiv:1106.0747]
2011 arXiv
-
[24]
Towards a nonequilibrium quantum field theory approach to electroweak baryogenesis,
A. Riotto, “Towards a nonequilibrium quantum field theory approach to electroweak baryogenesis,” Phys. Rev. D53(1996) 5834–5841[hep-ph/9510271]
1996 arXiv
-
[25]
Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations,
A. Riotto, “Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations,” Nucl. Phys. B518(1998) 339–360[hep-ph/9712221]
1998 arXiv
-
[26]
The More relaxed supersymmetric electroweak baryogenesis,
A. Riotto, “The More relaxed supersymmetric electroweak baryogenesis,” Phys. Rev. D58 (1998) 095009[hep-ph/9803357]
1998 arXiv
-
[28]
Fluid equations for fast-moving electroweak bubble walls,
B. Laurent and J. M. Cline, “Fluid equations for fast-moving electroweak bubble walls,” Phys. Rev. D102(2020) 063516[arXiv:2007.10935]
2020 arXiv
-
[29]
On the wall velocity dependence of electroweak baryogenesis,
G. C. Dorsch, S. J. Huber, and T. Konstandin, “On the wall velocity dependence of electroweak baryogenesis,” JCAP08(2021) 020[arXiv:2106.06547]
2021 arXiv
-
[30]
First principles determination of bubble wall velocity,
B. Laurent and J. M. Cline, “First principles determination of bubble wall velocity,” Phys. Rev. D106(2022) 023501[arXiv:2204.13120]
2022 arXiv
-
[31]
Finite Width in out-of-Equilibrium Propagators and Kinetic Theory,
B. Garbrecht and M. Garny, “Finite Width in out-of-Equilibrium Propagators and Kinetic Theory,” Annals Phys.327(2012) 914–934[arXiv:1108.3688]
2012 arXiv
-
[32]
The Semiclassical propagator in field theory,
M. Joyce, K. Kainulainen, and T. Prokopec, “The Semiclassical propagator in field theory,” Phys. Lett. B468(1999) 128–133[hep-ph/9906411]
1999 arXiv
-
[33]
Quantum transport equations for a scalar field,
M. Joyce, K. Kainulainen, and T. Prokopec, “Quantum transport equations for a scalar field,” Phys. Lett. B474(2000) 402–410[hep-ph/9910535]
2000 arXiv
-
[34]
Electroweak baryogenesis from light fermion sources: A critical study,
J. M. Cline and B. Laurent, “Electroweak baryogenesis from light fermion sources: A critical study,” Phys. Rev. D104(2021) 083507[arXiv:2108.04249]
2021 arXiv
-
[35]
Electroweak baryogenesis in the CP-violating two-Higgs doublet model,
P. Basler, L. Biermann, M. M¨ uhlleitner, and J. M¨ uller, “Electroweak baryogenesis in the CP-violating two-Higgs doublet model,” Eur. Phys. J. C83(2023) 57[arXiv:2108.03580]
2023 arXiv
-
[36]
Source terms for electroweak baryogenesis in the vev-insertion approximation beyond leading order,
M. Postma and J. van de Vis, “Source terms for electroweak baryogenesis in the vev-insertion approximation beyond leading order,” JHEP02(2020) 090[arXiv:1910.11794]
2020 arXiv
-
[37]
A different perspective on the vev insertion approximation for electroweak baryogenesis,
M. Postma, “A different perspective on the vev insertion approximation for electroweak baryogenesis,” JHEP09(2021) 055[arXiv:2107.05971]
2021 arXiv
-
[38]
Bubble Trouble: a Review on Electroweak Baryogenesis
J. van de Vis, J. de Vries, and M. Postma, “Bubble Trouble: a Review on Electroweak Baryogenesis.”arXiv:2508.09989. – 40 –
Reviewed August 15, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.