Helicity Decay to Baryons: The Cosmological Evolution of $L_\mu-L_\tau$ Gauge Fields and Baryogenesis

Di Wu; Fumio Uchida; Kohei Kamada

REVIEW

Helicity Decay to Baryons: The Cosmological Evolution of $L_\mu-L_\tau$ Gauge Fields and Baryogenesis

Kohei Kamada, Fumio Uchida, Di Wu

High Energy Physics - Phenomenology · Submitted 10 Nov 2026 · 63 references

Pith's verdict: Solid, honest extension of axion-inflation baryogenesis: the frozen-regime analysis is the real contribution, and the headline contour is conditional on Ref. [24]'s Schwinger-suppression setup, which the authors flag but do not demonstrate.

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CitationDi Wu, Fumio Uchida, Kohei Kamada. "Helicity Decay to Baryons: The Cosmological Evolution of $L_\mu-L_\tau$ Gauge Fields and Baryogenesis." arXiv:2611.13537 (2026). https://pith.science/paper/KDM3GEMO

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Editor's note

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Worth a careful read. The genuinely new content is the claim that baryogenesis from the decaying U(1)_{Lμ−Lτ} helicity is dominated by the pre-turbulent frozen stage, and the resulting contour in the (η_H, H_inf) plane. The ingredients — axion-inflation magnetogenesis, MHD helicity decay, sphaleron reprocessing — all existed, but nobody had traced baryon number through the frozen stage and mapped where the observed asymmetry is actually produced. The paper also gets a clean, non-obvious physical result: net baryon and lepton asymmetries come out with opposite signs, so the positive lepton asymmetry that would explain the ACT helium hint drags a negative baryon asymmetry along with it, forcing H_inf < 10^-7 GeV. That statement is sharp and new.

The internal machinery is sound. They reduce the full Boltzmann system to a single closed ODE for η_B via chemical equilibrium, and validate the reduction and the frozen-regime approximation against the full numerical integration to about 10% (Fig. 2). The neglect of the CME is quantified at the few-percent level, not merely asserted. That is how this kind of work should be done.

Soft spots, in proportion. First, and this is the load-bearing one: the large-η_H branch of the contour rests entirely on the heavy-during-inflation/light-after-inflation mass hierarchy that suppresses Schwinger production. That is an external input from Ref. [24]; this paper does not show the hierarchy is dynamically realized or that Schwinger production is actually negligible at the specific points on its contour. Footnote 4 asserts the Weinberg-operator construction is consistent with finite X·X̃ and no lepton-number generation — asserted, not shown. The authors do acknowledge this in the Discussion and note the light-fermion bound η_H ≲ 1.4e-6, so it is an open question, not a concealed one. But the headline range η_H < 2.2e-4 should be read as conditional on accepting the Ref. [24] setup. Second, the contour is computed for a single benchmark coupling g = 3e-4; the sensitivity to g is not mapped, though they are explicit about the choice. Third, the end-state dynamics at U(1) breaking — whether helicity decays cleanly into lepton number rather than into string networks or monopole pairs — is genuinely uncertain, and again the paper says so in the Discussion.

Net: an honest, internally consistent paper that refines a known mechanism rather than inventing one, and it deserves a real referee. The referee's job will be to make the Schwinger-suppression consistency argument actual rather than assumed.

Referee report

Significance

If it holds, this is a genuinely new baryogenesis channel: unlike U(1)_Y or U(1)_{B-L} helicity baryogenesis, the L_mu-L_tau helicity sources flavor-specific lepton asymmetries that are only partially reprocessed into baryon number before sphaleron freeze-out, so the final baryon asymmetry is controlled by the earliest, pre-turbulent stage of the MHD evolution. The paper delivers two clean, falsifiable statements: the successful-baryogenesis requirement cuts the (eta_H, H_inf) plane more strongly than the backreaction bound, and the sign correlation between eta_B and eta_L exposes a tension with the positive-lepton-asymmetry interpretation of the ACT helium data. The technical core is sound and partly machine-checkable: the chemical-equilibrium reduction of Sec. 3.3.2 is algebraically consistent (I verified the rational coefficients eta_5 = (277/252)eta_B, d eta_B/dx = (56/79)gamma_X, and eta_{B-L} = (79/28)eta_B, including the hypercharge-neutrality conditions of Eq. 3.38), and the analytic frozen-regime formula is validated against the full Boltzmann system at the 10% level (Fig. 2).

Major objections (1)

[Sec. 2.2, footnote 4; Sec. 3.4; Sec. 4 (b231-b236)] The central parameter region, in particular the large-eta_H branch with eta_H up to 2.2e-4 and the initial condition eta_Le = eta_Lmu = eta_Ltau = 0 (Eq. 2.12 and Sec. 2.2), rests entirely on the assumption that the U(1)_{L_mu-L_tau}-charged fermions are heavy during inflation and light afterward, realized through the Weinberg-operator construction of Ref. [24]. The authors state this assumption explicitly and acknowledge its fragility in the Sec. 4 discussion (if the fermions remain light, the helicity-to-entropy ratio is capped near 1.4e-6, which removes much of the turbulent branch), so this is not an undisclosed limitation. What remains unresolved in the present manuscript is threefold. (i) Footnote 4 asserts that a finite X X-tilde background 'without lepton number generation is consistent' with a lepton-number-violating mass term; since the anomaly equation (Eq. 2.9) holds as an operator statement regardless of the fermion mass, the resolution of this point needs a derivation or an explicit pointer to the argument in Ref. [24], because the zero-initial-asymmetry condition of Sec. 2.2 hangs on it. (ii) The paper assumes the same lepton-number-violating operator is inactive between reheating and electroweak symmetry breaking, but does not argue why; if it remained active, the chemical-potential history used in Sec. 3.3 would be modified. (iii) No check is presented that Schwinger pair production is quantitatively negligible for the specific (xi, H_inf) points on the blue contour of Fig. 3; the suppression condition (fermion mass relative to the scale sqrt(g E) of the amplified electric field) should be evaluated along the contour rather than only in a generic regime. Since the headline numbers H_inf > 3.2e-8 GeV and eta_H < 2.2e-4 are quoted unconditionally in the abstract and Sec. 4, I would like to see these three points addressed: a demonstration (or a precise citation of a derivation in Ref. [24]) that the mass hierarchy is realized with sufficient suppression at the contour points, an argument that the lepton-number-violating operator is inactive after reheating, and an estimate of any residual initial lepton asymmetry relative to eta_B^obs.

Minor objections (5)

[Sec. 3.1 (b87-b88)] The neglect of the chiral magnetic effect in the MHD evolution of B and xi_M is justified with a qualitative 'below a few percent' statement, but unlike the Boltzmann-washout ratio quantified in Eq. (3.55), no formula or numerical value is given for the CME-to-Ohmic ratio in the induction equation; adding the estimate would make this load-bearing-for-the-lepton-sector claim checkable.
[Abstract and Sec. 3.4] The phrase 'parameter spaces where the observed baryon asymmetry can be generated in both the turbulent and dissipation-dominated regimes' (abstract, and echoed in Sec. 3.4) is at risk of overstating, since the paper itself finds that in the Re_M > 1 region the baryon asymmetry is generated in the pre-turbulent nearly frozen stage (Sec. 3.4 and Sec. 4); I suggest rewording to 'regions with Re_M > 1 and Re_M < 1' or an equivalent formulation that keeps this distinction.
[Sec. 4 and Fig. 3] The headline bounds eta_H < 2.2e-4 and H_inf > 3.2e-8 GeV are tied to the specific choice Y_P^max = 0.248, the 1-sigma upper limit of the PDG value; the abstract and Sec. 4 quote these numbers without the 1-sigma qualifier, and a sentence stating how the corner of the allowed region shifts under the 2-sigma value (Y_P ~ 0.251) would calibrate the reported thresholds.
[Eq. (2.13) and Sec. 3] The instantaneous-reheating assumption fixes T_reh and hence the available window x_EW - x_reh that controls the frozen-regime baryon yield in the Re_M > 1 region; a brief robustness statement on how eta_B scales for lower reheating temperatures (e.g., non-instantaneous reheating) would be helpful, since the assumption currently appears only parenthetically.
[References] Refs. [17] (arXiv 2504.07937) and [29] (arXiv 2609.07467) are cited with arXiv numbers only, without journal or publication status; please update these entries if they have appeared in refereed venues.

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The paper

The paper claims

A helical U(1) L_mu minus L_tau gauge field produced during axion inflation can generate the observed baryon asymmetry through helicity dissipation and electroweak sphalerons, under a specified parameter region.

The reading

The universe is filled with a small excess of matter over antimatter, and the Standard Model of particle physics cannot explain it. This paper investigates a cosmological mechanism: an axion-like particle during inflation can amplify one polarization of a new force, U(1) L_mu minus L_tau, creating a helical magnetic field. After inflation, this field decays in a hot plasma, and a quantum anomaly converts some of its helicity into lepton number, which is then partially converted into baryon number by sphaleron processes. The authors track the magnetic field evolution using magnetohydrodynamic models and solve Boltzmann equations for the particle asymmetries. They claim that if the Hubble scale during inflation is above 3.2 times 10 to the minus 8 GeV, and the initial helicity-to-entropy ratio is below 2.2 times 10 to the minus 4, the observed baryon asymmetry can be reproduced, at least for the benchmark coupling 3 times 10 to the minus 4. The mechanism is reliable only if several conditions hold: the Schwinger effect is suppressed during inflation, the charged fermions become light after inflation, and the magnetic helicity dissipates before electroweak sphalerons freeze out. The authors identify the main result as a constraint rather than a prediction, since the parameters are fitted to produce the observed asymmetry.

Extended reading notes

Core claim

The central claim, from the abstract and Section 4, is that the observed baryon asymmetry can be generated from the post-inflationary decay of helical U(1) L_mu minus L_tau gauge fields, with the parameter region eta_B = eta_obs^B realized for H_inf > 3.2e-8 GeV and eta_H < 2.2e-4, at the benchmark coupling g = 3e-4. The key assertion is that baryogenesis is dominated by the frozen MHD regime or the diffusion-dominated regime, and that the baryon asymmetry requirement imposes stronger constraints on H_inf and eta_H than the gauge-field backreaction bound.

Load-bearing premise

The load-bearing assumption is that Schwinger pair production of L_mu minus L_tau charged fermions is suppressed during inflation by making them heavy, and that they become light after inflation (Section 2.1, footnote 4, and Section 4). If this suppression is imperfect, the helicity-to-entropy ratio eta_H is strongly limited, and the initial lepton asymmetry need not be negligible. The paper relies on a concrete model from reference [24], but does not demonstrate within this paper that such a mass hierarchy is realized consistently with the anomaly equation.

Original abstract

We study baryogenesis from the post-inflationary decay of helical U(1)$_{L_\mu-L_\tau}$ gauge fields generated during axion inflation. Assuming that Schwinger pair production is suppressed during inflation, a large helicity-to-entropy ratio $\eta_H$ can be generated while keeping the initial lepton asymmetry just after inflation negligible. After reheating, the dissipation of magnetic helicity sources a lepton asymmetry through the chiral anomaly, which is partially converted into a baryon asymmetry by electroweak sphaleron processes. We find that there are parameter spaces where the observed baryon asymmetry can be generated in both the turbulent and dissipation-dominated regimes of the U(1)$_{L_\mu-L_\tau}$ magnetic field evolution. The baryon asymmetry generation in the turbulent regime is, however, dominated by the pre-turbulent nearly frozen regime. We further find that the requirement of successful baryogenesis imposes stronger constraints on the inflationary Hubble parameter and the helicity density generated during axion inflation than the requirement for the gauge-field energy not to backreact on the inflaton dynamics.

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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-11: 1 request, 5,163 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study baryogenesis from the post-inflationary decay of helical U(1)$_{L_\mu-L_\tau}$ gauge fields generated during axion inflation. Assuming that Schwinger pair production is suppressed during inflation, a large helicity-to-entropy ratio $\eta_H$ can be generated while keeping the initial lepton asymmetry just after inflation negligible. After reheating, the dissipation of magnetic helicity sources a lepton asymmetry through the chiral anomaly, which is partially converted into a baryon asymmetry by electroweak sphaleron processes. We find that there are parameter spaces where the observed baryon asymmetry can be generated in both the turbulent and dissipation-dominated regimes of the U(1)$_{L_\mu-L_\tau}$ magnetic field evolution. The baryon asymmetry generation in the turbulent regime is, however, dominated by the pre-turbulent nearly frozen regime. We further find that the requirement of successful baryogenesis imposes stronger constraints on the inflationary Hubble parameter and the helicity density generated during axion inflation than the requirement for the gauge-field energy not to backreact on the inflaton dynamics.

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 study baryogenesis from the post-inflationary decay of helical U(1)$_{L_\mu-L_\tau}$ gauge fields generated during axion inflation.	contribution 1.00	0.89	0.09	asserted 0.84
s1	Assuming that Schwinger pair production is suppressed during inflation, a large helicity-to-entropy ratio $\eta_H$ can be generated while keeping the initial lepton asymmetry just after inflation negligible.	result 0.77	0.36	0.07	hedged possibility 0.79
s2	After reheating, the dissipation of magnetic helicity sources a lepton asymmetry through the chiral anomaly, which is partially converted into a baryon asymmetry by electroweak sphaleron processes.	method 0.56	0.26	0.15	asserted 1.00
s3	We find that there are parameter spaces where the observed baryon asymmetry can be generated in both the turbulent and dissipation-dominated regimes of the U(1)$_{L_\mu-L_\tau}$ magnetic field evolution.	result 1.00	0.96	0.46	asserted 0.98
s4	The baryon asymmetry generation in the turbulent regime is, however, dominated by the pre-turbulent nearly frozen regime.	result 0.97	0.94	0.12	asserted 1.00
s5	We further find that the requirement of successful baryogenesis imposes stronger constraints on the inflationary Hubble parameter and the helicity density generated during axion inflation than the requirement for the gauge-field energy not to backreact on the inflaton dynamics.	result 0.86	0.93	0.29	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 0.49.

What was examined, and what was not

sources read

arXiv listing abstract v1

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.** A schematic figure representing our scenario. We show the evolution of the U(1)Lµ−Lτ magnetic helicity ηH in the red-dotted line, the lepton asymmetry ηLµ and ηLτ in the green dashed line, and the baryon asymmetry ηB in the blue solid line. In the slow-roll phase in the inflation, the magnetic helicity is generated through the ϕXX˜ coupling, and end up with Eq. (2.14). We assume ηLµ,τ = ηB = 0 at the end of inflation. Afterwards, the magnetic helicity is dissipated in the MHD evolution, which is associated with the lepton asymmetry generation. Before the electroweak symmetry…

**Figure 2.** Comparison between the full numerical solution of the Boltzmann equations (solid lines, Eqs. (3.24) – (3.29)) and the analytic approximations in the frozen regime for the baryonnumber evolution with the chemical equilibrium conditions, neglecting the CME contribution. The constant γSource approximation ( dashed lines, Eq. (3.56) for x ≤ x¯) as well as the solution taking into account the γSource evolution ( dotted lines, Eq. (3.52)) are shown. The blue, orange, green, red, and purple lines correspond to Hinf = 10−9 , 10−5 , 10−2 , 105 , 108 GeV, respectively, while ξ is determined…

**Figure 3.** Parameter space in the (ηH, Hinf) plane for gLµ−Lτ = 3 × 10−4 . The blue solid line shows the contour on which the the Lµ − Lτ helicity dissipation generates the observed baryon asymmetry, ηB = η obs B , through the electroweak sphaleron process. The gray stippled region, upper side of this contour is excluded due to the baryon overproduction. The purple solid line marks the ReM = 1 boundary, which determines if the Lµ − Lτ magnetic field evolution is in the non-linear turbulent regime or dissipation-dominated regime. The dark-gray solid line denotes the S = Sc boundary between the S

Figures reproduced from arXiv:2611.13537 by the authors.

References

Works cited (63)

[24]

Y. Hu, K. Kamada and D. Wu,Large lepton asymmetry from axion inflation and helium abundance hinted by ACT,JCAP05(2026) 070 [2512.21117]

View on Pith arXiv 2026
[2]

A. D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,Pisma Zh. Eksp. Teor. Fiz.5(1967) 32

View on Pith 1967
[3]

A. D. Dolgov,NonGUT baryogenesis,Phys. Rept.222(1992) 309

View on Pith 1992
[4]

M. M. Anber and E. Sabancilar,Hypermagnetic Fields and Baryon Asymmetry from Pseudoscalar Inflation,Phys. Rev. D92(2015) 101501 [1507.00744]

View on Pith Pith review arXiv 2015
[5]

P. Adshead, J. T. Giblin, T. R. Scully and E. I. Sfakianakis,Magnetogenesis from axion inflation,JCAP10(2016) 039 [1606.08474]

View on Pith Pith review arXiv 2016
[6]

D. Jim´ enez, K. Kamada, K. Schmitz and X.-J. Xu,Baryon asymmetry and gravitational waves from pseudoscalar inflation,JCAP12(2017) 011 [1707.07943]

View on Pith Pith review arXiv 2017
[7]

V. Domcke and K. Mukaida,Gauge Field and Fermion Production during Axion Inflation, JCAP11(2018) 020 [1806.08769]

View on Pith Pith review arXiv 2018
[8]

V. Domcke, B. von Harling, E. Morgante and K. Mukaida,Baryogenesis from axion inflation,JCAP10(2019) 032 [1905.13318]

View on Pith Pith review arXiv 2019
[9]

M. M. Anber and L. Sorbo,N-flationary magnetic fields,JCAP10(2006) 018 [astro-ph/0606534]

View on Pith Pith review arXiv 2006
[10]

M. Giovannini and M. E. Shaposhnikov,Primordial hypermagnetic fields and triangle anomaly,Phys. Rev. D57(1998) 2186 [hep-ph/9710234]

View on Pith Pith review arXiv 1998
[11]

T. Fujita and K. Kamada,Large-scale magnetic fields can explain the baryon asymmetry of the Universe,Phys. Rev. D93(2016) 083520 [1602.02109]

View on Pith Pith review arXiv 2016
[12]

K. Kamada and A. J. Long,Baryogenesis from decaying magnetic helicity,Phys. Rev. D94 (2016) 063501 [1606.08891]

View on Pith Pith review arXiv 2016
[13]

K. Kamada and A. J. Long,Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field,Phys. Rev. D94(2016) 123509 [1610.03074]

View on Pith Pith review arXiv 2016
[14]

Y. Cado and E. Sabancilar,Asymmetric Dark Matter and Baryogenesis from Pseudoscalar Inflation,JCAP04(2017) 047 [1611.02293]

View on Pith Pith review arXiv 2017
[15]

V. Domcke, K. Kamada, K. Mukaida, K. Schmitz and M. Yamada,Wash-in leptogenesis after axion inflation,JHEP01(2023) 053 [2210.06412]

View on Pith Pith review arXiv 2023
[16]

V. Domcke, K. Kamada, K. Mukaida, K. Schmitz and M. Yamada,Wash-In Leptogenesis, Phys. Rev. Lett.126(2021) 201802 [2011.09347]

View on Pith Pith review arXiv 2021
[17]

T. Boyer and A. Neronov,Baryon asymmetry constraints on magnetic field from the Electroweak epoch,2504.07937

View on Pith Pith review arXiv
[18]

Y. Hamada, K. Mukaida and F. Uchida,Symmetries of hot SM, magnetic flux baryogenesis from helicity decay,JHEP01(2026) 040 [2507.01576]

View on Pith arXiv 2026
[19]

H. Fukuda, Y. Hamada, K. Kamada, K. Mukaida and F. Uchida,Magnetic helicity, magnetic monopoles, and Higgs winding,JHEP03(2026) 127 [2509.25734]

View on Pith arXiv 2026
[20]

M. Fukugita and T. Yanagida,Baryogenesis Without Grand Unification,Phys. Lett. B174 (1986) 45. – 23 –

View on Pith 1986
[21]

F. R. Klinkhamer and N. S. Manton,A Saddle Point Solution in the Weinberg-Salam Theory,Phys. Rev. D30(1984) 2212

View on Pith 1984
[22]

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

View on Pith 1985
[23]

H. Fukuda, K. Kamada and T. Sichanugrist,Leptogenesis from magnetic helicity of gauged U(1) B−L,JHEP02(2025) 192 [2410.04701]

View on Pith Pith review arXiv 2025
[25]

S. Y. Khlebnikov and M. E. Shaposhnikov,The Statistical Theory of Anomalous Fermion Number Nonconservation,Nucl. Phys. B308(1988) 885

View on Pith 1988
[26]

J. A. Harvey and M. S. Turner,Cosmological Baryon and Lepton Number in the Presence of Electroweak Fermion Number Violation,Phys. Rev. D42(1990) 3344

View on Pith 1990
[27]

E. Nardi, Y. Nir, J. Racker and E. Roulet,On Higgs and sphaleron effects during the leptogenesis era,JHEP01(2006) 068 [hep-ph/0512052]

View on Pith Pith review arXiv 2006
[28]

S. Davidson, E. Nardi and Y. Nir,Leptogenesis,Phys. Rept.466(2008) 105 [0802.2962]

View on Pith Pith review arXiv 2008
[29]

C. Benso, D. B¨ odeker, K. Kamada, K. Mukaida, L. Sagunski, P. Schicho et al.,Baryon number freeze-out in the Standard Model, precisely,2609.07467

View on Pith Pith review arXiv
[30]

M. Giovannini and M. E. Shaposhnikov,Primordial magnetic fields, anomalous isocurvature fluctuations and big bang nucleosynthesis,Phys. Rev. Lett.80(1998) 22 [hep-ph/9708303]

View on Pith Pith review arXiv 1998
[31]

F. Uchida, M. Fujiwara, K. Kamada and J. Yokoyama,New comprehensive description of the scaling evolution of the cosmological magneto-hydrodynamic system,JCAP08(2025) 017 [2405.06194]

View on Pith Pith review arXiv 2025
[32]

M. S. Turner and L. M. Widrow,Inflation Produced, Large Scale Magnetic Fields,Phys. Rev. D37(1988) 2743

View on Pith 1988
[33]

K. Freese, J. A. Frieman and A. V. Olinto,Natural Inflation with Pseudo - Nambu-Goldstone Bosons,Phys. Rev. Lett.65(1990) 3233

View on Pith 1990
[34]

W. D. Garretson, G. B. Field and S. M. Carroll,Primordial magnetic fields from pseudoGoldstone bosons,Phys. Rev. D46(1992) 5346 [hep-ph/9209238]

View on Pith Pith review arXiv 1992
[35]

M. M. Anber and L. Sorbo,Naturally inflating on steep potentials through electromagnetic dissipation,Phys. Rev. D81(2010) 043534 [0908.4089]

View on Pith Pith review arXiv 2010
[36]

R. Foot,New Physics From Electric Charge Quantization?,Mod. Phys. Lett. A6(1991) 527

View on Pith 1991
[37]

X. G. He, G. C. Joshi, H. Lew and R. R. Volkas,NEW Z-prime PHENOMENOLOGY,Phys. Rev. D43(1991) 22

View on Pith 1991
[38]

A. Brandenburg, K. Enqvist and P. Olesen,Large scale magnetic fields from hydromagnetic turbulence in the very early universe,Phys. Rev. D54(1996) 1291 [astro-ph/9602031]

View on Pith Pith review arXiv 1996
[39]

P. B. Arnold, G. D. Moore and L. G. Yaffe,Transport coefficients in high temperature gauge theories. 1. Leading log results,JHEP11(2000) 001 [hep-ph/0010177]

View on Pith Pith review arXiv 2000
[40]

K. Kamada, Y. Tsai and T. Vachaspati,Magnetic Field Transfer From A Hidden Sector, Phys. Rev. D98(2018) 043501 [1803.08051]

View on Pith Pith review arXiv 2018
[41]

M. Joyce and M. E. Shaposhnikov,Primordial magnetic fields, right-handed electrons, and the Abelian anomaly,Phys. Rev. Lett.79(1997) 1193 [astro-ph/9703005]. – 24 –

View on Pith Pith review arXiv 1997
[42]

Y. Akamatsu and N. Yamamoto,Chiral Plasma Instabilities,Phys. Rev. Lett.111(2013) 052002 [1302.2125]

View on Pith Pith review arXiv 2013
[43]

A. Brandenburg, K. Kamada and J. Schober,Decay law of magnetic turbulence with helicity balanced by chiral fermions,Phys. Rev. Res.5(2023) L022028 [2302.00512]

View on Pith Pith review arXiv 2023
[44]

A. Brandenburg, K. Kamada, K. Mukaida, K. Schmitz and J. Schober,Chiral magnetohydrodynamics with zero total chirality,Phys. Rev. D108(2023) 063529 [2304.06612]

View on Pith Pith review arXiv 2023
[45]

R. Banerjee and K. Jedamzik,The Evolution of cosmic magnetic fields: From the very early universe, to recombination, to the present,Phys. Rev. D70(2004) 123003 [astro-ph/0410032]

View on Pith Pith review arXiv 2004
[46]

D. Biskamp,Nonlinear magnetohydrodynamics. 1993

View on Pith 1993
[47]

D. N. Hosking and A. A. Schekochihin,Reconnection-Controlled Decay of Magnetohydrodynamic Turbulence and the Role of Invariants,Phys. Rev. X11(2021) 041005 [2012.01393]

View on Pith Pith review arXiv 2021
[48]

P. Bhat, M. Zhou and N. F. Loureiro,Inverse energy transfer in decaying, three-dimensional, non-helical magnetic turbulence due to magnetic reconnection,Mon. Not. Roy. Astron. Soc. 501(2021) 3074 [2007.07325]

View on Pith Pith review arXiv 2021
[49]

C. Anandavijayan and P. Bhat,Spectral Evolution and Current Sheet Analysis as Probes of Reconnection-Mediated Decay in Magnetically Dominated Turbulence,2601.17955

View on Pith arXiv
[50]

D. N. Hosking and A. A. Schekochihin,Cosmic-void observations reconciled with primordial magnetogenesis,Nature Commun.14(2023) 7523 [2203.03573]

View on Pith Pith review arXiv 2023
[51]

H. Ji and W. Daughton,Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas,Physics of Plasmas18(2011) 111207 [1109.0756]

View on Pith Pith review arXiv 2011
[52]

L. D. McLerran, E. Mottola and M. E. Shaposhnikov,Sphalerons and Axion Dynamics in High Temperature QCD,Phys. Rev. D43(1991) 2027

View on Pith 1991
[53]

J. Annala and K. Rummukainen,Electroweak sphaleron in a magnetic field,Phys. Rev. D 107(2023) 073006 [2301.08626]

View on Pith Pith review arXiv 2023
[54]

S. Y. Khlebnikov and M. E. Shaposhnikov,Melting of the Higgs vacuum: Conserved numbers at high temperature,Phys. Lett. B387(1996) 817 [hep-ph/9607386]

View on Pith Pith review arXiv 1996
[55]

M. Laine and M. E. Shaposhnikov,A Remark on sphaleron erasure of baryon asymmetry, Phys. Rev. D61(2000) 117302 [hep-ph/9911473]

View on Pith Pith review arXiv 2000
[56]

B. A. Campbell, S. Davidson, J. R. Ellis and K. A. Olive,On the baryon, lepton flavor and right-handed electron asymmetries of the universe,Phys. Lett. B297(1992) 118 [hep-ph/9302221]

View on Pith Pith review arXiv 1992
[57]

W. Buchmuller and M. Plumacher,Spectator processes and baryogenesis,Phys. Lett. B511 (2001) 74 [hep-ph/0104189]

View on Pith Pith review arXiv 2001
[58]

V. Domcke, Y. Ema, K. Mukaida and M. Yamada,Spontaneous Baryogenesis from Axions with Generic Couplings,JHEP08(2020) 096 [2006.03148]

View on Pith Pith review arXiv 2020
[59]

V. Domcke, M. Escudero, M. Fernandez Navarro and S. Sandner,A limit on the total lepton number in the Universe from BBN and the CMB,JCAP02(2026) 017 [2510.02438]. [60]Particle Data Groupcollaboration,Review of particle physics,Phys. Rev. D110(2024) 030001. – 25 – [61]Atacama Cosmology Telescopecollaboration,The Atacama Cosmology Telescope: DR6 power spect...

View on Pith arXiv 2026
[62]

H. Yanagisawa et al.,EMPRESS. XV. A New Determination of the Primordial Helium Abundance Suggesting a Moderately LowY P Value,2506.24050

View on Pith Pith review arXiv
[63]

K. Kamada, F. Uchida and J. Yokoyama,Baryon isocurvature constraints on the primordial hypermagnetic fields,JCAP04(2021) 034 [2012.14435]

View on Pith Pith review arXiv 2021
[64]

N. Bernal, J. P. Neto, J. Silva-Malpartida and F. S. Queiroz,Enabling thermal dark matter within the vanilla Lµ-Lτmodel,Phys. Rev. D112(2025) 075042 [2507.02048]

View on Pith arXiv 2025
[65]

E. V. Gorbar, K. Schmitz, O. O. Sobol and S. I. Vilchinskii,Gauge-field production during axion inflation in the gradient expansion formalism,Phys. Rev. D104(2021) 123504 [2109.01651]

View on Pith Pith review arXiv 2021
[66]

R. von Eckardstein, K. Schmitz and O. Sobol,On the Schwinger effect during axion inflation,JHEP02(2025) 096 [2408.16538]. – 26 –

View on Pith Pith review arXiv 2025

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] [24]

Y. Hu, K. Kamada and D. Wu,Large lepton asymmetry from axion inflation and helium abundance hinted by ACT,JCAP05(2026) 070 [2512.21117]

View on Pith arXiv 2026

[2] [2]

A. D. Sakharov,Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,Pisma Zh. Eksp. Teor. Fiz.5(1967) 32

View on Pith 1967

[3] [3]

A. D. Dolgov,NonGUT baryogenesis,Phys. Rept.222(1992) 309

View on Pith 1992

[4] [4]

M. M. Anber and E. Sabancilar,Hypermagnetic Fields and Baryon Asymmetry from Pseudoscalar Inflation,Phys. Rev. D92(2015) 101501 [1507.00744]

View on Pith Pith review arXiv 2015

[5] [5]

P. Adshead, J. T. Giblin, T. R. Scully and E. I. Sfakianakis,Magnetogenesis from axion inflation,JCAP10(2016) 039 [1606.08474]

View on Pith Pith review arXiv 2016

[6] [6]

D. Jim´ enez, K. Kamada, K. Schmitz and X.-J. Xu,Baryon asymmetry and gravitational waves from pseudoscalar inflation,JCAP12(2017) 011 [1707.07943]

View on Pith Pith review arXiv 2017

[7] [7]

V. Domcke and K. Mukaida,Gauge Field and Fermion Production during Axion Inflation, JCAP11(2018) 020 [1806.08769]

View on Pith Pith review arXiv 2018

[8] [8]

V. Domcke, B. von Harling, E. Morgante and K. Mukaida,Baryogenesis from axion inflation,JCAP10(2019) 032 [1905.13318]

View on Pith Pith review arXiv 2019

[9] [9]

M. M. Anber and L. Sorbo,N-flationary magnetic fields,JCAP10(2006) 018 [astro-ph/0606534]

View on Pith Pith review arXiv 2006

[10] [10]

M. Giovannini and M. E. Shaposhnikov,Primordial hypermagnetic fields and triangle anomaly,Phys. Rev. D57(1998) 2186 [hep-ph/9710234]

View on Pith Pith review arXiv 1998

[11] [11]

T. Fujita and K. Kamada,Large-scale magnetic fields can explain the baryon asymmetry of the Universe,Phys. Rev. D93(2016) 083520 [1602.02109]

View on Pith Pith review arXiv 2016

[12] [12]

K. Kamada and A. J. Long,Baryogenesis from decaying magnetic helicity,Phys. Rev. D94 (2016) 063501 [1606.08891]

View on Pith Pith review arXiv 2016

[13] [13]

K. Kamada and A. J. Long,Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field,Phys. Rev. D94(2016) 123509 [1610.03074]

View on Pith Pith review arXiv 2016

[14] [14]

Y. Cado and E. Sabancilar,Asymmetric Dark Matter and Baryogenesis from Pseudoscalar Inflation,JCAP04(2017) 047 [1611.02293]

View on Pith Pith review arXiv 2017

[15] [15]

V. Domcke, K. Kamada, K. Mukaida, K. Schmitz and M. Yamada,Wash-in leptogenesis after axion inflation,JHEP01(2023) 053 [2210.06412]

View on Pith Pith review arXiv 2023

[16] [16]

V. Domcke, K. Kamada, K. Mukaida, K. Schmitz and M. Yamada,Wash-In Leptogenesis, Phys. Rev. Lett.126(2021) 201802 [2011.09347]

View on Pith Pith review arXiv 2021

[17] [17]

T. Boyer and A. Neronov,Baryon asymmetry constraints on magnetic field from the Electroweak epoch,2504.07937

View on Pith Pith review arXiv

[18] [18]

Y. Hamada, K. Mukaida and F. Uchida,Symmetries of hot SM, magnetic flux baryogenesis from helicity decay,JHEP01(2026) 040 [2507.01576]

View on Pith arXiv 2026

[19] [19]

H. Fukuda, Y. Hamada, K. Kamada, K. Mukaida and F. Uchida,Magnetic helicity, magnetic monopoles, and Higgs winding,JHEP03(2026) 127 [2509.25734]

View on Pith arXiv 2026

[20] [20]

M. Fukugita and T. Yanagida,Baryogenesis Without Grand Unification,Phys. Lett. B174 (1986) 45. – 23 –

View on Pith 1986

[21] [21]

F. R. Klinkhamer and N. S. Manton,A Saddle Point Solution in the Weinberg-Salam Theory,Phys. Rev. D30(1984) 2212

View on Pith 1984

[22] [22]

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

View on Pith 1985

[23] [23]

H. Fukuda, K. Kamada and T. Sichanugrist,Leptogenesis from magnetic helicity of gauged U(1) B−L,JHEP02(2025) 192 [2410.04701]

View on Pith Pith review arXiv 2025

[24] [25]

S. Y. Khlebnikov and M. E. Shaposhnikov,The Statistical Theory of Anomalous Fermion Number Nonconservation,Nucl. Phys. B308(1988) 885

View on Pith 1988

[25] [26]

J. A. Harvey and M. S. Turner,Cosmological Baryon and Lepton Number in the Presence of Electroweak Fermion Number Violation,Phys. Rev. D42(1990) 3344

View on Pith 1990

[26] [27]

E. Nardi, Y. Nir, J. Racker and E. Roulet,On Higgs and sphaleron effects during the leptogenesis era,JHEP01(2006) 068 [hep-ph/0512052]

View on Pith Pith review arXiv 2006

[27] [28]

S. Davidson, E. Nardi and Y. Nir,Leptogenesis,Phys. Rept.466(2008) 105 [0802.2962]

View on Pith Pith review arXiv 2008

[28] [29]

C. Benso, D. B¨ odeker, K. Kamada, K. Mukaida, L. Sagunski, P. Schicho et al.,Baryon number freeze-out in the Standard Model, precisely,2609.07467

View on Pith Pith review arXiv

[29] [30]

M. Giovannini and M. E. Shaposhnikov,Primordial magnetic fields, anomalous isocurvature fluctuations and big bang nucleosynthesis,Phys. Rev. Lett.80(1998) 22 [hep-ph/9708303]

View on Pith Pith review arXiv 1998

[30] [31]

F. Uchida, M. Fujiwara, K. Kamada and J. Yokoyama,New comprehensive description of the scaling evolution of the cosmological magneto-hydrodynamic system,JCAP08(2025) 017 [2405.06194]

View on Pith Pith review arXiv 2025

[31] [32]

M. S. Turner and L. M. Widrow,Inflation Produced, Large Scale Magnetic Fields,Phys. Rev. D37(1988) 2743

View on Pith 1988

[32] [33]

K. Freese, J. A. Frieman and A. V. Olinto,Natural Inflation with Pseudo - Nambu-Goldstone Bosons,Phys. Rev. Lett.65(1990) 3233

View on Pith 1990

[33] [34]

W. D. Garretson, G. B. Field and S. M. Carroll,Primordial magnetic fields from pseudoGoldstone bosons,Phys. Rev. D46(1992) 5346 [hep-ph/9209238]

View on Pith Pith review arXiv 1992

[34] [35]

M. M. Anber and L. Sorbo,Naturally inflating on steep potentials through electromagnetic dissipation,Phys. Rev. D81(2010) 043534 [0908.4089]

View on Pith Pith review arXiv 2010

[35] [36]

R. Foot,New Physics From Electric Charge Quantization?,Mod. Phys. Lett. A6(1991) 527

View on Pith 1991

[36] [37]

X. G. He, G. C. Joshi, H. Lew and R. R. Volkas,NEW Z-prime PHENOMENOLOGY,Phys. Rev. D43(1991) 22

View on Pith 1991

[37] [38]

A. Brandenburg, K. Enqvist and P. Olesen,Large scale magnetic fields from hydromagnetic turbulence in the very early universe,Phys. Rev. D54(1996) 1291 [astro-ph/9602031]

View on Pith Pith review arXiv 1996

[38] [39]

P. B. Arnold, G. D. Moore and L. G. Yaffe,Transport coefficients in high temperature gauge theories. 1. Leading log results,JHEP11(2000) 001 [hep-ph/0010177]

View on Pith Pith review arXiv 2000

[39] [40]

K. Kamada, Y. Tsai and T. Vachaspati,Magnetic Field Transfer From A Hidden Sector, Phys. Rev. D98(2018) 043501 [1803.08051]

View on Pith Pith review arXiv 2018

[40] [41]

M. Joyce and M. E. Shaposhnikov,Primordial magnetic fields, right-handed electrons, and the Abelian anomaly,Phys. Rev. Lett.79(1997) 1193 [astro-ph/9703005]. – 24 –

View on Pith Pith review arXiv 1997

[41] [42]

Y. Akamatsu and N. Yamamoto,Chiral Plasma Instabilities,Phys. Rev. Lett.111(2013) 052002 [1302.2125]

View on Pith Pith review arXiv 2013

[42] [43]

A. Brandenburg, K. Kamada and J. Schober,Decay law of magnetic turbulence with helicity balanced by chiral fermions,Phys. Rev. Res.5(2023) L022028 [2302.00512]

View on Pith Pith review arXiv 2023

[43] [44]

A. Brandenburg, K. Kamada, K. Mukaida, K. Schmitz and J. Schober,Chiral magnetohydrodynamics with zero total chirality,Phys. Rev. D108(2023) 063529 [2304.06612]

View on Pith Pith review arXiv 2023

[44] [45]

R. Banerjee and K. Jedamzik,The Evolution of cosmic magnetic fields: From the very early universe, to recombination, to the present,Phys. Rev. D70(2004) 123003 [astro-ph/0410032]

View on Pith Pith review arXiv 2004

[45] [46]

D. Biskamp,Nonlinear magnetohydrodynamics. 1993

View on Pith 1993

[46] [47]

D. N. Hosking and A. A. Schekochihin,Reconnection-Controlled Decay of Magnetohydrodynamic Turbulence and the Role of Invariants,Phys. Rev. X11(2021) 041005 [2012.01393]

View on Pith Pith review arXiv 2021

[47] [48]

P. Bhat, M. Zhou and N. F. Loureiro,Inverse energy transfer in decaying, three-dimensional, non-helical magnetic turbulence due to magnetic reconnection,Mon. Not. Roy. Astron. Soc. 501(2021) 3074 [2007.07325]

View on Pith Pith review arXiv 2021

[48] [49]

C. Anandavijayan and P. Bhat,Spectral Evolution and Current Sheet Analysis as Probes of Reconnection-Mediated Decay in Magnetically Dominated Turbulence,2601.17955

View on Pith arXiv

[49] [50]

D. N. Hosking and A. A. Schekochihin,Cosmic-void observations reconciled with primordial magnetogenesis,Nature Commun.14(2023) 7523 [2203.03573]

View on Pith Pith review arXiv 2023

[50] [51]

H. Ji and W. Daughton,Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas,Physics of Plasmas18(2011) 111207 [1109.0756]

View on Pith Pith review arXiv 2011

[51] [52]

L. D. McLerran, E. Mottola and M. E. Shaposhnikov,Sphalerons and Axion Dynamics in High Temperature QCD,Phys. Rev. D43(1991) 2027

View on Pith 1991

[52] [53]

J. Annala and K. Rummukainen,Electroweak sphaleron in a magnetic field,Phys. Rev. D 107(2023) 073006 [2301.08626]

View on Pith Pith review arXiv 2023

[53] [54]

S. Y. Khlebnikov and M. E. Shaposhnikov,Melting of the Higgs vacuum: Conserved numbers at high temperature,Phys. Lett. B387(1996) 817 [hep-ph/9607386]

View on Pith Pith review arXiv 1996

[54] [55]

M. Laine and M. E. Shaposhnikov,A Remark on sphaleron erasure of baryon asymmetry, Phys. Rev. D61(2000) 117302 [hep-ph/9911473]

View on Pith Pith review arXiv 2000

[55] [56]

B. A. Campbell, S. Davidson, J. R. Ellis and K. A. Olive,On the baryon, lepton flavor and right-handed electron asymmetries of the universe,Phys. Lett. B297(1992) 118 [hep-ph/9302221]

View on Pith Pith review arXiv 1992

[56] [57]

W. Buchmuller and M. Plumacher,Spectator processes and baryogenesis,Phys. Lett. B511 (2001) 74 [hep-ph/0104189]

View on Pith Pith review arXiv 2001

[57] [58]

V. Domcke, Y. Ema, K. Mukaida and M. Yamada,Spontaneous Baryogenesis from Axions with Generic Couplings,JHEP08(2020) 096 [2006.03148]

View on Pith Pith review arXiv 2020

[58] [59]

V. Domcke, M. Escudero, M. Fernandez Navarro and S. Sandner,A limit on the total lepton number in the Universe from BBN and the CMB,JCAP02(2026) 017 [2510.02438]. [60]Particle Data Groupcollaboration,Review of particle physics,Phys. Rev. D110(2024) 030001. – 25 – [61]Atacama Cosmology Telescopecollaboration,The Atacama Cosmology Telescope: DR6 power spect...

View on Pith arXiv 2026

[59] [62]

H. Yanagisawa et al.,EMPRESS. XV. A New Determination of the Primordial Helium Abundance Suggesting a Moderately LowY P Value,2506.24050

View on Pith Pith review arXiv

[60] [63]

K. Kamada, F. Uchida and J. Yokoyama,Baryon isocurvature constraints on the primordial hypermagnetic fields,JCAP04(2021) 034 [2012.14435]

View on Pith Pith review arXiv 2021

[61] [64]

N. Bernal, J. P. Neto, J. Silva-Malpartida and F. S. Queiroz,Enabling thermal dark matter within the vanilla Lµ-Lτmodel,Phys. Rev. D112(2025) 075042 [2507.02048]

View on Pith arXiv 2025

[62] [65]

E. V. Gorbar, K. Schmitz, O. O. Sobol and S. I. Vilchinskii,Gauge-field production during axion inflation in the gradient expansion formalism,Phys. Rev. D104(2021) 123504 [2109.01651]

View on Pith Pith review arXiv 2021

[63] [66]

R. von Eckardstein, K. Schmitz and O. Sobol,On the Schwinger effect during axion inflation,JHEP02(2025) 096 [2408.16538]. – 26 –

View on Pith Pith review arXiv 2025