Oscillating Asymmetric Dark Matter

Hai-Bo Yu; Kathryn M. Zurek; Sean Tulin

REVIEW

Oscillating Asymmetric Dark Matter

Sean Tulin, Hai-Bo Yu, Kathryn M. Zurek

High Energy Physics - Phenomenology · Submitted 1 Feb 2012 · 42 references

Pith's verdict: The central claim is a clean, correct algebraic result that fixes a specific earlier treatment; the main soft spot is a numerical figure that doesn't reflect the paper's own decoherence estimate.

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arXiv ID1202.0283 (version 2)

Pith IDSLXFKYI6, Pith's permanent record of this paper and its review

CitationHai-Bo Yu, Kathryn M. Zurek, Sean Tulin. "Oscillating Asymmetric Dark Matter." arXiv:1202.0283 (2012). https://pith.science/paper/SLXFKYI6

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Editor's note

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Two things worth knowing. First, the central claim is right and it's a real correction to the literature. The collision term's matrix structure depends on the C-parity of the DM interaction: flavor-sensitive annihilation couples only to det(Y), and since det([H0, Y]) = 0, oscillations can't source it. That's a clean algebraic argument (Sec. III D), and it means flavor-sensitive annihilation doesn't recouple when coherent oscillations begin. The companion claim — flavor-blind scattering doesn't decohere because O_+ is the identity — is equally clean. The CTP derivation in the appendix is standard Kadanoff-Baym done carefully, and the paper is honest that it agrees with Ref. [22] in two of the four cases and differs qualitatively in the others. Second, the soft spot is the numerical figure for the flavor-sensitive, no-scattering case (Fig. 2 bottom left). The paper's own thermal-decoherence estimate (Eqs. 24-25) says the O(k^2/m_X^2) corrections restart annihilation on a timescale tau_dec ~ 1/(delta m v^2), which for the Fig. 2 benchmark is well inside the plotted range. The figure shows a flat density out to x~1000 because it solves Eq. (22), which the paper explicitly says neglects this effect. That's technically consistent, but the paper then states the relic density is 'fixed by the initial asymmetry' for this case without qualifying that the full physics would deplete it. A reader could take the flat curve as the physical answer. The fix is a sentence in the caption or text saying the curve is the solution of Eq. (22) only, and marking where the approximation breaks down. Other soft spots, in proportion: the flavor-blind scattering result relies on the contact-interaction form and on neglecting the medium-induced mass shift, which the paper flags in footnote 6 but doesn't quantify. The formalism citation to Ref. [27] is to a forthcoming paper, though the appendix is self-contained enough that this doesn't block reimplementation. The numerical benchmarks are illustrative, not fitted, so no circularity. Who should read it: anyone working on asymmetric DM, oscillating DM, or density-matrix Boltzmann equations in cosmology. The flavor-sensitive/flavor-blind distinction is a useful organizing principle that will show up in later work. Recommendation: send it out. The central claim is correct and the correction to Ref. [22] matters. The figure issue is a presentation fix, not a reason to hold it up.

Referee report

Major objections (3)

[Sec. III C, Fig. 2 bottom left (and Fig. 3 bottom left)] The flat density curve out to x ~ 1000 is a solution of Eq. (22), which by construction neglects the O(k^2/m_X^2) corrections to omega_osc that the paper itself identifies in Sec. III A (Eqs. 24-25) as the source of thermal decoherence. For the benchmark parameters m_X = 300 GeV and delta m = 10^-7 eV, the paper's own estimate tau_dec ~ 1/(delta m v^2) implies that decoherence and renewed annihilation should set in around x ~ 300-1000, so the figure overstates the persistence of the frozen-out density. The caption and the accompanying statement in Sec. III C that Omega_DM = m_X eta_DM s_0/rho_c is fixed by the initial asymmetry for the flavor-sensitive kappa = 0 case should be qualified, or the decoherence scale should be overlaid on the figure.
[Sec. II B, Eq. (18)] The ansatz F_k = exp(-omega_k/T) n_eq assumes that all density-matrix elements share a common Maxwell-Boltzmann momentum dependence. The paper's justification -- that omega_osc is approximately k-independent in the nonrelativistic limit -- is a plausibility argument rather than a derivation, and the neglected O(k^2/m_X^2) corrections are precisely the ones that drive thermal decoherence. It would be useful to state explicitly that Eq. (18) is an approximation and to estimate its accuracy, or to show that the collision term does not generate a different momentum dependence for the off-diagonal elements.
[Sec. III C] The paper states that for cases other than flavor-blind annihilation without scattering and flavor-sensitive annihilation with scattering, its results differ from Ref. [22] by an order of magnitude in the relic density. This is a strong quantitative claim about another work, but no direct comparison (figure or table) is shown. A side-by-side comparison of the relic densities obtained with the two collision-term structures would make the claim verifiable and would clarify exactly which matrix-structure difference is responsible.

Minor objections (6)

[Abstract] The statement that flavor-sensitive annihilation 'does not recouple when coherent oscillations begin' should be qualified, since the body of the paper (Sec. III A) shows that thermal decoherence or flavor-sensitive scattering will eventually restart annihilation. A phrase such as 'does not recouple until coherence is broken' would be more precise.
[Eq. (33)] The CMB line appears to contain a typo. With T in TeV, the prefactor should be 10^8 rather than 10^-16; equivalently, the formula should use (T/eV)^2 with prefactor 10^-16. As written, the CMB velocity estimate is off by 24 orders of magnitude.
[Sec. III B] The claim that flavor-blind scattering does not lead to decoherence follows from O_+ = identity in Eq. (10) and the assumption f_p = f_bar_p. It would be useful to state these conditions explicitly, since a more general flavor-blind interaction (e.g., with derivative couplings or a different momentum dependence) could in principle generate decoherence.
[Eq. (10)] The scattering term includes Xf <-> Xf and X_bar f <-> X_bar f but not oscillation-induced processes such as Xf <-> X_bar f. It would be useful to state whether these are negligible (e.g., suppressed by delta m/omega) or whether they should be included in a more complete treatment.
[Eq. (16)] The notation for O_pm and M_pm could be clarified. The subscript pm on O refers to the diagonal structure (1, pm 1), while the subscript pm on M refers to the C-parity of the amplitude; a sentence spelling this out would help the reader.
[Fig. 2 and Fig. 3 captions] The kappa = 0 curves should be labeled explicitly as solutions of Eq. (22) that neglect thermal decoherence, so that the reader does not interpret the flat curves as physical at arbitrarily late times.

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The paper

The paper claims

Whether dark matter annihilation restarts after freeze-out depends on how the dark matter interaction behaves under charge conjugation, and the paper derives the density-matrix equations that make this distinction unavoidable.

The reading

Asymmetric dark matter assumes a stored particle-antiparticle imbalance set by a conserved charge, so that annihilation has already wiped out the symmetric part of the population long before today. A tiny charge-violating Majorana mass makes the dark particle oscillate into its own antiparticle, and the natural expectation is that this oscillation refills the antiparticle population and switches annihilation back on. This paper re-derives the governing equations from nonequilibrium field theory rather than borrowing the neutrino-oscillation template, and finds that the answer depends on a property previous treatments ignored: whether the dark matter bilinear coupling to lighter states is even or odd under charge conjugation. For the odd, or flavor-sensitive, case — annihilation through a new vector boson — the annihilation term couples only to $Y_{11}Y_{22}-Y_{12}Y_{21}$, and because the oscillation commutator generates no determinant, coherent oscillations do not restart annihilation at all. The paper also shows the mirror statement for scattering: flavor-blind scattering drops out of the collision term entirely and cannot destroy coherence, so only flavor-sensitive scattering can decohere the oscillating state.

What carries the argument

The load-bearing object is the integrated density-matrix Boltzmann equation, $Y'(x) = -frac{i}{Hx}[H_0,Y] - frac{Gamma_pm}{2Hx}[O_pm,[O_pm,Y]] - frac{s langle sigma v rangle_pm}{Hx}left(frac{1}{2}{Y, O_pm Ybar O_pm} - Y_{eq}^2right)$, obtained by projecting the Kadanoff-Baym equations of the closed-time-path formalism onto a number-density matrix and then integrating over momenta with a Maxwell-Boltzmann factorization ansatz. Its work is to separate three effects that ordinary Boltzmann equations fuse together: the coherent rotation generated by the Majorana splitting $delta m$, the decohering effect of elastic scattering, and the depletion from annihilation, each of which carries a different matrix structure in the two-flavor space spanned by particle and antiparticle. The charge-conjugation parity of the interaction, encoded in $O_pm$, is what decides whether each term acts on the diagonal populations, on the off-diagonal coherences, or on the determinant alone.

Extended reading notes

Core claim

The paper's central claim is that the matrix structure of the collision term in the dark matter density-matrix Boltzmann equation is not universal but is fixed by the transformation property of the interaction under $X$ to $X^C$. Writing the amplitude matrices as $C_a = M(X X^C to f f) O_pm$ with $O_pm = mathrm{diag}(1, pm 1)$, the flavor-blind ($+$) annihilation term is $frac{1}{2}{Y, O_+ Ybar O_+}$ while the flavor-sensitive ($-$) term reduces to $mathrm{diag}(Y_{11}Y_{22}-Y_{12}Y_{21},, Y_{11}Y_{22}-Y_{12}Y_{21})$, i.e. it depends only on $det Y$. Since $det([H_0,Y])=0$, the oscillation term cannot source flavor-sensitive annihilation, so a dark sector that froze out as a pure particle state and is now oscillating coherently stays frozen out. The authors back this with an analytic solution of the flavor-sensitive system, showing $Sigma = Y_{11}+Y_{22}$ remains pinned at the asymmetry $eta_{DM}$ while $Delta$ and $Xi$ oscillate as $cos(delta m/H)$ and $sin(delta m/H)$. The companion result is that the scattering double commutator $frac{Gamma_pm}{2}[O_pm,[O_pm,Y]]$ vanishes identically for $O_+$, so flavor-blind scattering causes no decoherence, whereas flavor-sensitive scattering damps $Y_{12}$ and $Y_{21}$ and, when $Gamma_- gg omega_{osc}$, suppresses oscillation through the quantum Zeno effect.

Load-bearing premise

The derivation integrates the momentum-resolved equations using a factorization ansatz in which every element of the density matrix shares one Maxwell-Boltzmann momentum profile, which is precisely what discards the $O(k^2/m_X^2)$ spread in oscillation frequency that the paper elsewhere identifies as the mechanism by which flavor-sensitive annihilation eventually switches back on.

Editorial extensions

If this is right

For flavor-sensitive annihilation with negligible scattering, the relic abundance is fixed by the initial asymmetry alone, $Omega_{DM} = m_X eta_{DM} s_0/rho_c$, so weak-scale asymmetric dark matter cannot be washed down to the observed density by this mechanism.
Indirect-detection bounds derived by requiring the oscillation time $delta m^{-1}$ to exceed the BBN, CMB, and present-epoch annihilation constraints apply only to flavor-blind annihilation; for the flavor-sensitive case the authors estimate the bounds weaken by roughly six to sixteen orders of magnitude.
Flavor-sensitive scattering delays the onset of oscillation through the quantum Zeno effect until $omega_{osc} > Gamma_-$, and only after that does decoherence-driven annihilation deplete the density, which the numerical examples show can still give an order-of-magnitude reduction.
The framework widens asymmetric dark matter model building by making the relic density depend on interaction type rather than only on cross section and asymmetry, and it supplies a natural bridge between symmetric WIMP freeze-out and asymmetric freeze-out.

Reading between the lines

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

If flavor-sensitive annihilation truly stays off while coherence persists, the late-time annihilation rate in such models is controlled not by the oscillation frequency but by whatever breaks coherence, which makes the present-day annihilation signal a direct probe of the decoherence channel rather than of the Majorana mass.
The paper's own momentum-spread argument, $tau_{dec} sim 1/(delta m, v^2)$, suggests the flavor-sensitive suppression is temporary in any realistic thermal ensemble; a full momentum-resolved solution would then translate into a sharp prediction for the epoch at which the annihilation signal switches on, testable against CMB energy-injection limits.
The same even/odd bookkeeping should apply to any two-state system coupled to a bath through a bilinear whose parity under the state-swapping symmetry is definite, so the result plausibly carries over to oscillating scalar dark matter, to neutron-antineutron-like oscillations, and to any hidden-sector particle mixing with its own antiparticle.

Original abstract

We study the dynamics of dark matter (DM) particle-antiparticle oscillations within the context of asymmetric DM. Oscillations arise due to small DM number-violating Majorana-type mass terms, and can lead to recoupling of annihilation after freeze-out and washout of the DM density. We derive the density matrix equations for DM oscillations and freeze-out from first principles using nonequilibrium field theory, and our results are qualitatively different than in previous studies. DM dynamics exhibits particle-vs-antiparticle "flavor" effects, depending on the interaction type, analogous to neutrino oscillations in a medium. "Flavor-sensitive" DM interactions include scattering or annihilation through a new vector boson, while "flavor-blind" interactions include scattering or s-channel annihilation through a new scalar boson, or annihilation to pairs of bosons. In particular, we find that flavor-sensitive annihilation does not recouple when coherent oscillations begin, and that flavor-blind scattering does not lead to decoherence.

The compiled record

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,070 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study the dynamics of dark matter (DM) particle-antiparticle oscillations within the context of asymmetric DM. Oscillations arise due to small DM number-violating Majorana-type mass terms, and can lead to recoupling of annihilation after freeze-out and washout of the DM density. We derive the density matrix equations for DM oscillations and freeze-out from first principles using nonequilibrium field theory, and our results are qualitatively different than in previous studies. DM dynamics exhibits particle-vs-antiparticle "flavor" effects, depending on the interaction type, analogous to neutrino oscillations in a medium. "Flavor-sensitive" DM interactions include scattering or annihilation through a new vector boson, while "flavor-blind" interactions include scattering or s-channel annihilation through a new scalar boson, or annihilation to pairs of bosons. In particular, we find that flavor-sensitive annihilation does not recouple when coherent oscillations begin, and that flavor-blind scattering does not lead to decoherence.

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 the dynamics of dark matter (DM) particle-antiparticle oscillations within the context of asymmetric DM.	contribution 0.83	0.87	0.04	asserted 0.90
s1	Oscillations arise due to small DM number-violating Majorana-type mass terms, and can lead to recoupling of annihilation after freeze-out and washout of the DM density.	background 0.95	0.16	0.12	hedged possibility 0.80
s2	We derive the density matrix equations for DM oscillations and freeze-out from first principles using nonequilibrium field theory, and our results are qualitatively different than in previous studies.	contribution 0.57	0.97	0.13	asserted 1.00
s3	DM dynamics exhibits particle-vs-antiparticle "flavor" effects, depending on the interaction type, analogous to neutrino oscillations in a medium.	result 0.82	0.68	0.09	asserted 0.99
s4	"Flavor-sensitive" DM interactions include scattering or annihilation through a new vector boson, while "flavor-blind" interactions include scattering or s-channel annihilation through a new scalar boson, or annihilation to pairs of bosons.	background 0.44	0.27	0.05	asserted 1.00
s5	In particular, we find that flavor-sensitive annihilation does not recouple when coherent oscillations begin, and that flavor-blind scattering does not lead to decoherence.	result 1.00	0.96	0.64	asserted 1.00

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

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

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

levels run

P abstract

not run

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

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

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B. Garbrecht and M. Herranen, arXiv:1112.5954 [hep-ph ]

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[42]

M. Garny, A. Kartavtsev and A. Hohenegger, arXiv:1112. 6428 [hep-ph]. 23

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Cited by 23 Pith papers

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

Mass-Dependent Dark Matter Deficit from Inelastic Scattering
astro-ph.GA 2026-09 conditional novelty 6.0 of 10

Exothermic inelastic dark matter with a strongly velocity-dependent cross section can reproduce the stellar-mass-dependent central dark matter deficit in galaxies while remaining weak at dwarf and cluster scales.
dSphobic Dark Matter
hep-ph 2025-04 conditional novelty 6.0 of 10

A two-state dark matter model with velocity-dependent upscattering can produce a Galactic Center gamma-ray signal while suppressing dwarf galaxy signals, breaking the usual correlation between the two.
Baryogenesis and Dark Matter from $B$ Mesons
hep-ph 2018-10 conditional novelty 6.0 of 10

A new mechanism generates the baryon asymmetry and dark matter abundance from CP-violating B meson oscillations and decays, predicting a positive leptonic asymmetry and B decays to a baryon plus missing energy.
Baryogenesis from Oscillations of Charmed or Beautiful Baryons
hep-ph 2017-08 conditional novelty 6.0 of 10

A model in which CP-violating oscillations of heavy-flavored neutral baryons at a few MeV generate the observed baryon asymmetry, with parameters that collider and Belle II searches could probe.
Coherent Propagation of PeV Neutrinos and the Dip in the Neutrino Spectrum at IceCube
hep-ph 2015-04 conditional novelty 6.0 of 10

A flavor-dependent MeV-scale force between neutrinos can produce the observed dip in the IceCube PeV spectrum without fully absorbing any single flavor, because oscillations leave a floor in the survival probability.

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Dark Nuclei I: Cosmology and Indirect Detection
hep-ph 2014-06 conditional novelty 6.0 of 10

Dark nucleosynthesis, the dark-sector analogue of Big Bang nucleosynthesis, can produce indirect-detection signals from asymmetric dark matter without requiring any symmetric component.
Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure
hep-ph 2013-02 accept novelty 6.0 of 10

Self-interacting dark matter with a light mediator can resolve small-scale structure anomalies across a wide range of masses and couplings, and the resonant scattering regime is now both computable and describable by ...
Energy Injection And Absorption In The Cosmic Dark Ages
astro-ph.CO 2012-11 accept novelty 6.0 of 10

The paper tabulates, for photons, electrons and electron-positron pairs over 1 keV to 10 TeV and redshifts 10 to 3000, what fraction of injected energy is absorbed by the gas at each later redshift, and shows how to f...
Thermal Dark Matter from a Confining Sector
hep-ph 2012-09 conditional novelty 6.0 of 10

A stable pseudo-Nambu-Goldstone baryon of a new SU(2) confining force can be thermally produced dark matter at hundreds of GeV, well below the 20 TeV unitarity bound for composite dark matter.
Bounds on self-interacting fermion dark matter from observations of old neutron stars
hep-ph 2013-10 conditional novelty 5.0 of 10

Fermionic dark matter with an attractive Yukawa self-interaction escapes old-neutron-star bounds once it self-annihilates faster than roughly 1e-40 cm^3/s, or co-annihilates with baryons faster than roughly 1e-50 cm^3/s.
Three Exceptions for Thermal Dark Matter with Enhanced Annihilation to Gamma Gamma
hep-ph 2012-07 accept novelty 5.0 of 10

Coannihilation, forbidden channels, and asymmetric dark matter can each reconcile a 130 GeV dark matter gamma-ray line with the observed relic density and with continuum gamma-ray limits.
Leptogenesis from a GeV Seesaw without Mass Degeneracy
hep-ph 2012-06 conditional novelty 5.0 of 10

Flavoured leptogenesis with GeV-scale sterile neutrinos works without mass degeneracy, because the lepton-number-conserving source term is enhanced by T-squared over the mass-squared splitting at temperatures around 10^6 GeV.
Light Magnetic Dark Matter in Direct Detection Searches
hep-ph 2012-03 conditional novelty 5.0 of 10

A 10 GeV fermion with a magnetic dipole moment of about 1.5e-18 e cm can fit the DAMA, CoGeNT and CRESST signals while evading null-result experiments under conservative assumptions.
Can a secluded self-interacting dark sector generate detectable gravitational waves?
hep-ph 2025-02 conditional novelty 4.0 of 10

In a secluded self-interacting dark sector with a dark U(1)' and dark radiation, existing Neff and Lyman-alpha limits remove nearly all gravitational-wave-detectable parameter space; one charge assignment keeps a smal...
Constraints on Bosonic Dark Matter From Observations of Old Neutron Stars
hep-ph 2013-01 conditional novelty 4.0 of 10

Bosonic dark matter captured by old neutron stars collapses into black holes unless it annihilates with a cross section above about 10^-38 cm^3/s or has repulsive self-interactions.
Asymmetric Dark Matter and Dark Radiation
hep-ph 2012-03 conditional novelty 4.0 of 10

A dark sector with light dark radiation and heavier states that heat it produces a calculable extra relativistic energy density, and dark matter scattering off that radiation leaves a measurable imprint on the matter ...
The Maximal $U(1)_L$ Inverse Seesaw from $d=5$ Operator and Oscillating Asymmetric Sneutrino Dark Matter
hep-ph 2011-02 conditional novelty 4.0 of 10

A dimension-five operator involving the NMSSM singlet dynamically generates the small lepton-number-violating mass of the inverse seesaw, and the lightest sneutrino becomes a viable weak-scale asymmetric dark matter c...
On Relating the Genesis of Cosmic Baryons and Dark Matter
hep-ph 2012-03 accept novelty 3.0 of 10

Asymmetric dark matter, in which the visible and dark sectors share a common origin and comparable number densities, is surveyed across two model classes together with the collider, direct-detection, and astrophysical...
Rich Phenomenology from Simple Ingredients: A Review of Confining Dark Sectors
hep-ph 2026-06 unverdicted novelty 2.0 of 10

Review of confining dark sectors summarizing dark matter candidates, abundance mechanisms, discovery channels, and applications to the abundance similarity puzzle.
TASI Lectures on Indirect Detection of Dark Matter
hep-ph 2017-10 accept novelty 2.0 of 10

The notes derive the thermal relic cross section from a Boltzmann estimate, show how to convert photon, neutrino and cosmic-ray observations into dark matter limits, and survey the 2016 experimental status.
Asymmetric Dark Matter: Theories, Signatures, and Constraints
hep-ph 2013-08 accept novelty 2.0 of 10

Asymmetric dark matter ties the dark matter density to the baryon density through a shared matter-antimatter asymmetry, and this review organizes the models, transfer mechanisms, and observational constraints into a s...
Indirect Searches for Dark Matter: a status review
hep-ph 2012-02 accept novelty 2.0 of 10

No new data or derivation: the review concludes that the cosmic-ray electron excesses, if dark matter, require a multi-TeV leptophilic particle annihilating far above the thermal rate, and that gamma-ray, neutrino and...
Review of asymmetric dark matter
hep-ph 2013-05 accept

Asymmetric dark matter, in which dark matter and ordinary matter share a common asymmetry origin, is a well-motivated alternative to WIMP dark matter, though most models still lack a compelling explanation for the few...

How later papers used it

49 later papers cite it

Evidence: substantial. 47 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 12 of the 77 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

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 7 papers with this label

We follow the density matrix formalism described in [ref] in order to incorporate the oscillation dynamics in the early universe.

Leptogenesis and Neutrino Masses Via Pseudo-Dirac Gauginos (2025) · Oscillations in the early universe · 1.00
Followed this paper to write the Boltzmann equations governing the evolution of the number density of the B-Bbar system.

Baryogenesis from Oscillations of Charmed or Beautiful Baryons (2017) · 0.82 · paraphrased: the licence does not allow quoting

How the literature uses it

47 arXiv papers cite this in 73 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 · 55 sentences without a confident label

Uses its method or tool 7 papers

We follow the density matrix formalism described in [ref] in order to incorporate the oscillation dynamics in the early universe.

Leptogenesis and Neutrino Masses Via Pseudo-Dirac Gauginos · Oscillations in the early universe · 1.00
[ref] , which we follow closely in the present work.

Late-Time Dark Matter Oscillations and the Core-Cusp Problem · Introduction · 0.89
Following Ref. [ref] (see [ref] for a similar analysis in the context of baryogenesis-related oscillations), we can write the Boltzmann equations that govern the evolution of the number density of the $B$-$B̅$ system, [equation] where the last term describes $B$ and $B̅$ production through $χ_3$ decay. $Br_χ_3→B$ is the branching ratio for $χ_3$ to decay to $B$ or $B̅$.

Baryogenesis from Oscillations of Charmed or Beautiful Baryons · Cosmological Production of the Baryon Asymmetry · 0.82

Cites it as support 1 paper

Condition (i) is generally satisfied since $X_2$ undergoes rapid gauge scatterings with SM fermions $f$ in the plasma, which delays oscillations [ref] .

Higgsogenesis · Introduction · 0.97

Cites it as background 10 papers

This phenomena was first touched in [ref] and then was systematically studied by several groups in a model independent way [ref] .

Oscillating Asymmetric Sneutrino Dark Matter from the Maximally $U(1)_L$ Supersymmetric Inverse Seesaw · Sneutrino-antisneutrino oscillating and symmetry regeneration · 0.95
Possible effects of dark matter oscillations have been studied in Refs. [ref] .

Inert Scalar Doublet Asymmetry as Origin of Dark Matter · $𝐓<𝐓_𝐄𝐖$: Symmetric annihilations after EWSB · 0.88
Self-interacting dark matter (SIDM) [ref] is an interesting and well-motivated hypothesis, both from the astrophysics and particle physics perspectives of dark matter (e.g. [ref] or see [ref] for a review).

Towards an improved model of self-interacting dark matter haloes · Introduction · 0.94

What it cites · 36 sentences without a confident label

Contests 1 paper

Similar results were presented in Ref. [ref] , but do not capture the correct matrix structure of the annihilation and scattering terms, nor the distinction between flavor-blind and flavor-sensitive interactions.

Consequences of DM/antiDM Oscillations for Asymmetric WIMP Dark Matter · Nonrelativistic limit · contest 0.83

Uses the method or tool of 2 papers

In this appendix, we use these methods to derive a Boltzmann-like equation for the density matrix describing DM freeze-out and oscillations, following Ref. [ref] .

Flavored Quantum Boltzmann Equations · Nonequilibrium field theory derivation · 0.97
Following Ref. [ref] , we express the density matrix equation [ref] as a system of coupled differential equations in terms of the variables Σ(x) ≡Y_11+Y_22 , Δ(x) ≡Y_11-Y_22 , Ξ(x) ≡Y_12-Y_21 , Π(x) ≡Y_12+Y_21 .

Consequences of DM/antiDM Oscillations for Asymmetric WIMP Dark Matter · Analytical Analysis for Flavor-Sensitive Annihilation · 0.88

Compares with 1 paper

Similar results were presented in Ref. [ref] .

Consequences of DM/antiDM Oscillations for Asymmetric WIMP Dark Matter · Numerical results · 0.93

Cites as background 12 papers

This effect has been discussed within the context of specific models [ref] , and emphasized more generally in Refs. [ref] .

Leptophilic Dark Matter from the Lepton Asymmetry · Introduction · 0.86
This effect has been discussed within the context of specific models [ref] , and emphasized more generally in Refs. [ref] .

Leptonic Indirect Detection Signals from Strongly Interacting Asymmetric Dark Matter · Introduction · 0.86
This effect has been discussed within the context of specific models [ref] , and emphasized more generally in Refs. [ref] .

Asymmetric Dark Matter from Leptogenesis · Introduction · 0.86

Discussion

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