Primordial Hypermagnetic Fields and Triangle Anomaly

Cambridge); M. E. Shaposhnikov (CERN); M. Giovannini (DAMTP

REVIEW

Primordial Hypermagnetic Fields and Triangle Anomaly

M. Giovannini (DAMTP, Cambridge), M. E. Shaposhnikov (CERN)

High Energy Physics - Phenomenology · Submitted 3 Oct 1997 · 53 references

Pith's verdict: A clean, honest derivation of anomalous MHD with a self-consistent BBN bound, but the abstract oversells the fluctuation amplitude and the promised nonlinear check never arrives.

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CitationCambridge), M. E. Shaposhnikov (CERN), M. Giovannini (DAMTP. "Primordial Hypermagnetic Fields and Triangle Anomaly." arXiv:hep-ph/9710234 (1997). https://pith.science/paper/RC3OM3LY

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Editor's note

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The thing worth knowing: the AMHD formalism here is real and cleanly done. Eqs. (2.14), (2.19), (2.22) and (2.24) generalize ordinary MHD to the anomalous case in a way that is straightforward to follow, and the correlation-function algebra in Appendices A and B — particularly the four-point helicity correlator (4.14) — is explicit enough to re-derive. The Meissner-pressure argument in §6.1 (Eq. 6.2) is a nice, simple, checkable point about making the EW transition first order. Credit where due: the authors are unusually candid about their own limits, stating that the approximation breaks down for ε < 0.05 and calling the Δ ~ 10³ estimate of Eq. (5.1) 'unlikely to be correct.' That honesty is to their credit and it is also the source of my main reservation about the abstract, not the body. The stress-test note is right on the key point: the BBN bound (5.4) is derived at Δ ~ 10⁻¹⁰, deep in the linear regime, so the back-reaction worry does not land on the bound itself. The bound is internally self-consistent. The soft spot is the abstract's 'sizeable matter–antimatter fluctuations' (abstract:s3), which requires extrapolating (4.15) to Δ ~ 1 where the authors themselves say the linear treatment fails. They promise to return to this in Section 6; Section 6 discusses the phase transition and Chern–Simons condensates, not the nonlinear fluctuation problem. That gap is real. Second, §5.3 shows that at the bound Γ < ΓH unless TR > 10⁵ TeV, so the whole stochastic story is conditional on BSM physics (MSSM with large tan β, say). The abstract does not say this. The Chern–Simons section is explicitly speculative and the authors say so. None of this is fatal; the framework holds and the derivations are reproducible. Who should read it: anyone working on primordial magnetic fields, anomalous transport, or EW baryogenesis. The AMHD equations are the durable contribution and will be cited. The BBN exclusion plot is worth taking seriously as a constraint, with the caveat that it lives in a specific BSM corner. I would send this to a serious referee — the formalism deserves scrutiny and the abstract should be tightened to match the body's caveats.

Referee report

Significance

The AMHD formalism is a genuine and durable contribution: the derivation from the anomaly equation through the effective Lagrangian to the coupled field-chemical-potential system is explicit, and Appendices A and B supply the correlation-function algebra needed to turn a stochastic background into a computable fluctuation amplitude. The BBN bound (5.4) is a new, falsifiable constraint on small-scale primordial hypermagnetic fields, and the comparison with existing CMB and Faraday-rotation bounds in §5.2 is useful. The observation in §6.1 that a primordial field can make the electroweak phase transition strongly first order even for large Higgs masses is an interesting and physically motivated idea. The paper is honest about its approximations in the body, and the overlap with the companion paper [26] is properly disclosed.

Major objections (3)

[§5.1, Eq. (5.1), Fig. 1, and abstract:s3] The abstract's claim that 'sizeable matter-antimatter fluctuations can be generated' rests on extrapolating the linear formula (4.15) to Δ ~ 1. The authors themselves state in §5.1 that the Δ ~ 10^3 estimate of Eq. (5.1) is 'unlikely to be correct' because back-reaction must be included, and they write 'we will come back to it in Section 6.' Section 6, however, discusses the electroweak phase transition and Chern-Simons condensates and does not return to the nonlinear fluctuation problem. The promised numerical check of the nonlinear AMHD system is therefore absent. Either the check should be supplied, or the abstract and Fig. 1 should be softened to state that the large-Δ values are extrapolations of the linear formula whose physical validity is not established. Note that the bound (5.4) itself is derived at Δ ~ 10^-10, deep in the linear regime, and is not affected by this concern.
[§5.3 and abstract:s5] The bound (5.4) is derived under the hierarchy Γ > ΓH, but §5.3 shows that in the minimal standard model this requires H^2/T^4 < 10^-11, i.e. essentially no interesting field, and that for the bound to be relevant one needs the right-electron perturbative freezing temperature T_R > 10^5 TeV, which is a BSM regime. The body is explicit about this ('for MSM, one hardly expects any cosmological consequences'), but the abstract presents the BBN constraint as general and does not state the BSM requirement. The abstract should either state the regime of validity or qualify the claim that constraints are derived.
[§6.1, Eq. (6.2), and abstract:s6] The claim that a strong enough hypermagnetic field makes the electroweak phase transition strongly first order is based on the Meissner-pressure estimate (6.2), which assumes a uniform field and a planar domain wall and explicitly neglects loop corrections associated with the magnetic field. For a stochastic background whose correlation length may be comparable to or shorter than the bubble size, the pressure argument needs justification; the paper acknowledges this only for bubbles larger than the diffusivity scale. The quantitative thresholds quoted (⟨|H|^2⟩/T_c^4 > 0.06 for m_H = 80 GeV and > 0.3 for m_H = 160 GeV) are presented without an error estimate. Since this is one of the abstract's headline claims, the authors should either justify the uniform-field approximation more carefully or attach a conservative uncertainty to the thresholds.

Minor objections (7)

[Eq. (4.15) and Eq. (5.1)] The coefficient C(ε) in (4.15) contains Γ(ε/2), which diverges as 2/ε when ε → 0, so the flat-spectrum estimate (5.1) is not the ε → 0 limit of (4.15). The paper restricts the plots to ε > 0.05 because 'the corrections appearing in Eq. (4.15) are not under control' below that, but the tension between (5.1) and (4.15) should be stated explicitly so that readers do not take (5.1) as the ε → 0 value of the general formula.
[§4, notation] The quantity ⃗B(τ_c) = ⃗H(τ_c)/T^2(τ_c) is introduced in §4 and then used interchangeably with ⃗H in Eqs. (4.14)-(4.16) and in Appendix B. A single definition and consistent notation would make the correlation-function algebra easier to follow.
[Fig. 1 caption] The caption should state that the plotted values are evaluations of the linear formula (4.15) and that for Δ ≳ 1 the linear treatment is not under control, as the authors themselves note in §5.1. As it stands, the figure can be read as a physical prediction of matter-antimatter domains with Δ ~ 10^3-10^4.
[Eq. (2.16)] The chemical potentials are quoted as a multi-line array without derivation. A short appendix or a pointer to the specific equations in [34] from which the coefficients follow would help the reader verify the numerical factors, particularly the coefficient 783/88 that propagates into (2.24) and (2.32).
[§6.2] The Chern-Simons wave configuration (6.3) is assumed rather than derived, and the authors state 'We have no idea whether these types of background can or cannot be generated by some mechanism.' A sentence identifying the class of mechanisms (inflationary, phase-transition, or dynamo) that could plausibly produce such a configuration would make the conditional claim easier to assess.
[§2.3, Eqs. (2.29)-(2.32)] The time integral in (2.29) is evaluated at t ~ t_c. Since Γ_H scales as T^6 (for a frozen-in field with H ∝ T^2) while Γ scales roughly as T, the ratio Γ/Γ_H varies by many orders of magnitude over the integration range, and the regime Γ > Γ_H may not hold throughout. The paper should show explicitly that the integrand is dominated by t ~ t_c, or state the approximation under which the replacement is made.
[typographical] There are several typographical errors: 'resepctively' (p. 35), 'are no under control' (p. 26), and 'Enqvis' in Ref. [11]. The OCR-garbled radical in the definition of C(ε) in (4.15) should be replaced by an explicit √π.

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The paper

The paper claims

A tangled primordial hypercharge field could have written fermion number into the early plasma, leaving matter-antimatter domains that standard nucleosynthesis would forbid.

The reading

The paper asks what a primordial hypercharge magnetic field does in the hot plasma above the electroweak scale, where the field couples chirally to fermions instead of vectorially as the ordinary photon does. The authors' point of departure is that any non-uniform hypermagnetic field necessarily drags a hyperelectric field along with it through finite conductivity, so the anomaly source $g'^2/(4π^2)$ times the helicity density $H_Y · ∇ × H_Y$ need not vanish, and the triangle anomaly then converts field energy into right-handed electron number. Generalizing magnetohydrodynamics to include this anomalous term lets them solve for the induced chemical potential and, at the electroweak phase transition, for the Chern-Simons number that must be dumped back into real fermions when the hypermagnetic field becomes an ordinary magnetic field. If that chain holds, a stochastic hypermagnetic background would leave the early universe with matter-antimatter domains near the neutron diffusion scale, and demanding that homogeneous Big Bang nucleosynthesis survive turns into a bound on the slope and amplitude of the primordial magnetic spectrum. The same field, acting through Meissner pressure on the phase boundary, could also make the electroweak transition strongly first order, and a topologically non-trivial Chern-Simons wave could generate net baryon number outright.

What carries the argument

The carrying object is the anomalous magnetohydrodynamics (AMHD) system: the hypermagnetic diffusivity equation $∂H_Y/∂t = -(4α'/πσ) ∇ × (µ_R H_Y) + (1/σ_c)∇^2 H_Y$, derived from a generalized Ohm's law whose extra term $(α'/π)µ_R H_Y$ is a current parallel to the field, fed by finite fermion density. Coupled to the kinetic equation $∂(µ_R/T)/∂t = -(g'^2/4π^2σ_cT^3)(783/88) H_Y · ∇ × H_Y - (Γ+Γ_H)(µ_R/T)$, this closes into a system in which the field and the fermion number exchange energy. The anomaly-induced current is the formal analogue of the dynamo $α$-term of ordinary MHD, and the authors use that analogy explicitly: both are mean ohmic currents along the field, one fed by vorticity, the other by fermion density. Solving in the adiabatic approximation $∂µ_R/∂t ~ 0$ gives the chemical potential as a local functional of the field configuration, which is what makes the whole construction predictive for a generic stochastic background.

Extended reading notes

Core claim

The central claim is Eq. (2.30) together with Eq. (2.32): the baryon number released at the electroweak phase transition is fixed by the time-integrated anomaly, $n_B(t_c) = -(n_f/2) Δn_{CS}(t_c)$ with $Δn_{CS} = -y_R^2 g'^2/(16π^2) ∫_0^{t_c} E_Y · H_Y dt$, and in the adiabatic regime this evaluates to a fluctuation $δ(n_B/s) = (α'/2πσ_c)(n_f/s) (H_Y · ∇ × H_Y)/(Γ+Γ_H) (Γ M_0/T_c^2)$, where $Γ_H = (783/22)(α'^2σ_c/π^2)|H_Y|^2T^2$. Two features carry the argument. First, the anomaly source is the helicity density $H_Y · ∇ × H_Y$ rather than the field strength alone, so a parity-invariant stochastic background with zero mean helicity still produces non-zero fluctuations with zero mean, giving inhomogeneities rather than a net asymmetry. Second, the time integration gives an amplification $Γ M_0/T_c^2$, and in the regime $Γ_H < Γ$ the chirality-flip rate cancels out entirely, leaving a fluctuation fixed by the spatial shape of the field rather than its magnitude. For a flat spectrum with field energy comparable to radiation energy at the smallest surviving scale $r_σ ~ 10^{-9}$ of the electroweak horizon, the authors estimate $Δ ~ 10^3$, far above the observed $n_B/s ~ 10^{-10}$, and they state plainly that this number is large enough that back-reaction must matter. Requiring $Δ(L_{diff},t_c) < n_B/s$ at the neutron diffusion scale instead yields the exclusion curve of Eq. (5.4) in the amplitude-slope plane, which the authors show lies below the corresponding bounds from microwave-background isotropy (Eq. 5.7), Faraday rotation (Eq. 5.8) and the direct nucleosynthesis limit on magnetic energy density (Eq. 5.9) for blue spectra.

Load-bearing premise

The derivation assumes the right-electron chemical potential adjusts adiabatically ($∂µ_R/∂t ~ 0$) and ignores back-reaction of the fermions just created on the field, an approximation the authors themselves flag: they call the $Δ ~ 10^3$ estimate of Eq. (5.1) 'unlikely to be correct' and say that numerical solutions of the nonlinear system are required once $Δ ~ 1$, which is exactly the regime the headline numbers occupy.

Editorial extensions

If this is right

A stochastic hypermagnetic background with a sufficiently flat (blue) energy spectrum produces matter-antimatter domains at and above the neutron diffusion scale, which standard homogeneous nucleosynthesis does not cover.
The requirement that homogeneous Big Bang nucleosynthesis be unchanged converts into the exclusion curve of Eq. (5.4) on the slope-amplitude plane, which is more restrictive than the microwave-background, Faraday-rotation and direct magnetic-energy bounds for spectra with $ε > 0.05$.
The Meissner pressure $\tfrac{1}{2}|\vec H_Y|^2\sin^2θ_W$ on the phase boundary can make the electroweak transition strongly first order even for Higgs masses up to about 160 GeV, removing a standard objection to electroweak baryogenesis in the minimal model.
A Chern-Simons wave configuration with $\vec H_Y\cdot\vec∇\times\vec H_Y = k_0 H^2(t)$ yields a net asymmetry of the right order $10^{-10}$ for $k_0/T_c ~ 10^{-12}$ in the minimal model, or for $k_0/T_c ~ 10^{-16}$ and $H^2 ~ 10^{-4}T_c^4$ in extensions with a larger electron Yukawa coupling.

Reading between the lines

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

The bound in Eq. (5.4) is a genuinely new handle on sub-horizon primordial fields: the microwave-background and Faraday constraints only reach fields coherent on enormous scales today, whereas this one probes the smallest scales that survive hyperconductivity, roughly $10^{-9}$ of the electroweak horizon.
Because the fluctuation amplitude in the $Γ_H < Γ$ regime is independent of the field magnitude, an experimental or observational determination of small-scale magnetic helicity would translate directly into a prediction for baryon inhomogeneity, with no amplitude calibration needed.
If matter-antimatter domains of this kind are allowed rather than excluded, the standard practice of quoting a single baryon-to-photon ratio from nucleosynthesis would need revision, since the local ratio would vary by orders of magnitude across the neutron diffusion length.
The same anomaly coupling runs in reverse, so a pre-existing right-electron asymmetry should regenerate hypermagnetic field on the scales that survive diffusion, a channel worth checking against any claimed seed-field generation mechanism.

Original abstract

The high-temperature plasma above the electroweak scale $\sim 100$ GeV may have contained a primordial hypercharge magnetic field whose anomalous coupling to the fermions induces a transformation of the hypermagnetic energy density into fermionic number. In order to describe this process, we generalize the ordinary magnetohydrodynamical equations to the anomalous case. We show that a not completely homogeneous hypermagnetic background induces fermion number fluctuations, which can be expressed in terms of a generic hypermagnetic field configuration. We argue that, depending upon the various particle physics parameters involved in our estimate (electron Yukawa coupling, strength of the electroweak phase transition) and upon the hypermagnetic energy spectrum, sizeable matter-antimatter fluctuations can be generated in the plasma. These fluctuations may modify the predictions of the standard Big Bang nucleosynthesis (BBN). We derive constraints on the magnetic fields from the requirement that the homogeneous BBN is not changed. We analyse the influence of primordial magnetic fields on the electroweak phase transition and show that some specific configurations of the magnetic field may be converted into net baryon number at the electroweak scale.

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The abstract, sentence by sentence

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

The high-temperature plasma above the electroweak scale $\sim 100$ GeV may have contained a primordial hypercharge magnetic field whose anomalous coupling to the fermions induces a transformation of the hypermagnetic energy density into fermionic number. In order to describe this process, we generalize the ordinary magnetohydrodynamical equations to the anomalous case. We show that a not completely homogeneous hypermagnetic background induces fermion number fluctuations, which can be expressed in terms of a generic hypermagnetic field configuration. We argue that, depending upon the various particle physics parameters involved in our estimate (electron Yukawa coupling, strength of the electroweak phase transition) and upon the hypermagnetic energy spectrum, sizeable matter-antimatter fluctuations can be generated in the plasma. These fluctuations may modify the predictions of the standard Big Bang nucleosynthesis (BBN). We derive constraints on the magnetic fields from the requirement that the homogeneous BBN is not changed. We analyse the influence of primordial magnetic fields on the electroweak phase transition and show that some specific configurations of the magnetic field may be converted into net baryon number at the electroweak scale.

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	The high-temperature plasma above the electroweak scale $\sim 100$ GeV may have contained a primordial hypercharge magnetic field whose anomalous coupling to the fermions induces a transformation of the hypermagnetic energy density into fermionic number.	background 0.99	0.10	0.17	hedged possibility 1.00
s1	In order to describe this process, we generalize the ordinary magnetohydrodynamical equations to the anomalous case.	method 0.93	0.91	0.03	asserted 0.83
s2	We show that a not completely homogeneous hypermagnetic background induces fermion number fluctuations, which can be expressed in terms of a generic hypermagnetic field configuration.	result 0.88	0.94	0.12	asserted 1.00
s3	We argue that, depending upon the various particle physics parameters involved in our estimate (electron Yukawa coupling, strength of the electroweak phase transition) and upon the hypermagnetic energy spectrum, sizeable matter-antimatter fluctuations can be generated in the plasma.	result 0.61	0.75	0.42	hedged possibility 0.88
s4	These fluctuations may modify the predictions of the standard Big Bang nucleosynthesis (BBN).	interpretation 0.95	0.28	0.13	hedged possibility 1.00
s5	We derive constraints on the magnetic fields from the requirement that the homogeneous BBN is not changed.	result 0.63	0.94	0.14	asserted 0.99
s6	We analyse the influence of primordial magnetic fields on the electroweak phase transition and show that some specific configurations of the magnetic field may be converted into net baryon number at the electroweak scale.	result 0.66	0.93	0.34	hedged possibility 0.61

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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

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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.** We plot the level of fluctuations given in Eq. (4.15) for differ

**Figure 2.** We plot the constraint on the stochastic background of m

**Figure 3.** We plot the expected level of fluctuations given in Eq. (4.15

**Figure 4.** We plot our bound (lower curve) obtained in Eq. (5.4) and th

**Figure 5.** We compare the bounds of Eqs. (5.4) and (5.8). The most c

**Figure 6.** We compare the direct bound on primordial magnetic fields a

**Figure 7.** We plot the constraint derived on the basis of BBN consider

**Figure 8.** We plot the requirement obtained in Eq. (6.2) in the case of a

Figures reproduced from arXiv:hep-ph/9710234 by the authors.

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Forward citations

Cited by 27 Pith papers

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

Baryon number freeze-out in the Standard Model, precisely
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Precise Standard Model sphaleron conversion factors: Csph = 0.3328(5) and Fsph = 0.0279(19).
The strong backreaction regime in axion inflation
astro-ph.CO 2023-03 conditional novelty 7.0 of 10

Fully inhomogeneous lattice simulations of axion inflation through strong backreaction show extra efoldings growing with coupling, smoothed and broadened gauge spectra, and scale-dependent chirality loss.
Holographic Gravitational Anomaly and Chiral Vortical Effect
hep-th 2011-07 conditional novelty 7.0 of 10

A holographic model with a mixed gauge-gravitational Chern-Simons term yields the same T-squared chiral vortical conductivity as free chiral fermions, suggesting the coefficient is not renormalized.
Helicity Decay to Baryons: The Cosmological Evolution of $L_\mu-L_\tau$ Gauge Fields and Baryogenesis
hep-ph 2026-11 conditional novelty 6.0 of 10

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.
Magnetic Catalysis and Fermion Mass Generation in de Sitter Spacetime
hep-th 2026-08 conditional novelty 6.0 of 10

In de Sitter space with a background magnetic field, the field catalyzes chiral symmetry breaking while Hubble curvature restores it, with a second-order phase boundary.

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Resonant magnetogenesis from axions
astro-ph.CO 2019-08 conditional novelty 6.0 of 10

Axion resonance with delayed oscillation onset can seed helical cosmic magnetic fields of about 3e-15 Gauss today with O(1) coupling.
Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe
hep-ph 2019-08 conditional novelty 6.0 of 10

A nonzero primordial vorticity seeds a hypermagnetic field from zero in the symmetric phase; the chiral magnetic effect then amplifies it and converts lepton into baryon asymmetry.
Gauge Field and Fermion Production during Axion Inflation
hep-ph 2018-06 conditional novelty 6.0 of 10

Fermion backreaction caps helical gauge field production in axion inflation, suppressing the small-scale scalar power spectrum that these models otherwise predict.
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...
Large-scale magnetic fields can explain the baryon asymmetry of the Universe
hep-ph 2016-02 conditional novelty 6.0 of 10

Primordial helical hypermagnetic fields, evolving through an inverse cascade before the electroweak transition, can reproduce the observed baryon asymmetry using only standard model physics.
Leptogenesis and Primordial Magnetic Fields
astro-ph.CO 2013-09 conditional novelty 6.0 of 10

The anomalous lepton-to-baryon conversion in leptogenesis produces a right-handed helical hypermagnetic field whose helicity density is fixed by the observed baryon asymmetry.
Anomaly related transport of Weyl fermions for Weyl semi-metals
hep-th 2013-06 conditional novelty 6.0 of 10

In equilibrium Weyl semimetals the bulk chiral magnetic current vanishes but the chiral vortical current persists, with the magnetic effect realized as anomaly-driven edge charge accumulation.
Triangle anomaly in Weyl semi-metals
hep-th 2013-05 conditional novelty 6.0 of 10

The chiral magnetic current in a Weyl semimetal vanishes in equilibrium unless the two valleys are filled to different energies, and the anomaly also produces rotation-driven cooling, Burgers-equation charge transport...
Chern-Simons Inflation and Baryogenesis
hep-th 2011-07 conditional novelty 6.0 of 10

A time-like U(1) gauge field growing as the scale factor while a fermionic charge dilutes as its inverse yields a constant interaction energy that can drive inflation, and the same field can seed a lepton asymmetry.
Anomalous transport coefficients from Kubo formulas in Holography
hep-th 2011-02 accept novelty 6.0 of 10

A new Kubo formula expresses the chiral vortical conductivity as a current-momentum-density correlator, verified analytically and numerically in a holographic R-charged black hole.
Revisiting constraints on magnetogenesis from baryon asymmetry
hep-ph 2025-09 unverdicted novelty 5.0 of 10

Maximally helical primordial U(1)_Y magnetic fields can generate both intergalactic magnetic fields and baryon asymmetry; non-helical fields may work if Higgs dynamics compensate helicity loss to ≲10^{-9-10} precision...
Impact of Primordial Magnetic Fields on the First-Order Electroweak Phase Transition
hep-ph 2025-08 conditional novelty 5.0 of 10

A primordial hypermagnetic field slows the first-order electroweak transition, forms Higgs vortices above g'B/m_W^2 ~ 3.63, and helical fields boost sphaleron rates and baryon asymmetry.
Lattice formulation of axion inflation. Application to preheating
astro-ph.CO 2018-12 accept novelty 5.0 of 10

A lattice discretization that keeps gauge and shift symmetry exact on the grid is used to map preheating after axion inflation, finding a threshold coupling near 1/Lambda = 9.5/m_pl that separates failed from near-com...
Baryon Asymmetry and Gravitational Waves from Pseudoscalar Inflation
hep-ph 2017-07 conditional novelty 5.0 of 10

Requiring the observed baryon asymmetry fixes the axion-hypercharge coupling to about 3×10^17 GeV, which in turn predicts a gravitational wave peak at MHz frequencies too high for current detectors.
Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field
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A time-varying weak mixing angle during the electroweak crossover adds a new helicity-sourced term to the baryon kinetic equation, enhancing the predicted relic baryon asymmetry and creating tension with strong interg...
Hypermagnetic Fields and Baryon Asymmetry from Pseudoscalar Inflation
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Helical hypermagnetic fields from pseudoscalar inflation source the B+L anomaly and overproduce the baryon asymmetry for natural inflation with H_inf above about 6 times 10^10 GeV.
Electroweak-Scale Cosmic Magnetism: Magnetogenesis, Baryogenesis, Phase Transitions and Gravitational Waves
hep-ph 2026-11 accept novelty 4.0 of 10

A comprehensive review arguing that baryogenesis, primordial magnetic fields, and gravitational waves near the electroweak scale should be calculated from the same microscopic model with a shared magnetohydrodynamic a...
Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma
hep-ph 2015-01 conditional novelty 4.0 of 10

A chiral fermion imbalance in a magnetized quark-gluon plasma generates magnetic helicity on few-fm time scales, and the reverse process can generate chirality from pre-existing helical fields.
Chiral effects in astrophysics and cosmology
astro-ph.CO 2022-07 accept novelty 2.0 of 10

Chirality of Standard Model fermions generates anomaly-driven transport that has been proposed as a mechanism for neutron-star kicks, magnetar fields, supernova turbulence, primordial magnetogenesis, baryogenesis, and...
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cond-mat.mes-hall 2021-10 accept novelty 2.0 of 10

Quantum anomalies fix anomaly-induced electric and thermal transport coefficients in Dirac and Weyl semimetals, linking heat flow, spacetime geometry, and high-energy field theory.
Anomalous Transport from Kubo Formulae
hep-th 2012-07 conditional novelty 2.0 of 10

The chiral vortical conductivity of a relativistic fluid contains a temperature-squared term proportional to the mixed gauge-gravitational anomaly, reproduced by both free-fermion and holographic calculations.
Primordial magnetogenesis
astro-ph.CO 2010-07 accept novelty 2.0 of 10

Standard inflation dilutes magnetic seeds to roughly 10^-50 G, so viable primordial fields require modified electromagnetism, non-flat cosmology, or non-standard physics.

How later papers used it

81 later papers cite it

Evidence: substantial. 77 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 159 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 3 papers with this label

Said that its values of the magnetic field and correlation length for the collision dominated case are similar to those given in this paper, and believed they are also consistent with BBN constraints.

Origin and dynamics of the Primordial Magnetic field in a parity violating plasma (2017) · 0.84 · paraphrased: the licence does not allow quoting

How the literature uses it

65 arXiv papers cite this in 134 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 · 98 sentences without a confident label

Builds on it 1 paper

This work was soon extended by Giovannini and Shaposhnikov [ref] to consider the generation of baryon-number isocurvature fluctuations from a preexisting stochastic hypermagnetic field.

Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field · Introduction · 0.83

Compares with it 2 papers

In summary, we obtain the two-point correlation function of the helicity in terms of the power spectrum as [equation] We can easily check that Eq. [ref] is consistent with the one given in Ref. [ref] .

Baryon isocurvature constraints on the primordial hypermagnetic fields · Correlation functions in the position space · 1.00
Thus the values of the magnetic field and the correlation length scale estimated by us can be consistent with the current bounds obtained from CMB observation and necessary for current observed baryon asymmetry Since the values of $ℬ_p$ and $λ_B$ for the collision dominated case are similar to those given in the Ref. [ref] , we believe that they are also consistent with BBN constraints.

Origin and dynamics of the Primordial Magnetic field in a parity violating plasma · Discussion · 0.84

Cites it as support 2 papers

We find that since the baryon isocurvature perturbation is generated even from non-helical hypermagnetic fields [ref] , the constraint becomes severer for less helical hypermagnetic fields, in which case hypermagnetic fields with longer coherence length are needed for the BAU.

Baryon isocurvature constraints on the primordial hypermagnetic fields · Introduction · 0.96
Once we assume that helical hypermagnetic fields are generated before the electroweak symmetry breaking at $T≳100 GeV$, it is found that the baryon asymmetry is generated automatically through the hypermagnetic helicity decay without introducing any new physics [ref] (see also Ref. [ref] ).

Chiral effects in astrophysics and cosmology · Baryogenesis · 0.97

Cites it as background 23 papers

Recently, increasing efforts and interests have been devoted to the baryogenesis mechanisms via the decay of magnetic helicity of the $U(1)_Y$ gauge field in the standard model [ref] .

Leptogenesis from magnetic helicity of gauged $\text{U}(1)_{B-L}$ · Introduction · 0.94
Here, $g'$ is the U$_Y$(1) gauge coupling [ref] .

The effects of the U$_\textrm{Y}$(1) Chern-Simons term and its baryonic contribution on matter asymmetries and hypermagnetic fields · Introduction · 0.83
In the presence of these anomalous effects, the ordinary magnetohydrodynamic (MHD) equations are generalized to the equations of anomalous magnetohydrodynamics (AMHD) [ref] .

Contribution of the thermal mass to the chiral vortical effect and magnetobaryogenesis · Introduction · 0.81

Discussion

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