AGN and DSNB Neutrino Oscillation in Dark Matter Background

Po-Yan Tseng; Yu-Min Yeh

REVIEW

AGN and DSNB Neutrino Oscillation in Dark Matter Background

Po-Yan Tseng, Yu-Min Yeh

High Energy Physics - Phenomenology · Submitted 18 Sep 2026 · 17 references

Pith's verdict: A well-executed phenomenological study of neutrino flavor ratios from AGN and DSNB under an unverified neutrino–dark matter interaction; the results' overlap with IceCube data is interesting but fragile, depending critically on the assumed DM spike density.

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arXiv ID2609.21768 (version 1)

Pith IDCIU66ETV, Pith's permanent record of this paper and its review

CitationPo-Yan Tseng, Yu-Min Yeh. "AGN and DSNB Neutrino Oscillation in Dark Matter Background." arXiv:2609.21768 (2026). https://pith.science/paper/CIU66ETV

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Editor's note

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This paper applies the authors' previously proposed neutrino–scalar dark matter interaction to compute flavor ratios from two AGN sources and the DSNB, then compares them with current and future experimental contours. The main new result is that for certain DM masses (e.g., 1 feV) the predicted flavor ratios partially overlap with IceCube MESE data, suggesting that IceCube-Gen2 could probe the scenario. The calculations are internally consistent, and the paper is honest about its assumptions.

The softest spot is the obvious one: the entire analysis rests on an unverified interaction. The authors acknowledge this, and the paper is framed as a phenomenology exercise, but it limits the impact. The more specific concern raised by the stress test—the sensitivity to the DM spike density—is real. The effective potential scales linearly with ρ_DM, and the spike profile used (Eq. 2.11) is many orders above NFW. The paper varies the production radius but never the overall density normalization. If the actual density is lower (e.g., no spike or spike weakened by annihilation), the flavor ratios revert toward the vacuum point, which lies far outside the IceCube contours. That makes the claimed overlap less robust than it appears.

A secondary issue is that the comparison with IceCube is qualitative: the paper shows that some Monte Carlo points fall inside the experimental contours, but there is no statistical test (e.g., a chi-squared or likelihood). A more quantitative treatment would strengthen the constraints.

That said, the paper is well written, the methodology is clear, and the results are reproducible from the given equations. It does not oversell itself—the summary notes that the distributions "partially overlap" with data. For a reader working on neutrino–DM phenomenology or multi-messenger astrophysics, this is a useful mapping of a speculative parameter space.

Verdict: This paper deserves a serious referee. A referee should ask for a sensitivity study of the DM density normalization and a more quantitative comparison with IceCube data. But the core work is solid and internally consistent. I would not cite it in my own work (too speculative for my lines of research), but I might bring it to a reading group focused on neutrino or dark matter phenomenology.

Referee report

Major objections (3)

[§2.1, Eq. (2.11)] The predicted flavor deviations depend crucially on the assumed DM spike density profile (Eq. 2.11). The effective potential V_{αβ} ∝ ρ_{DM}/m_ϕ, so a lower density normalization (e.g., NFW-only or a spike suppressed by annihilation) would move the predictions toward the vacuum flavor ratio f⊕_0, which lies outside the IceCube MESE contours shown in Figs. 2-1 and 3-1. The paper tests different production radii (App. A) but does not vary the overall density normalization or consider alternative density profiles. Without a sensitivity study of this assumption, the claimed overlap with IceCube data is not robust—it may be an artifact of the spike profile. The authors should estimate how the flavor distributions change if the density normalization is reduced by a factor, or discuss under what conditions the spike profile is theoretically motivated for the specific AGN considered.
[§3.1, Figs. 2-1, 3-1] The comparison with IceCube MESE and future contours is qualitative: the paper states that the simulated points 'partially overlap' with the experimental confidence regions. To strengthen the claim, the authors should quantify the degree of overlap—e.g., the fraction of Monte Carlo points that lie within the 68% and 95% CL contours for each scenario. This would allow a more objective assessment of which parameter choices are allowed or excluded, and would make the derived coupling constraints (Figs. 4,5,8) more robust.
[§2.1, footnote 1] The paper assumes TXS 0506+056 neutrinos originate from the corona region ([10^2,10^5]Rs or [10,10^2]Rs in App. A), but it cites Ref. [24] stating that a coronal origin is insufficient to explain the observed IceCube flux. This potential inconsistency with the observational motivation for TXS as a neutrino source should be discussed. If a jet origin is more plausible, the DM density in the jet region may differ significantly from the spike profile around the supermassive black hole, affecting the predictions.

Minor objections (7)

[Abstract] Typo: 'cause' should be 'causes'.
[Eq. (2.13)] The expression for the mean free path uses σ_{νϕ} whose form is only given in the text; it would be helpful to write it explicitly (σ_{νϕ} ∝ y_α^2 y_β^2 m_ϕ E / (32π m_F^4) ) in the main text for clarity.
[Figs. 2-1, 3-1, 6-1] The ternary plots are informative but the labels for the experimental contours (IceCube MESE, IceCube-Gen2, future) are given only in the captions; consider adding a legend directly in the figures or a clearer explanation in the text.
[§3.1, first paragraph] The lower limit on Yukawa couplings is set to 0.1. This choice should be justified briefly; is it based on the perturbative limit or the condition that the effective potential be non-negligible?
[Eq. (2.9)] The adiabatic parameter η is defined with anble-brackets denoting averaging over matrix elements. The specific averaging procedure is not described; a short explanation would aid repoducibility.
[§3.2] For DSNB, the paper finds that the flavor distributions lie inside the combined HK/DUNE/JUNO contour. It would be interesting to state the minimial coupling required to produce observable deviations, rather than only noting that the current distributions are indistinguishable.
[References] Several references are given with only arXiv IDs and no journal identification (e.g., [6], [7]). While acceptable, adding publication information would be helpful.

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The paper

The paper claims

Neutrinos propagating through ultra-light scalar dark matter acquire flavor ratios that differ from vacuum expectations, and for AGN sources the predicted compositions partially match IceCube observations, offering a testable signature…

The reading

This paper introduces a hypothetical interaction between neutrinos and ultra-light scalar dark matter, replacing the standard MSW potential in the neutrino oscillation Hamiltonian. The authors consider two neutrino sources: active galactic nuclei (AGN) producing TeV neutrinos with initial flavor ratio (ν_e:ν_μ:ν_τ)=(1:2:0), and the diffuse supernova neutrino background (DSNB) with MeV energies. Using spike dark matter density profiles around NGC 1068 and TXS 0506+056, they compute the averaged flavor ratio at Earth under adiabatic propagation and compare with IceCube MESE data and future IceCube-Gen2 sensitivities. They find that for certain dark matter masses (e.g., m_φ=1 feV) the predicted flavor distributions partially overlap with current data, and that the coupling constants can be constrained by upcoming neutrino telescopes. For the DSNB, with m_φ=$10^{{-22}}$ eV, the predicted flavor ratios lie within the combined sensitivity of Hyper-Kamiokande, DUNE, and JUNO but are not yet distinguishable from the vacuum case.

What carries the argument

The key object is the flavor-dependent effective potential V_{αβ} = (y_α y_β / $m_F^{2}$) (ρ_{DM} / m_φ), which modifies the vacuum neutrino Hamiltonian. For AGNs, the dark matter density follows a spike profile (Eq. 2.11) around the supermassive black hole, with parameters taken from Refs. [2, 3]. The propagation is treated as adiabatic (adiabatic parameter η ≪ 1), so the final averaged flavor ratio is computed by iterating Eq. (2.8) once, using the mixing matrix that diagonalizes the total Hamiltonian at the production site and at Earth. The analysis also enforces a mean-free-path constraint (Eq. 2.13) to ensure forward scattering, and the coupling constants are varied in the range 0.1 ≤ y_α ≤ 10.

Extended reading notes

Core claim

The central claim is that a neutrino–dark matter interaction, parameterized by an effective potential V_{αβ} = (y_α y_β / $m_F^{2}$) (ρ_{DM} / m_φ), can systematically shift the final flavor composition of astrophysical neutrinos away from the vacuum expectation. For AGN neutrinos, the tau-neutrino fraction tends to decrease while the muon-neutrino fraction increases relative to the vacuum point (0.34, 0.31, 0.35). For m_φ = 1 feV and mediator mass m_F = 1 TeV, the predicted flavor distributions for NGC 1068 partially overlap the 68% and 95% confidence contours of IceCube MESE data. Combining IceCube-Gen2 with other future telescopes (KM3NeT, Baikal-GVD, P-ONE, TAMBO) can exclude a larger region of the coupling parameter space and may distinguish normal from inverted neutrino mass ordering. For the DSNB, with m_φ = $10^{{-22}}$ eV and m_F = 0.1 GeV, the flavor distributions remain inside the combined HK/DUNE/JUNO contour but show a mild depletion of muon/tau flavors relative to the vacuum prediction.

Load-bearing premise

The existence of an ultra-light scalar dark matter particle φ that couples to neutrinos via the Lagrangian of Eq. (2.1), a particle that has no independent observational support and is introduced solely for this analysis.

Editorial extensions

If this is right

If the ν-φ interaction exists, the flavor composition of AGN neutrinos becomes a direct probe of ultra-light dark matter properties, with IceCube-Gen2 expected to constrain coupling constants down to y_α ∼ 0.1 for m_φ = 1 feV.
The difference in flavor-ratio distributions between NGC 1068 and TXS 0506+056 (due to different energy ranges and spike profiles) means that multi-source measurements can break degeneracies between dark matter mass and coupling combinations.
For the DSNB, current and near-future detectors are not sensitive enough to distinguish the ν-φ signal from vacuum oscillations; higher statistics or lower m_φ (below 10^{-22} eV) would be needed.
The analysis provides explicit excluded regions in the (y_e, y_μ, y_τ) parameter space for normal and inverted mass ordering, which can be used to guide model building for neutrino–dark matter interactions.

Reading between the lines

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

The same flavor-oscillation framework could be applied to other hypothetical neutrino–dark matter interactions (e.g., vector or tensor mediators), with the effective potential replaced by the appropriate Lorentz structure.
If an ultra-light scalar with mass ~1 feV is detected through other means (e.g., cosmological structure or atomic spectroscopy), the neutrino oscillation signature provides an independent cross-check of its coupling to neutrinos.
The flavor-ratio predictions for AGNs might be degenerate with other beyond-standard-model effects such as neutrino decay or sterile neutrinos; joint spectral and flavor analysis would be needed to disentangle them.
The DSNB flavor prediction, though currently indistinguishable, could become a target for a future mega-tonne water Cherenkov detector or a next-generation liquid argon experiment with enhanced ν_e sensitivity.

Original abstract

The neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum. In this work we consider neutrinos interact with ultra-light scalar dark matters $\phi$ ($m_\phi\ll 1\,{\rm eV}$). When the neutrinos emitted from a distant source and propagate through the dark matter medium, the MSW potential in the Hamiltonian is replaced by the hypothetical $\nu\phi$ effective potential. Two types of neutrino sources are adopted in our calculations. The first is point-like neutrino source, the Active Galactic Nuclei (AGN), which produce $\mathcal{O}({\rm TeV})$ neutrinos primarily through charged pion decay, yielding an initial flavor ratio of ($\nu_e,\nu_\mu,\nu_\tau$)=($1:2:0$). We focus on two specific AGNs, NGC 1068 and TXS 0506+056 in our analysis, whose distances from Earth are much larger than the neutrino oscillation lengths. We consider the range of $\nu\phi$ coupling constant such that the adiabatic condition and mean free path can be satisfied. Hence, by assuming neutrinos are produced randomly from their corona regions, we compute the averaged flavor ratio at Earth with $m_\phi=10,1,0.1\,{\rm peV}$ and $m_\phi=1,0.1,0.01\,{\rm feV}$, generate the ternary plots of neutrino flavors, and compare the results with the IceCube present and future sensitivities. The second source considered is the Diffuse Supernova Neutrino Background (DSNB), it is an isotropic neutrino source with energy $\mathcal{O}({\rm MeV})$. Applying the core-collapse simulation neutrino temperatures to the DSNB flux, we repeat the similar analysis for the DSNB with $m_\phi=10^{-22}\,{\rm eV}$, and we estimate different neutrino flavors lies in the HK/DUNE/JUNO combined sensitivities limit.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923 + fulltext-p1-20260923, 2026-09-24: 274 requests, 363,210 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.27 · randomized assignment 0.06 · states quantitative result 0.34 · compares with prior results 0.75 · 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.

The neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum. In this work we consider neutrinos interact with ultra-light scalar dark matters $φ$ ($m_φ\ll 1\,{\rm eV}$). When the neutrinos emitted from a distant source and propagate through the dark matter medium, the MSW potential in the Hamiltonian is replaced by the hypothetical $νφ$ effective potential. Two types of neutrino sources are adopted in our calculations. The first is point-like neutrino source, the Active Galactic Nuclei (AGN), which produce $\mathcal{O}({\rm TeV})$ neutrinos primarily through charged pion decay, yielding an initial flavor ratio of ($ν_e,ν_μ,ν_τ$)=($1:2:0$). We focus on two specific AGNs, NGC 1068 and TXS 0506+056 in our analysis, whose distances from Earth are much larger than the neutrino oscillation lengths. We consider the range of $νφ$ coupling constant such that the adiabatic condition and mean free path can be satisfied. Hence, by assuming neutrinos are produced randomly from their corona regions, we compute the averaged flavor ratio at Earth with $m_φ=10,1,0.1\,{\rm peV}$ and $m_φ=1,0.1,0.01\,{\rm feV}$, generate the ternary plots of neutrino flavors, and compare the results with the IceCube present and future sensitivities. The second source considered is the Diffuse Supernova Neutrino Background (DSNB), it is an isotropic neutrino source with energy $\mathcal{O}({\rm MeV})$. Applying the core-collapse simulation neutrino temperatures to the DSNB flux, we repeat the similar analysis for the DSNB with $m_φ=10^{-22}\,{\rm eV}$, and we estimate different neutrino flavors lies in the HK/DUNE/JUNO combined sensitivities limit.

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 neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum.	background 1.00	0.07	0.10	asserted 1.00
s1	In this work we consider neutrinos interact with ultra-light scalar dark matters $φ$ ($m_φ\ll 1\,{\rm eV}$).	contribution 0.84	0.48	0.03	asserted 0.87
s2	When the neutrinos emitted from a distant source and propagate through the dark matter medium, the MSW potential in the Hamiltonian is replaced by the hypothetical $νφ$ effective potential.	method 0.89	0.23	0.04	asserted 0.93
s3	Two types of neutrino sources are adopted in our calculations.	method 0.90	0.77	0.02	asserted 0.94
s4	The first is point-like neutrino source, the Active Galactic Nuclei (AGN), which produce $\mathcal{O}({\rm TeV})$ neutrinos primarily through charged pion decay, yielding an initial flavor ratio of ($ν_e,ν_μ,ν_τ$)=($1:2:0$).	method 0.88	0.24	0.03	asserted 1.00
s5	We focus on two specific AGNs, NGC 1068 and TXS 0506+056 in our analysis, whose distances from Earth are much larger than the neutrino oscillation lengths.	method 0.82	0.68	0.02	asserted 1.00
s6	We consider the range of $νφ$ coupling constant such that the adiabatic condition and mean free path can be satisfied.	method 0.96	0.64	0.03	asserted 0.76
s7	Hence, by assuming neutrinos are produced randomly from their corona regions, we compute the averaged flavor ratio at Earth with $m_φ=10,1,0.1\,{\rm peV}$ and $m_φ=1,0.1,0.01\,{\rm feV}$, generate the ternary plots of neutrino flavors, and compare the results with the IceCube present and future sensitivities.	method 0.95	0.95	0.10	asserted 0.97
s8	The second source considered is the Diffuse Supernova Neutrino Background (DSNB), it is an isotropic neutrino source with energy $\mathcal{O}({\rm MeV})$.	method 0.54	0.31	0.03	asserted 1.00
s9	Applying the core-collapse simulation neutrino temperatures to the DSNB flux, we repeat the similar analysis for the DSNB with $m_φ=10^{-22}\,{\rm eV}$, and we estimate different neutrino flavors lies in the HK/DUNE/JUNO combined sensitivities limit.	method 0.40	0.91	0.17	asserted 0.88

What kind of paper the classifier reports this is: simulation study 0.76 · evidence from simulation or computation 1.00.

What the paper reports

Result sentences with where each is established. A qualification the authors state beside a result is attached to it.

Concerning this extreme case, we find $l_min∼1.81×10^-4 pc$ ($l_min∼1.85×10^-4 pc$) for NGC 1068 (TXS 0506+056) when $ρ_DM$ is evaluated at $10R_s$ and $y_α,β=10$.

derivation asserted Active Galactic Nuclei p 0.96

In terms of Schwarzschild radius, $l_min/R_s∼190$ ($l_min/R_s∼6$) for NGC 1068 (TXS 0506+056).

derivation asserted Active Galactic Nuclei p 0.93

The flavor distributions in Fig. [ref] for Case-(a,b,c,d) extend along the common direction and tend to have smaller values of $f̅_ν_x^⊕$ and larger values of $f̅_ν_e^⊕$.

simulation asserted Summary p 0.91

From all of the ternary plots we see that the final tau fraction $f̅^⊕_τ$ under the influence of $νϕ$ interaction tends to be decreased from $f^⊕_0τ$, and $f̅^⊕_μ$ are mostly be increased from $f^⊕_0μ$.

observation asserted Summary p 0.90

It turns out $l∼400 kpc$ around Earth (the maximum DM density is $ρ^⊕_DM=0.4 GeV/cm^3$) and $l∼130 Gpc$ in extragalactic medium.

derivation asserted Diffuse Supernova Neutrino Background p 0.90

The flavor ratio distributions are almost identical for the four coupling combinations Case-(a,b,c,d), and the distribution points lie within the combined experimental contour.

observation asserted DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO p 0.86

These distributions exhibit some common features: (i) for $m_ϕ=10$ peV, the electron flavor ratio $f̅^⊕_e$ tends to increase rather than decrease relative to the red point, while $f̅^⊕_μ,τ$ tends to change in the opposite direction; (ii) for $m_ϕ≤0.1$ peV, the electron flavor ratio $f̅^⊕_e$ mildly increase, while $f̅^⊕_τ$ ($f̅^⊕_μ$) tends to substantially decrease (increase) relative to the red point $f^⊕_0=(0.34,0.31,0.35)$.

simulation asserted AGN Neutrino Flavor Ratio in IceCube p 0.85

The anti-electron neutrino fraction is mildly shifted away from the vacuum case (red point).

observation asserted DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO p 0.83

The parameters $(y_e, y_μ , y_τ)$ of Case-(d) excluded by IceCube MESE 95% C.L. contour are shown in Fig. [ref].

measurement asserted AGN Neutrino Flavor Ratio in IceCube p 0.83

The constraint boundaries of the first row of Fig. [ref] are roughly consistent with the color boundaries in Fig. [ref] because darker regions indicate points that significantly deviate from $f^⊕_0$, and thus be excluded by the experiments.

interpretation asserted AGN Neutrino Flavor Ratio in IceCube p 0.83

Fig [ref] shows the correspoding flavor ratio distribution for the production range $[10^2,10^5]R_s$.

simulation asserted AGN Neutrino Flavor Ratio in IceCube p 0.83

This patch arises from the nonzero value of the third coupling constant.

interpretation asserted AGN Neutrino Flavor Ratio in IceCube p 0.82

In Fig. [ref], we demonstrate the constraints on the coupling constants for $m_ϕ=1 feV$.

derivation asserted AGN Neutrino Flavor Ratio in IceCube p 0.82

However, shapes of the distributions are almost identical for Case-(a,c,d), only Case-(b) $(0,y_μ,y_τ)$ exhibits a mild difference.

simulation asserted Summary p 0.82

Therefore, the Hamiltonian is dominated by $V^⊕$ and the final flavor ratio depends on the relative strength between each $V^⊕_αβ$.

interpretation asserted AGN Neutrino Flavor Ratio in IceCube p 0.81

Conditions under which these results were obtained

Sentences the authors wrote about who was studied, how they were assigned, and what they received. Selected from the Methods; nothing inferred.

assumption or scope We assume the DM density between CCSN and Earth varies as a linear function of $z$, denoted by $ρ_DM(z)$. Diffuse Supernova Neutrino Background · p 0.97

assumption or scope We assume neutrinos are Majorana fermions and couple to hypothetical dark scalar $ϕ$ through a fermionic mediator $F$. Neutrino Oscillation in Dark Matter · p 0.96

assumption or scope The coupling constants are chosen below 10 by the perturbative condition, and the lower limit of $y_α$ is fixed at $0.1$, which is not too low for DMs to affect the neutrino flavor. AGN Neutrino Flavor Ratio in IceCube · p 0.96

assumption or scope We consider the range of $νϕ$ coupling constant such that the adiabatic condition and mean free path can be satisfied. Introduction · p 0.95

assumption or scope We assume neutrinos from NGC are produced within the corona, which possess radius $R∈[10,10^2]R_s$[NGC's corona radius is estimated by $R∈[3,100]R_s$ [ref] . Active Galactic Nuclei · p 0.95

assumption or scope For the analysis of AGNs, $m_F$ is fixed to $1 TeV$. Active Galactic Nuclei · p 0.95

assumption or scope Due to the adiabatic condition, we only need to consider the average flavor ratio at the production location and the Earth. AGN Neutrino Flavor Ratio in IceCube · p 0.95

assumption or scope For each event, the neutrinos are assumed to be produced within the range $[10,10^2]R_s$ randomly in logarithmic scale. AGN Neutrino Flavor Ratio in IceCube · p 0.95

assumption or scope The neutrino production regions for NGC 1068 and TXS 0506+056 are assumed to be $[10,10^2]R_s$ (corona region) and $[10^2,10^5]R_s$, respectively. Summary · p 0.95

assumption or scope The distances between Earth and AGNs are much longer than the oscillation length, and the adiabatic parameter is extremely small, so the neutrino propagates adiabatically and the final averaged flavor ratio at Earth is obtained from Eq.([ref]) with $n=1$. Summary · p 0.95

assumption or scope Considering two sets of dark matter mass, $m_ϕ=10, 1, 0.1 peV$ and $m_ϕ=1, 0.1, 0.01 feV$, with the mediator mass fixed at $m_F=1 TeV$, and assuming the neutrinos are produced randomly inside corona region, we generate the ternary plots of $f̅^⊕_e,μ,τ$ with four cases, $(y_e, y_μ, 0)$, $(0, y_μ, y_τ)$, $(y_e, 0, y_τ)$, and all $y_e,μ,τ$ nonzero. Summary · p 0.95

assumption or scope Hence, by assuming neutrinos are produced randomly from their corona regions, we compute the averaged flavor ratio at Earth with $m_ϕ=10,1,0.1 peV$ and $m_ϕ=1,0.1,0.01 feV$, generate the ternary plots of neutrino flavors, and compare the results with the IceCube present and future sensitivities. Introduction · p 0.94

assumption or scope The mean free path $l$ is related to the scattering cross section and the number density of DM [equation] The cross section is given by $σ_νϕ=y^2_αy^2_βm_ϕE/(32πm_F^4)$ under the heavy mediator limit, i.e. $m_F≥1 TeV$ and $m_F^2≫m_ϕE$. Active Galactic Nuclei · p 0.94

assumption or scope The $𝒪(TeV)$ neutrinos are assumed to be produced from NGC 1068 and TXS 0506+056 via pion decay with initial flavor ratio $(ν_e:ν_μ:ν_τ)=(1:2:0)$. Summary · p 0.94

assumption or scope We assumed the flavor-dependent interaction between neutrinos and complex dark scalar $ϕ$ [ref] , and computed the flavor ratio by adding the effective potential to the Hamiltonian using the spiked density profile of NGC 1068 and TXS 0506+056. Introduction · p 0.93

assumption or scope The propagation of neutrinos is adiabatic if $η≪1$. Neutrino Oscillation in Dark Matter · p 0.93

assumption or scope For detection on Earth, we require that the neutrinos be forward-scattered through their path. Active Galactic Nuclei · p 0.93

assumption or scope So the mean free path should be longer than the distance between AGN and Earth. Active Galactic Nuclei · p 0.93

assumption or scope We fixed $z_max=5$ for which there is a reasonable amount of star formation. Diffuse Supernova Neutrino Background · p 0.93

assumption or scope The upper limit for $y_e,μ,τ$ is 10, and we fix the lower limit at 0.1. Summary · p 0.93

Measurements

Numbers as the authors wrote them, bound to what they measure. Units, degrees of freedom and arithmetic checks are code, not the model.

Quantity	Value	Where	Checked by code
interact with ultra-light scalar dark matters ϕ (m_ϕ≪	1 eV p 0.79	Introduction	consistent number matches the authors' source text
the similar analysis for the DSNB with m_ϕ=10^	-22 eV p 0.78	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction)
and the DM mass is fixed at 10^	-22 eV p 0.83	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction)
over energy and coupling constant is around 10^	-6 pc p 0.99	Active Galactic Nuclei	consistent number matches the authors' source text
The relevant parameters for TXS 0506+056 are η≃	6×10^-11 p 0.97	Active Galactic Nuclei	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Acknowledgment)
TXS 0506+056 are η≃6×10^-11 and averaged L_ij ∼10^	-4 pc p 0.97	Active Galactic Nuclei	consistent number matches the authors' source text
σ_νϕ=y^2_αy^2_βm_ϕE/(32πm_F^4) under the heavy mediator limit, i.e. m_F≥	1 TeV p 0.59	Active Galactic Nuclei	consistent number matches the authors' source text
the analysis of AGNs, m_F is fixed to	1 TeV p 0.69	Active Galactic Nuclei	consistent number matches the authors' source text
Concerning this extreme case, we find l_min∼	1.81×10^-4 pc p 0.98	Active Galactic Nuclei	consistent number matches the authors' source text not repeated same number stated elsewhere in the paper (stated once)
this extreme case, we find l_min∼1.81×10^-4 pc (l_min∼	1.85×10^-4 pc p 0.98	Active Galactic Nuclei	consistent number matches the authors' source text not repeated same number stated elsewhere in the paper (stated once)
We adopt T_ν_e=	5 MeV p 0.96	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text
We adopt T_ν_e=5 MeV, T_ν̅_e=	6 MeV p 0.96	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text
We adopt T_ν_e=5 MeV, T_ν̅_e=6 MeV, and T_ν_x=	7 MeV p 0.96	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text
fix m_ϕ to this value and m_F to	0.1 GeV p 0.75	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (AGN Neutrino Flavor Ratio in IceCube, DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Introduction)
It turns out l∼	400 kpc p 0.98	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
around Earth (the maximum DM density is ρ^⊕_DM=	0.4 GeV p 0.98	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (AGN Neutrino Flavor Ratio in IceCube, Active Galactic Nuclei)
The maximum average oscillation length is ∼10^	-5 pc p 0.97	Diffuse Supernova Neutrino Background	consistent number matches the authors' source text
potentials at Earth lie within the range [	3.1×10^-21 p 0.99	AGN Neutrino Flavor Ratio in IceCube	consistent number matches the authors' source text not repeated same number stated elsewhere in the paper (stated once)
at Earth lie within the range [3.1×10^-21	3.1×10^-17 p 0.99	AGN Neutrino Flavor Ratio in IceCube	consistent number matches the authors' source text not repeated same number stated elsewhere in the paper (stated once)
is obtained from Eq.([ref]a) with the temperature T_ν_e=	5 MeV p 0.98	DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	consistent number matches the authors' source text
from Eq.([ref]a) with the temperature T_ν_e=5 MeV, T_ν̅_e=	6 MeV p 0.98	DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	consistent number matches the authors' source text
the temperature T_ν_e=5 MeV, T_ν̅_e=6 MeV, and T_ν_x=	7 MeV p 0.98	DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	consistent number matches the authors' source text
order smaller than AGN neutrino, we consider m_ϕ=10^	-22 eV p 0.97	DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction)
AGN neutrino, we consider m_ϕ=10^-22 eV and m_F=	0.1 GeV p 0.97	DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (AGN Neutrino Flavor Ratio in IceCube, DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background)
Even though, the m_ϕ=10^	-22 eV p 0.92	DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction)
feV, with the mediator mass fixed at m_F=	1 TeV p 0.53	Summary	consistent number matches the authors' source text
We adopt the lower limit of m_ϕ=10^	-22 eV p 0.90	Summary	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction)
eV and fix the mediator mass m_F to	0.1 GeV p 0.90	Summary	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (AGN Neutrino Flavor Ratio in IceCube, DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background)
sensitivities is much smaller than the IceCube MESE	95% p 0.94	The Coupling Constants Excluded by Combined $ν$ Telescopes	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (AGN Neutrino Flavor Ratio in IceCube, TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$)

Limitations the authors state

Since the location of neutrino production is under investigation. AGN Neutrino Flavor Ratio in IceCube · p 0.86

The full text, sentence by sentence

Does the body support the main claim as the abstract states it? The classifier reports supported 0.87, and the claim asserting more than the results show 0.63.

207 body sentences from the LaTeX source, each with the classifier's labels. The number is the probability it gave the label.

section	sentence	role	the authors' own work	states the main conclusion	states a condition	quantitative
Introduction	The neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum.	background 0.62	0.15	0.09	0.26	0.07
Introduction	In this work we consider neutrinos interact with ultra-light scalar dark matters $ϕ$ ($m_ϕ≪1 eV$).	setup 1.00	0.65	0.06	0.87	0.79
Introduction	When the neutrinos emitted from a distant source and propagate through the dark matter medium, the MSW potential in the Hamiltonian is replaced by the hypothetical $νϕ$ effective potential.	setup 0.99	0.31	0.08	0.82	0.05
Introduction	Two types of neutrino sources are adopted in our calculations.	setup 0.68	0.83	0.04	0.42	0.31
Introduction	The first is point-like neutrino source, the Active Galactic Nuclei (AGN), which produce $𝒪(TeV)$ neutrinos primarily through charged pion decay, yielding an initial flavor ratio of ($ν_e,ν_μ,ν_τ$)=($1:2:0$).	setup 0.96	0.31	0.05	0.47	0.82
Introduction	We focus on two specific AGNs, NGC 1068 and TXS 0506+056 in our analysis, whose distances from Earth are much larger than the neutrino oscillation lengths.	setup 0.91	0.77	0.04	0.88	0.89
Introduction	We consider the range of $νϕ$ coupling constant such that the adiabatic condition and mean free path can be satisfied.	method 0.54	0.67	0.06	0.95	0.06
Introduction	Hence, by assuming neutrinos are produced randomly from their corona regions, we compute the averaged flavor ratio at Earth with $m_ϕ=10,1,0.1 peV$ and $m_ϕ=1,0.1,0.01 feV$, generate the ternary plots of neutrino flavors, and compare the results with the IceCube present and future sensitivities.	method 1.00	0.93	0.12	0.94	0.58
Introduction	The second source considered is the Diffuse Supernova Neutrino Background (DSNB), it is an isotropic neutrino source with energy $𝒪(MeV)$.	setup 0.86	0.43	0.06	0.39	0.51
Introduction	Applying the core-collapse simulation neutrino temperatures to the DSNB flux, we repeat the similar analysis for the DSNB with $m_ϕ=10^-22 eV$, and we estimate different neutrino flavors lies in the HK/DUNE/JUNO combined sensitivities limit.	method 0.90	0.89	0.18	0.80	0.78
Introduction	Neutrinos are known to oscillate between different flavor eigenstates while propagating in vacuum due to their tiny but non-negligible mass differences.	background 1.00	0.05	0.04	0.11	0.16
Introduction	It is also known that neutrinos interact with electrons in the medium, and the Hamiltonian of neutrinos must be modified by an additional “effective potential.” This is known as the Mikheyev–Smirnov–Wolfenstein (MSW) effect.	background 1.00	0.05	0.03	0.10	0.04
Introduction	The neutrino-matter interaction will change the averaged flavor ratio between different flavor eigenstates in the vacuum.	background 0.98	0.10	0.13	0.16	0.05
Introduction	In this work, we consider neutrinos interacting with ultra-light scalar dark matter (DM) $ϕ$	setup 0.98	0.80	0.04	0.76	0.04
Introduction	Active Galactic Nuclei (AGNs) are point-like sources of neutrinos with energy scale $𝒪(TeV)$, and the DM density around the central supermassive black hole has been proposed to be a spiked-like distribution [ref] .	background 0.76	0.14	0.06	0.49	0.27
Introduction	The IceCube collaboration has identified high energy neutrinos from two distinct AGNs, the NGC 1068 and TXS 0506+056, with energy $E∈[1.5,15] TeV$ and $[40,4000] TeV$, respectively [ref] .	background 0.99	0.09	0.05	0.12	0.95
Introduction	We assumed the flavor-dependent interaction between neutrinos and complex dark scalar $ϕ$ [ref] , and computed the flavor ratio by adding the effective potential to the Hamiltonian using the spiked density profile of NGC 1068 and TXS 0506+056.	method 0.92	0.86	0.11	0.93	0.12
Introduction	The Medium Energy Starting Event (MESE), which is based on the 11.4 years of IceCube data, measures whole sky neutrino events with energies of at least 1 TeV and provides a three-flavor composition of astrophysical neutrinos [ref] .	background 0.97	0.12	0.05	0.21	0.90
Introduction	Therefore, we compared our predictions for AGN-produced neutrinos, produced from pion decay and the initial flavor ratio $(ν_e:ν_μ:ν_τ)=(1:2:0)$, with the IceCube MESE data.	method 0.83	0.82	0.11	0.27	0.78
Introduction	The future IceCube-Gen2 [ref]	future work 0.64	0.15	0.03	0.11	0.05
Introduction	In addition to IceCube observations, KM3NeT [ref] , Baikal-GVD [ref] , P-ONE [ref] , and TAMBO [ref] have the potential to detect high energy neutrinos and contribute to the flavor ratio constraints.	background 0.79	0.09	0.04	0.08	0.06
Introduction	Combining IceCube MESE, IceCube-Gen2, and additional contributions from future neutrino telescopes [ref] ,	background 0.45	0.15	0.03	0.16	0.05
Introduction	we are able to distinguish the flavor ratio signal from different DM mass	result 0.71	0.77	0.45	0.28	0.11
Introduction	and from different production sources.	other 0.57	0.13	0.04	0.19	0.03
Introduction	Furthermore, the couplings of the neutrino-DM interactions would be constrained by these experimental limits.	interpretation 0.78	0.17	0.18	0.18	0.04
Introduction	The Diffuse Supernova Neutrino Background (DSNB) is an alternative neutrino source considered in this work, with energy scale $𝒪(10 MeV)$.	setup 0.80	0.48	0.05	0.36	0.71
Introduction	The neutrino fluxes with certain flavor structure are produced by core-collapse supernovae that have occurred throughout the cosmic history and are nearly isotropic.	background 0.78	0.10	0.05	0.41	0.08
Introduction	Detectors such as Super-Kamiokande/Hyper-Kamiokande (SK/HK) [ref] , Deep Underground Neutrino Experiment (DUNE) [ref] , and Jiangmen Underground Neutrino Observatory (JUNO) [ref] are aimed to detect the DSNB flux and their flavor ratio.	background 0.81	0.11	0.04	0.09	0.05
Introduction	The detection of DSNB from these experiments relies on different neutrino interactions.	background 0.51	0.13	0.05	0.13	0.04
Introduction	For example, the DUNE depends on the charge current interaction on liquid Argon to identify electron neutrino; the SK/HK and JUNO depend on the Inverse Beta Decay (IBD), which is sensitive to $ν̅_e$.	background 0.50	0.10	0.04	0.13	0.06
Introduction	On the other hand, the muon and tau neutrinos can be detected from neutrino-electron elastic scattering.	setup 0.54	0.12	0.04	0.23	0.04
Introduction	Applying the $νϕ$ interactions into the Hamiltonian would alter the neutrino flavors from DSNB, and we compared the final flavor ratio with the experimental limits.	method 0.77	0.91	0.29	0.29	0.26
Introduction	The paper is organized as follow: In Section [ref], we introduce the model of $νϕ$ interaction, the spiked DM density around AGN, the DSNB flux from core-collapse supernovae, and modified the vacuum neutrino Hamiltonian by adding the effective potential.	other 0.94	0.43	0.03	0.17	0.05
Introduction	Then we compute the average flavor ratio by taking the oscillation length and the adiabatic condition into account.	method 0.92	0.88	0.04	0.77	0.08
Introduction	We set our analysis upper limit on coupling constant with the neutrino mean free path.	method 0.74	0.90	0.19	0.51	0.09
Introduction	In Section [ref], we generate and analyze the ternary plot of flavor ratio distributions for AGN neutrinos with different set of DM mass, the event averaged deviation of final flavor ratio from neutrinos propagate in the vacuum with initial flavor ratio $(1:2:0)$, and show the constraint on coupling constant with normal and inverse mass ordering.	other 0.52	0.86	0.12	0.56	0.43
Introduction	We repeat the similar analysis for DSNB neutrinos but with the flavor component $(ν_e,ν_μ,ν_τ)$ replaced by $(ν̅_e,ν_x,ν_e)$, and the DM mass is fixed at $10^-22 eV$.	method 0.80	0.87	0.06	0.90	0.83
Introduction	We summarize our work in Section [ref].	other 1.00	0.25	0.03	0.06	0.03
Neutrino Oscillation in Dark Matter	We assume neutrinos are Majorana fermions and couple to hypothetical dark scalar $ϕ$ through a fermionic mediator $F$.	setup 1.00	0.45	0.04	0.96	0.04
Neutrino Oscillation in Dark Matter	The Lagrangian is given by [ref] [equation] where the Greek alphabet $α=e,μ,τ$ is the neutrino flavor label, $y_α$ is coupling constant.	setup 1.00	0.51	0.03	0.45	0.05
Neutrino Oscillation in Dark Matter	In the flavor basis, the Hamiltonian is [equation] where $U$ is the PMNS matrix, $V$ is the effective potential matrix and it depends on the $νϕ$ interaction.	setup 0.99	0.59	0.04	0.31	0.04
Neutrino Oscillation in Dark Matter	The differences of mass square for Normal Ordering (Inverse Ordering) are given by [ref]	setup 0.51	0.25	0.03	0.16	0.06
Neutrino Oscillation in Dark Matter	[equation] From ([ref]), we can write down the components of $V$: [equation] The Feynman diagram of $νϕ$ scattering is shown in Fig. [ref].	setup 0.89	0.49	0.03	0.10	0.05
Neutrino Oscillation in Dark Matter	The effective mass squared is given by [equation] where $U'$ is the mixing matrix that diagonalized the flavor basis total Hamiltonian Eq.([ref]).	setup 0.94	0.65	0.03	0.17	0.05
Neutrino Oscillation in Dark Matter	Then oscillation length is [equation] where the Latin alphabets $i,j$ are the mass eigenstate label.	setup 0.96	0.60	0.03	0.19	0.06
Neutrino Oscillation in Dark Matter	We denote the initial flavor ratio by $f_0=(f_0e,f_0μ,f_0τ)$, then after propagating a distance that is far longer than the oscillation length, the final average flavor ratio is given by [ref] [equation] where $r_0$ is the distance to the source.	setup 0.59	0.48	0.06	0.88	0.14
Neutrino Oscillation in Dark Matter	By iterating Eq.([ref]) $n+1$ times, we obtain the final average ratio at Earth [equation] If the DM density changes slowly along the path, the neutrino propagates adiabatically.	method 0.82	0.78	0.07	0.90	0.14
Neutrino Oscillation in Dark Matter	The adiabatic parameter is defined by [equation] where $I$ is the $3×3$ identity matrix.	setup 0.96	0.65	0.04	0.38	0.06
Neutrino Oscillation in Dark Matter	The $⟨...⟩$ denotes the average over all the matrix elements.	setup 0.97	0.39	0.03	0.17	0.04
Neutrino Oscillation in Dark Matter	The propagation of neutrinos is adiabatic if $η≪1$.	setup 0.94	0.43	0.09	0.93	0.86
Active Galactic Nuclei	The neutrino spectrum from AGN can be expressed by the power law $Φ(E)∝E^-γ$ [ref] .	setup 0.58	0.18	0.04	0.45	0.07
Active Galactic Nuclei	Assuming $N_tot$ the total event number measured by IceCube, the differential event contributed from certain energy $E$ is written as [equation] where $E_max(min)$ is the energy upper (lower) limit of neutrino from AGN.	setup 0.54	0.52	0.03	0.74	0.08
Active Galactic Nuclei	The DM density around AGN is given by the spike-profile, [equation] where $R_s$ is the Schwarzschild radius.	setup 0.98	0.40	0.04	0.53	0.05
Active Galactic Nuclei	The saturation density $ρ_sat$ depends on the $ϕϕ^∗$ annihilation, and the cross section is proportional to $y_α^2y^2_β$ [ref] .	setup 0.80	0.26	0.04	0.41	0.05
Active Galactic Nuclei	The total contributions to annihilation cross section is $∑_α,βσ_ϕϕ^∗→ν_αν̅_β$. $ρ_sp$ is the spike density around the central supermassive black hole and is given by [ref] [equation] where $R_sp$ indicates the size of the spike.	setup 0.94	0.28	0.04	0.18	0.05
Active Galactic Nuclei	For $r≥R_sp$ the spike density is replace by the Navarro-Frenk-White (NFW) profile.	setup 0.97	0.37	0.03	0.83	0.07
Active Galactic Nuclei	For NGC 1068, the oscillation length averaged over energy and coupling constant is around $10^-6 pc$, which is much shorter than the distance from NGC 1068 to Earth.	result 0.92	0.87	0.14	0.52	0.99
Active Galactic Nuclei	The maximum of adiabatic parameter $η$ is below $10^-10$, which means neutrinos propagates extremely adiabatically.	result 0.63	0.89	0.15	0.69	0.98
Active Galactic Nuclei	Therefore, we can simply consider the DM density at the source location and around the Earth.	method 0.50	0.79	0.13	0.89	0.06
Active Galactic Nuclei	We assume neutrinos from NGC are produced within the corona, which possess radius $R∈[10,10^2]R_s$[NGC's corona radius is estimated by $R∈[3,100]R_s$ [ref] .	setup 0.98	0.71	0.06	0.95	0.90
Active Galactic Nuclei	Ref. [ref] states that the TXS's neutrino flux from corona isn't sufficient enough to produce IceCube observed neutrino.].	background 0.93	0.10	0.09	0.20	0.52
Active Galactic Nuclei	The DM density around the Earth is taken to be $ρ^⊕_DM=0.4 GeV/cm^3$.	setup 0.99	0.49	0.03	0.90	0.94
Active Galactic Nuclei	The relevant parameters for TXS 0506+056 are $η≃6×10^-11$ and averaged $L_ij ∼10^-4 pc$.	setup 0.88	0.68	0.04	0.51	0.97
Active Galactic Nuclei	The $νϕ$ scattering may affect the direction of propagation.	setup 0.48	0.24	0.08	0.24	0.03
Active Galactic Nuclei	For detection on Earth, we require that the neutrinos be forward-scattered through their path.	setup 0.75	0.35	0.09	0.93	0.04
Active Galactic Nuclei	So the mean free path should be longer than the distance between AGN and Earth.	setup 0.73	0.39	0.11	0.93	0.82
Active Galactic Nuclei	The mean free path $l$ is related to the scattering cross section and the number density of DM [equation] The cross section is given by $σ_νϕ=y^2_αy^2_βm_ϕE/(32πm_F^4)$ under the heavy mediator limit, i.e. $m_F≥1 TeV$ and $m_F^2≫m_ϕE$.	setup 0.80	0.53	0.05	0.94	0.59
Active Galactic Nuclei	The $ρ_DM$ is nearly independent of $m_ϕ$ when $m_ϕ≪m_F$, so $l$ depends mainly on the coupling constant and neutrino energy.	method 0.31	0.67	0.10	0.92	0.11
Active Galactic Nuclei	For the analysis of AGNs, $m_F$ is fixed to $1 TeV$.	setup 0.95	0.84	0.04	0.95	0.69
Active Galactic Nuclei	For a given $y_α,β$, $l$ reaches its minimum when (i) $ρ_DM$ is maximum, i.e., the peaked spike density, and (ii) $E=E_max$.	result 0.59	0.86	0.10	0.84	0.14
Active Galactic Nuclei	Concerning this extreme case, we find $l_min∼1.81×10^-4 pc$ ($l_min∼1.85×10^-4 pc$) for NGC 1068 (TXS 0506+056) when $ρ_DM$ is evaluated at $10R_s$ and $y_α,β=10$.	result 1.00	0.96	0.07	0.92	0.98
Active Galactic Nuclei	In terms of Schwarzschild radius, $l_min/R_s∼190$ ($l_min/R_s∼6$) for NGC 1068 (TXS 0506+056).	result 1.00	0.93	0.09	0.34	0.99
Active Galactic Nuclei	As neutrinos propagate outward, $l$ increases because $ρ_DM$ gets lower.	interpretation 0.47	0.78	0.10	0.46	0.06
Active Galactic Nuclei	Therefore, neutrinos produced in the direction forward to Earth are rarely deflected by DM.	interpretation 0.80	0.85	0.15	0.39	0.10
Diffuse Supernova Neutrino Background	The neutrino spectrum emitted from a supernova is given by [ref] [equation] where $E_tot=3×10^53 erg$ is the total emitted energy, the factor $1/6$ factor stands for energy of one of $ν_e$, $ν_e̅$, $ν_μ$, $ν_μ̅$, $ν_τ$, $ν_τ̅$, and $T$ is the neutrino temperature.	setup 0.88	0.25	0.03	0.35	0.89
Diffuse Supernova Neutrino Background	The diffuse differential neutrino flux is given by [equation] The core-collapse supernova rate $R_CCSN$ and the star-formation rate are parameterized as [ref]	setup 0.82	0.30	0.03	0.13	0.06
Diffuse Supernova Neutrino Background	where $B=2^1-α/β$, $C=2^(β-α)/γ·5^1-β/γ$, $ρ̇_0=0.0178^+0.0035_-0.0036 M_⊙ yr^-1 Mpc^-3$, and $α=3.4±0.2$, $β=-0.3±0.2$, $γ=-3.5±1$.	setup 0.91	0.43	0.03	0.27	0.97
Diffuse Supernova Neutrino Background	The initial mass function $ψ(M)$ is proportional to $M^-2.35$ [ref] .	setup 0.66	0.22	0.03	0.36	0.68
Diffuse Supernova Neutrino Background	We fixed $z_max=5$ for which there is a reasonable amount of star formation.	setup 0.93	0.88	0.03	0.93	0.74
Diffuse Supernova Neutrino Background	The neutrino temperature can be obtained by the core-collapse simulation of neutrino emissions [ref] .	method 0.40	0.28	0.04	0.37	0.08
Diffuse Supernova Neutrino Background	The simulations predict the temperature hierarchy $T_ν_e<T_ν̅_e<T_ν_x$.	background 0.67	0.15	0.09	0.34	0.97
Diffuse Supernova Neutrino Background	We adopt $T_ν_e=5 MeV$, $T_ν̅_e=6 MeV$, and $T_ν_x=7 MeV$ in our calculations.	setup 0.92	0.87	0.04	0.89	0.96
Diffuse Supernova Neutrino Background	where $ν_x$ is the collective notation of $ν_μ,ν̅_μ,ν_τ,ν̅_τ$.	setup 1.00	0.33	0.03	0.21	0.06
Diffuse Supernova Neutrino Background	Eq.([ref]a) indicates the initial flavor ratio of the DSNB flux, while Eq.([ref]b) is the initial ratio for each energy bin.	setup 0.96	0.43	0.04	0.17	0.08
Diffuse Supernova Neutrino Background	Since the neutrinos are propagating in the extragalactic medium, the dark matter density is far smaller than the AGN spike density.	setup 0.75	0.36	0.08	0.61	0.94
Diffuse Supernova Neutrino Background	Furthermore, the neutrino energy from DSNB scales around $𝒪(MeV)$, hence the vacuum Hamiltonian is several order larger than those of AGN neutrinos.	setup 0.55	0.48	0.07	0.46	0.93
Diffuse Supernova Neutrino Background	We must therefore increase the value of effective potential $V_αβ$.	interpretation 0.38	0.42	0.07	0.40	0.07
Diffuse Supernova Neutrino Background	The theoretical lower limit of ultra-light dark matter mass is approximately $10^-22 eV$.	setup 0.53	0.22	0.07	0.58	0.93
Diffuse Supernova Neutrino Background	We fix $m_ϕ$ to this value and $m_F$ to $0.1 GeV$, then use the exact $σ_νϕ$ [ref] to compute the neutrino mean free path.	method 0.89	0.88	0.06	0.83	0.75
Diffuse Supernova Neutrino Background	It turns out $l∼400 kpc$ around Earth (the maximum DM density is $ρ^⊕_DM=0.4 GeV/cm^3$) and $l∼130 Gpc$ in extragalactic medium.	result 0.99	0.91	0.12	0.47	0.98
Diffuse Supernova Neutrino Background	The maximum average oscillation length is $∼10^-5 pc$.	result 0.68	0.65	0.05	0.32	0.97
Diffuse Supernova Neutrino Background	We assume the DM density between CCSN and Earth varies as a linear function of $z$, denoted by $ρ_DM(z)$.	setup 1.00	0.75	0.04	0.97	0.05
Diffuse Supernova Neutrino Background	When $z=0$, $ρ_DM(0)=ρ^⊕_DM$.	setup 1.00	0.44	0.03	0.89	0.16
Diffuse Supernova Neutrino Background	Suppose a single CCSN locates at redshift $z_0$, then $ρ_DM(z_0)=1.27 GeV/m^3$ is the average extragalactic DM density.	setup 0.95	0.37	0.05	0.82	0.96
Diffuse Supernova Neutrino Background	Then the adiabatic parameter $η∼10^-19∼10^-13$ for $z=5∼10^-5$.	result 0.80	0.79	0.06	0.62	0.97
Diffuse Supernova Neutrino Background	The contribution to the number of events from certain energy $E$ is [equation]	method 0.86	0.61	0.04	0.15	0.07
AGN Neutrino Flavor Ratio in IceCube	The neutrinos from AGN are mainly produced from the charged pion decay, which yields the initial flavor ratio $f_0=(1,2,0)/3$.	setup 0.77	0.19	0.06	0.30	0.71
AGN Neutrino Flavor Ratio in IceCube	Due to the adiabatic condition, we only need to consider the average flavor ratio at the production location and the Earth.	method 0.78	0.58	0.09	0.95	0.05
AGN Neutrino Flavor Ratio in IceCube	Fig. [ref] shows ternary plots of the average flavor ratio emitted from NGC 1068 and detected on Earth.	result 0.87	0.86	0.06	0.12	0.07
AGN Neutrino Flavor Ratio in IceCube	Following Ref. [ref] , we obtain the average flavor ratio	method 0.43	0.50	0.05	0.22	0.05
AGN Neutrino Flavor Ratio in IceCube	by [equation] where $f^⊕_0=(0.34,0.31,0.35)$ is the flavor ratio detected at Earth when neutrinos propagate in vacuum without DM interactions, referring to the red point in each ternary plot.	setup 0.81	0.47	0.07	0.44	0.96
AGN Neutrino Flavor Ratio in IceCube	$N$ is the total numbers of event.	setup 0.88	0.39	0.02	0.16	0.08
AGN Neutrino Flavor Ratio in IceCube	For each event, the neutrinos are assumed to be produced within the range $[10,10^2]R_s$ randomly in logarithmic scale.	setup 0.58	0.82	0.03	0.95	0.48
AGN Neutrino Flavor Ratio in IceCube	The coupling constants are chosen below 10 by the perturbative condition, and the lower limit of $y_α$ is fixed at $0.1$, which is not too low for DMs to affect the neutrino flavor.	setup 0.86	0.86	0.05	0.96	0.86
AGN Neutrino Flavor Ratio in IceCube	Throughout this work, we examine four classified coupling combinations: * Case-(a): $(y_e,y_μ,0)$ , * Case-(b): $(0,y_μ,y_τ)$ , * Case-(c): $(y_e,0 ,y_τ)$ , * Case-(d): $(y_e,y_μ,y_τ)$ ,	setup 0.89	0.86	0.04	0.73	0.17
AGN Neutrino Flavor Ratio in IceCube	The MSW resonance effective potential is given by [equation] Although this resonance potential is obtained by considering only $V_ee$, we included it in our plots as a reference and see whether the effective potential within these reference values deviates the flavor ratio.	setup 0.52	0.77	0.06	0.70	0.11
AGN Neutrino Flavor Ratio in IceCube	The ranges of resonance effective potential for NGC 1068 and TXS 0506+056 are given by [equation]	result 0.59	0.81	0.05	0.22	0.16
AGN Neutrino Flavor Ratio in IceCube	In the first row of Fig. [ref], i.e. panels (a1, b1, c1, d1), the $m_ϕ$ is chosen to be 0.1 peV (cyan), 1 peV (blue), and 10 peV (black).	setup 0.68	0.86	0.04	0.32	0.41
AGN Neutrino Flavor Ratio in IceCube	For $m_ϕ=10$ peV, the effective potentials at Earth lie within the range $[3.1×10^-21 , 3.1×10^-17]$ eV, which is less than $V_31^r$.	result 0.91	0.84	0.10	0.53	0.99
AGN Neutrino Flavor Ratio in IceCube	Since $V^⊕_αβ=G_αβρ^⊕_DM/m_ϕ$ is proportional to $m^-1_ϕ$, it gradually covers $V_31^r$ as $m_ϕ$ decreases to $1$ and $0.1$ peV.	interpretation 0.75	0.69	0.10	0.50	0.40
AGN Neutrino Flavor Ratio in IceCube	The distribution of the flavor ratio spreads significantly when $V^⊕$ (The matrix element of $V^⊕$ is $V^⊕_αβ$) covers the whole range of $V_31^r$.	interpretation 0.58	0.85	0.22	0.68	0.15
AGN Neutrino Flavor Ratio in IceCube	In the second row of Fig. [ref] we consider lighter DM masses, $m_ϕ=$0.01 feV (cyan), 0.1 feV (blue), and 1 feV (black).	setup 0.54	0.86	0.05	0.40	0.57
AGN Neutrino Flavor Ratio in IceCube	In this case, only the effective potential of $m_ϕ=1 feV$ case covers $V_31^r$, and most of the values of $V^⊕$ for $m_ϕ=0.1 feV$ and $0.01 feV$ are larger than $V_31^r$.	interpretation 0.68	0.86	0.10	0.67	0.97
AGN Neutrino Flavor Ratio in IceCube	Therefore, the Hamiltonian is dominated by $V^⊕$ and the final flavor ratio depends on the relative strength between each $V^⊕_αβ$.	interpretation 0.97	0.84	0.17	0.76	0.49
AGN Neutrino Flavor Ratio in IceCube	These distributions exhibit some common features: (i) for $m_ϕ=10$ peV, the electron flavor ratio $f̅^⊕_e$ tends to increase rather than decrease relative to the red point, while $f̅^⊕_μ,τ$ tends to change in the opposite direction; (ii) for $m_ϕ≤0.1$ peV, the electron flavor ratio $f̅^⊕_e$ mildly increase, while $f̅^⊕_τ$ ($f̅^⊕_μ$) tends to substantially decrease (increase) relative to the red point $f^⊕_0=(0.34,0.31,0.35)$.	result 0.95	0.90	0.27	0.27	0.97
AGN Neutrino Flavor Ratio in IceCube	We included the Single-Power Law (SPL) best fitting of IceCube MESE data with 68% and 95% confidence level [ref] and the combined limit using 15 years of IceCube plus 10 years of IceCube-Gen2 and the future neutrino telescopes [ref] in our plots.	method 0.57	0.76	0.06	0.14	0.35
AGN Neutrino Flavor Ratio in IceCube	Our simulations are partially overlap with the IceCube observations.	result 0.54	0.90	0.16	0.16	0.26
AGN Neutrino Flavor Ratio in IceCube	In Fig. [ref], we show $R̅_e,μ,τ$ for the three coupling combinations, Case-(a,b,c), with the corresponding labels (a), (b), (c).	result 0.79	0.89	0.05	0.13	0.10
AGN Neutrino Flavor Ratio in IceCube	The color bar on the right of each panel indicates the deviation from $f^⊕_0$.	setup 0.47	0.64	0.04	0.09	0.12
AGN Neutrino Flavor Ratio in IceCube	The darker red (darker blue) regions correspond to larger (smaller) values of $f̅^⊕_e,μ,τ$ compared with $f^⊕_0 e,0μ,0τ$.	setup 0.53	0.62	0.06	0.12	0.91
AGN Neutrino Flavor Ratio in IceCube	In addition, the transparent vertical and horizontal bands in each panel indicate the resonance range of $V^31_r$ from Eq.([ref]), and the color gradient of $R̅_e,μ,τ$ guides us to read the flavor ratio distributions.	interpretation 0.55	0.73	0.04	0.14	0.07
AGN Neutrino Flavor Ratio in IceCube	We illustrate this point by taking Fig. [ref](a) as an example.	interpretation 0.52	0.79	0.03	0.12	0.06
AGN Neutrino Flavor Ratio in IceCube	The bottom-left black and upper-right green squares in each panel of Fig. [ref](a1,a2,a3) are the range of $V^⊕$ for $m_ϕ=10 peV$ and $m_ϕ=1 feV$ respectively, corresponding to the black points in Fig. [ref](a1) and (a2).	interpretation 0.71	0.86	0.05	0.24	0.56
AGN Neutrino Flavor Ratio in IceCube	The $m_ϕ=10 peV$ black squares in $R̅_e,μ,τ$ containing both light red and light blue portions are consistent with the distribution of the black points that aggregate around the red point in Fig. [ref](a1), where their values are close to $f^⊕_0$.	result 0.52	0.85	0.14	0.20	0.79
AGN Neutrino Flavor Ratio in IceCube	In particular, the bottom-right corner in this square of $R̅_e$ is covered by light red indicating the mild enhancement of $f̅^⊕_e$ from $f̅^⊕_0e$, meanwhile the corresponding squares for $R̅_μ,τ$ show light blue in the bottom-right corner implying the decrements of $f̅^⊕_μ,τ$.	result 0.63	0.85	0.11	0.11	0.65
AGN Neutrino Flavor Ratio in IceCube	Therefore, the black points in Fig. [ref](a1) form a strip extending to lower-right direction.	result 0.77	0.87	0.10	0.07	0.11
AGN Neutrino Flavor Ratio in IceCube	Similarly, from the $m_ϕ=1 feV$ green squares in $R̅_e,μ,τ$ of Fig. [ref](a1,a2,a3), we can infer that the corresponding black points in Fig. [ref](a2) form a strip oriented along the upper-right direction.	interpretation 0.88	0.83	0.08	0.16	0.27
AGN Neutrino Flavor Ratio in IceCube	Particularly, the black points in Fig. [ref] (a2), the value of $f̅^⊕_μ$ ($f̅^⊕_τ$) is greater (smaller) than that of $f̅^⊕_0μ$ ($f̅^⊕_0τ$), which is consistent with darker red (darker blue) region in the green square of Fig. [ref] (a2) (Fig. [ref] (a3)).	interpretation 0.77	0.88	0.11	0.14	0.95
AGN Neutrino Flavor Ratio in IceCube	Following the same logic, the distributions for Case-(b) and Case-(c) in Fig. [ref] can be inferred from Fig. [ref].	interpretation 0.77	0.51	0.06	0.36	0.07
AGN Neutrino Flavor Ratio in IceCube	For TXS 0506+056 with a higher neutrino energy, we repeated the same analysis.	method 0.96	0.89	0.04	0.32	0.09
AGN Neutrino Flavor Ratio in IceCube	Since the location of neutrino production is under investigation.	limitation 0.86	0.12	0.02	0.28	0.03
AGN Neutrino Flavor Ratio in IceCube	The first range is $[10^2,10^5]R_s$, where $10^5R_s$ is the influence radius of TXS 0506+056 [ref] .	setup 0.80	0.37	0.03	0.77	0.93
AGN Neutrino Flavor Ratio in IceCube	The second range is chosen to be the same as NGC 1068, i.e. $[10,10^2]R_s$.	setup 0.56	0.83	0.03	0.82	0.86
AGN Neutrino Flavor Ratio in IceCube	The results of second production range are shown in Appendix [ref].	result 0.50	0.87	0.04	0.20	0.07
AGN Neutrino Flavor Ratio in IceCube	Fig [ref] shows the correspoding flavor ratio distribution for the production range $[10^2,10^5]R_s$.	result 0.92	0.90	0.05	0.57	0.42
AGN Neutrino Flavor Ratio in IceCube	The event-averaged deviation for Fig. [ref] is shown in Fig. [ref].	result 0.53	0.80	0.07	0.10	0.08
AGN Neutrino Flavor Ratio in IceCube	The current IceCube sensitivity is able to distinguish the flavor ratio distributions from NGC 1068 and TXS 0506+056 according to their “shapes.” Taking Case-(d) as an example, the $m_ϕ=10 peV$ distribution (black points) of Fig. [ref](d1) is a strip extended in enlarging $f̅_e^⊕$ and reducing $f̅_μ,τ^⊕$ direction, while the $m_ϕ=10 peV$ distribution of Fig. [ref](d1) is like a crab claw increasing $f̅_μ^⊕$ and decreasing $f̅_τ^⊕$.	interpretation 0.70	0.83	0.29	0.50	0.47
AGN Neutrino Flavor Ratio in IceCube	Including the constraint from the combined future neutrino telescopes, IceCube-Gen2 /KM3NeT/Baikal-GVD/P-ONE/TAMBO, we are able to set the limits on the coupling constants.	result 0.83	0.86	0.26	0.62	0.06
AGN Neutrino Flavor Ratio in IceCube	In Fig. [ref], we demonstrate the constraints on the coupling constants for $m_ϕ=1 feV$.	result 0.93	0.88	0.17	0.54	0.33
AGN Neutrino Flavor Ratio in IceCube	These figures are obtained by showing the excluded regions for three coupling combinations Case-(a,b,c), selecting the points such that their $f̅^⊕_e,μ,τ$ lie outside the confidence contours, which is shown in Fig. [ref].	method 0.87	0.87	0.11	0.45	0.20
AGN Neutrino Flavor Ratio in IceCube	The labels (a-NO), (b-NO), and (c-NO) correspond to the coupling combinations Case-(a,b,c) with normal-ordering assumption of neutrino mass.	setup 0.85	0.72	0.06	0.89	0.06
AGN Neutrino Flavor Ratio in IceCube	We can understand these patterns by referring to the $m_ϕ=1 feV$ green squares in Fig. [ref] (a1,a2,a3), (b1,b2,b3), and (c1,c2,c3), where the coupling constants are related to the effective potential via Eq.([ref]).	interpretation 0.98	0.77	0.08	0.28	0.29
AGN Neutrino Flavor Ratio in IceCube	The constraint boundaries of the first row of Fig. [ref] are roughly consistent with the color boundaries in Fig. [ref] because darker regions indicate points that significantly deviate from $f^⊕_0$, and thus be excluded by the experiments.	interpretation 1.00	0.83	0.13	0.36	0.28
AGN Neutrino Flavor Ratio in IceCube	The dark scalar mass $m_ϕ$ also affects the value of $V^⊕_αβ$ which scales as $m^-1_ϕ$ in Eq.([ref]).	setup 0.51	0.63	0.10	0.42	0.30
AGN Neutrino Flavor Ratio in IceCube	According to Fig. [ref] for $m_ϕ=1 feV$ and Fig. [ref], we can derive the boundaries for other values of $m_ϕ$.	method 0.67	0.83	0.09	0.37	0.24
AGN Neutrino Flavor Ratio in IceCube	For completeness, we include the corresponding limits on coupling constants considering inverted mass ordering in (a-IO), (b-IO), and (c-IO) of Fig. [ref].	result 0.61	0.89	0.09	0.56	0.08
AGN Neutrino Flavor Ratio in IceCube	Comparing the first and second rows in Fig. [ref], the future combined $ν$ telescope will have the sensitivity to differentiate normal ordering from inverted ordering.	interpretation 0.86	0.72	0.22	0.22	0.33
AGN Neutrino Flavor Ratio in IceCube	The parameters $(y_e, y_μ , y_τ)$ of Case-(d) excluded by IceCube MESE 95% C.L. contour are shown in Fig. [ref].	result 0.97	0.86	0.08	0.31	0.15
AGN Neutrino Flavor Ratio in IceCube	Similar to Fig. [ref], the constraint boundaries of the first row of Fig. [ref] are roughly consistent with the color boundaries in the $m_ϕ=1 feV$ green squares of Fig. [ref], except for the light red patch at the lower left corner of Fig. [ref](d1-NO) and (d3-NO).	interpretation 0.52	0.87	0.10	0.35	0.76
AGN Neutrino Flavor Ratio in IceCube	This patch arises from the nonzero value of the third coupling constant.	interpretation 0.98	0.84	0.07	0.31	0.08
AGN Neutrino Flavor Ratio in IceCube	The coupling constants excluded in this patch contributes to the region $(0.45≤f̅^⊕_e≤0.85, 0.15≤f̅^⊕_μ≤0.45, 0≤f̅^⊕_τ≤0.1 )$ of $m_ϕ=1 feV$ flavor ratio distribution in Fig. [ref](d2).	result 0.52	0.90	0.11	0.30	0.92
AGN Neutrino Flavor Ratio in IceCube	The same calculation is repeated using the combined $ν$-telescope contour, and the results are shown in Appendix [ref].	method 0.71	0.92	0.04	0.23	0.05
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	The similar calculations for DSNB neutrinos are shown in Fig. [ref] and [ref].	other 0.65	0.83	0.04	0.11	0.07
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	Since the experiments that may detect the DSNB flux is more sensitive to $ν_e$ and $ν̅_e$, we adopt the three axes of ternary plot to be $(ν̅_e,ν_x,ν_e)$.	method 0.53	0.87	0.05	0.74	0.17
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	The initial flavor ratio $f_0=(f_0e̅,f_0x,f_0e)=(0.179,0.605,0.216)$ is obtained from Eq.([ref]a) with the temperature $T_ν_e=5 MeV$, $T_ν̅_e=6 MeV$, and $T_ν_x=7 MeV$.	setup 0.61	0.72	0.06	0.70	0.98
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	After the propagation in vacuum, the final flavor ratio at Earth is $f^⊕_0=(0.166,0.647,0.187)$.	result 0.93	0.82	0.11	0.62	0.98
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	The final flavor ratio of DSNB neutrinos, shown in Fig. [ref], is obtained by weighted averaging the initial flavor ratio of each energy bin Eq.([ref]b) and energy distribution of the event number in Eq.([ref]).	method 0.95	0.89	0.08	0.51	0.14
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	The combined limit from HK, DUNE, and JUNO [ref] is included in Fig. [ref].	result 0.42	0.67	0.07	0.13	0.09
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	The flavor ratio distributions are almost identical for the four coupling combinations Case-(a,b,c,d), and the distribution points lie within the combined experimental contour.	result 0.99	0.87	0.28	0.25	0.82
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	Only Case-(b) exhibits a mild difference, and this can be seen from the color map of Fig. [ref] (d1,d2,d3) in which the diagonal regions are narrower than that of the corresponding panels for Case-(a,b).	result 0.81	0.89	0.13	0.22	0.80
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	As a result, the distribution in Fig. [ref](b) is “shorter” than others.	result 0.72	0.88	0.10	0.12	0.70
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	Overall, the neutrino dark matter interaction tends to decrease the fractions of $μ$ and $τ$ flavor, and the fraction of electron neutrino is increased.	interpretation 0.57	0.88	0.46	0.20	0.72
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	The anti-electron neutrino fraction is mildly shifted away from the vacuum case (red point).	result 0.96	0.87	0.14	0.14	0.51
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	Since the neutrino energy from diffuse supernovae is several order smaller than AGN neutrino, we consider $m_ϕ=10^-22 eV$ and $m_F=0.1 GeV$ to enhance the effective potential.	method 0.50	0.86	0.11	0.89	0.97
DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO	Even though, the $m_ϕ=10^-22 eV$ already reaches the mass lower bound of ultra-light DM, it is still not enough to make the flavor distribution distinguishable from $f^⊕_0$.	interpretation 0.47	0.86	0.28	0.64	0.92
Summary	We consider high-energy neutrinos from astrophysical sources oscillating under the presence of neutrino-scalar DM interactions, including four coupling combinations: Case-(a) $(y_e,y_μ,0)$, Case-(b) $(0,y_μ,y_τ)$, Case-(c) $(y_e,0,y_τ)$, and Case-(d) $(y_e,y_μ,y_τ)$.	setup 0.99	0.85	0.09	0.75	0.12
Summary	The effective potential $V_αβ$ depends on the coupling constant $y_e,μ,τ$, scalar DM mass $m_ϕ$, and the mediator mass $m_F$.	setup 1.00	0.59	0.07	0.36	0.04
Summary	We take the AGNs and the DSNB as our sources that produce neutrinos at different energy scales.	setup 0.93	0.81	0.08	0.57	0.12
Summary	The $𝒪(TeV)$ neutrinos are assumed to be produced from NGC 1068 and TXS 0506+056 via pion decay with initial flavor ratio $(ν_e:ν_μ:ν_τ)=(1:2:0)$.	setup 0.99	0.68	0.08	0.94	0.70
Summary	The neutrino production regions for NGC 1068 and TXS 0506+056 are assumed to be $[10,10^2]R_s$ (corona region) and $[10^2,10^5]R_s$, respectively.	setup 0.99	0.77	0.05	0.95	0.72
Summary	The distances between Earth and AGNs are much longer than the oscillation length, and the adiabatic parameter is extremely small, so the neutrino propagates adiabatically and the final averaged flavor ratio at Earth is obtained from Eq.([ref]) with $n=1$.	method 0.94	0.75	0.18	0.95	0.78
Summary	The coupling constant is restricted by the mean free path of neutrino, which depends on the spike density of AGN.	method 0.51	0.71	0.09	0.85	0.06
Summary	The upper limit for $y_e,μ,τ$ is 10, and we fix the lower limit at 0.1.	setup 0.80	0.86	0.05	0.93	0.89
Summary	Considering two sets of dark matter mass, $m_ϕ=10, 1, 0.1 peV$ and $m_ϕ=1, 0.1, 0.01 feV$, with the mediator mass fixed at $m_F=1 TeV$, and assuming the neutrinos are produced randomly inside corona region, we generate the ternary plots of $f̅^⊕_e,μ,τ$ with four cases, $(y_e, y_μ, 0)$, $(0, y_μ, y_τ)$, $(y_e, 0, y_τ)$, and all $y_e,μ,τ$ nonzero.	method 0.86	0.92	0.13	0.95	0.53
Summary	From all of the ternary plots we see that the final tau fraction $f̅^⊕_τ$ under the influence of $νϕ$ interaction tends to be decreased from $f^⊕_0τ$, and $f̅^⊕_μ$ are mostly be increased from $f^⊕_0μ$.	result 0.97	0.93	0.44	0.17	0.90
Summary	The limits from IceCube MESE, IceCube-Gen2, and future neutrino telescope are included, and all of the distributions are partially overlap with the experimental sensitivities.	result 0.85	0.75	0.22	0.22	0.30
Summary	We set the constraint on the coupling constants by excluding the event average points outside the experiment sensitivity contours, and the constraint for $m_ϕ=1 feV$ is shown in Fig. [ref] and [ref].	method 0.51	0.93	0.34	0.48	0.17
Summary	In these figures, the results of normal and inverted mass ordering are both included, but from the shape of the constraint we find the effect of the mass ordering is minor.	interpretation 0.80	0.93	0.19	0.47	0.66
Summary	We also define the deviation parameters $R̅_e,μ,τ$ and generate their color maps for the distributions in the ternary plots.	method 0.68	0.93	0.07	0.11	0.07
Summary	The color maps indicate the difference between $f̅^⊕_e,μ,τ$ and $f^⊕_0e,0μ,0τ$ with different values of the effective potential around the Earth.	interpretation 0.67	0.86	0.14	0.27	0.37
Summary	Accordingly, given a set of $(V^⊕_αα,V^⊕_ββ)$, we can roughly infer the position of $f̅^⊕_e,μ,τ$ relative to $f^⊕_0e,0μ,0τ$ in a ternary plot.	interpretation 0.85	0.84	0.15	0.65	0.12
Summary	The neutrino energy from the DSNB is much smaller than that from the AGNs, so the vacuum term of the Hamiltonian Eq.([ref]) becomes larger.	setup 0.46	0.55	0.11	0.36	0.95
Summary	Furthermore, the neutrinos from CCSN propagate in the extragalactic medium, where the DM density is extremely low.	setup 0.73	0.32	0.07	0.79	0.33
Summary	The effective potential should then be enhanced to make significant change in flavor ratio.	setup 0.43	0.44	0.18	0.69	0.07
Summary	We adopt the lower limit of $m_ϕ=10^-22 eV$ and fix the mediator mass $m_F$ to $0.1 GeV$, then repeat the same calculation on the flavor ratio.	method 0.63	0.91	0.08	0.93	0.90
Summary	Given the temperature of $ν_e$, $ν̅_e$, and $ν_x$, we may compute the DSNB flux and the initial flavor ratio.	method 0.95	0.66	0.06	0.45	0.07
Summary	The flavor distributions in Fig. [ref] for Case-(a,b,c,d) extend along the common direction and tend to have smaller values of $f̅_ν_x^⊕$ and larger values of $f̅_ν_e^⊕$.	result 0.98	0.93	0.20	0.18	0.86
Summary	However, shapes of the distributions are almost identical for Case-(a,c,d), only Case-(b) $(0,y_μ,y_τ)$ exhibits a mild difference.	result 0.88	0.93	0.14	0.27	0.77
Summary	This can also be inferred from Fig. [ref], where the color map corresponding to the coupling constant $(0,y_μ,y_τ)$ differs slightly from the other two cases.	interpretation 0.88	0.88	0.08	0.15	0.56
Summary	We include the combined constraint from HK/DUNE/JUNO and find that all the points stay inside the sensitivity contour.	result 0.80	0.91	0.21	0.42	0.45
Acknowledgment	We acknowledge the kind support of the National Science and Technology Council of Taiwan, with grant number NSTC 115-2112-M-007-010-.	other 1.00	0.09	0.01	0.04	0.60
Acknowledgment	P.Y.T. acknowledges support from the Physics Division of the National Center for Theoretical Sciences of Taiwan with grant NSTC 114-2124-M-002-003.	other 1.00	0.18	0.01	0.04	0.44
Acknowledgment	Y.M.Y. is supported in part by NSTC Grant No. 115B0061I4.	other 1.00	0.11	0.01	0.04	0.42
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	In this section we consider the neutrino production location of TXS 0506+056 to be corona region, i.e. $[10,10^2]R_s$, and repeate the analysis in Section [ref].	setup 0.63	0.81	0.04	0.90	0.35
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	Unfortunately, the $m_ϕ=0.1 peV$ and $m_ϕ=1 peV$ distributions nearly completely overlap.	limitation 0.59	0.91	0.07	0.26	0.86
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	Hence we replace the set of DM mass from $m_ϕ=10, 1, 0.1 peV$ by $m_ϕ=100, 10, 1 peV$ to obtain three distinguishable regions in Fig. [ref](a1,b1,c1,d1).	method 0.93	0.94	0.07	0.46	0.79
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	Comparing the patterns of Fig. [ref] and Fig. [ref] from the same $m_ϕ$, we see that the flavor ratio distributions are barely influenced by the production location and thus the DM density around AGN.	result 0.53	0.91	0.24	0.33	0.68
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	As an another illustrative example of correspondence between the event-averaged deviation plots and the flavor ratio distribution plots, we compare the $m_ϕ=100 peV$ distributions (black) and $m_ϕ=10 peV$ distributions (blue) of Fig. [ref] (a1,b1,c1).	result 0.31	0.88	0.05	0.15	0.64
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	The red squares in Fig. [ref] (a3,b3,c3) depicts the range of $V^⊕$ of $m_ϕ=100 peV$ distributions.	result 0.40	0.85	0.05	0.16	0.18
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	The regions enclosed by these squares are very lightly colored.	result 0.91	0.84	0.04	0.09	0.13
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	Comparing to the black squares in Fig. [ref] (a3,b3,c3), they contains small amount of darker-blue areas.	result 0.61	0.86	0.07	0.12	0.74
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	Therefore, the $m_ϕ=10 peV$ case of Fig. [ref] have more points with $f̅^⊕_τ≤f̅^⊕_0τ$ than the $m_ϕ=100 peV$.	result 0.51	0.89	0.11	0.14	0.95
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	The black square in Fig. [ref] (a3,b3,c3) is the range $V^⊕$ of $m_ϕ=10 peV$ case of Fig. [ref], and the enclosed regions also contain some darker-blue areas, similar to those in Fig. [ref] (a3,b3,c3).	interpretation 0.66	0.78	0.07	0.16	0.42
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	So, the $m_ϕ=10 peV$ distributions (blue) in Fig. [ref] have similar shapes to those (black) in Fig. [ref].	interpretation 0.64	0.82	0.10	0.12	0.59
TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$	Due to these features, we infer that the IceCube 95% C.L. sensitivity may not distinguish the TXS 0506+056 signals from different range of production locations.	interpretation 0.90	0.81	0.22	0.40	0.34
The Coupling Constants Excluded by Combined $ν$ Telescopes	Fig. [ref] shows the constraint on the coupling constants of Case-(d), which is obtained from the combined $ν$ telescopes sensitivities.	result 0.94	0.86	0.16	0.33	0.14
The Coupling Constants Excluded by Combined $ν$ Telescopes	Since the contour of the combined $ν$ telescopes sensitivities is much smaller than the IceCube MESE 95% C.L. contour, there are more points in $(y_e,y_μ,y_τ)$ parameter space be excluded comparing to Fig. [ref].	interpretation 0.92	0.82	0.20	0.23	0.94

How this paper uses its references

31 references. For each citing sentence, the use is labeled and, where the cited paper has a compiled record, whether that paper's own main claim supports the use. 40 shown.

P.-Y. Tseng and Y.-M. Yeh, ``Phenomenology of neutrino-dark matter interaction in DSNB and AGN'', JCAP 08 (2025) 038, http://arxiv.org/abs/2412.08537 arXiv:2412.08537.

We assumed the flavor-dependent interaction between neutrinos and complex dark scalar $ϕ$ [ref] , and computed the flavor ratio by adding the effective potential to the Hamiltonian using the spiked density profile of NGC 1068 and TXS 0506+056. method or tool p 0.81 · load-bearing 0.77 · Introduction

IceCube Collaboration, A.~Balagopal~V. et~al., ``Measurement of the Three-Flavor Composition of Astrophysical Neutrinos with Contained IceCube Events'', PoS ICRC2025 (2025) 983, http://arxiv.org/abs/2507.07212 arXiv:2507.07212.

The Medium Energy Starting Event (MESE), which is based on the 11.4 years of IceCube data, measures whole sky neutrino events with energies of at least 1 TeV and provides a three-flavor composition of astrophysical neutrinos [ref] . data used p 0.78 · load-bearing 0.74 · Introduction

IceCube Collaboration, R.~Abbasi et~al., ``Evidence for neutrino emission from the nearby active galaxy NGC 1068'', Science 378 (2022), no.~6619, 538--543, http://arxiv.org/abs/2211.09972 arXiv:2211.09972.

The IceCube collaboration has identified high energy neutrinos from two distinct AGNs, the NGC 1068 and TXS 0506+056, with energy $E∈[1.5,15] TeV$ and $[40,4000] TeV$, respectively [ref] . data used p 0.72 · load-bearing 0.67 · Introduction

P.-Y. Tseng and Y.-M. Yeh, ``Phenomenology of neutrino-dark matter interaction in DSNB and AGN'', JCAP 08 (2025) 038, http://arxiv.org/abs/2412.08537 arXiv:2412.08537.

The Lagrangian is given by [ref] [equation] where the Greek alphabet $α=e,μ,τ$ is the neutrino flavor label, $y_α$ is coupling constant. supports this paper p 0.41 · load-bearing 0.65 · Neutrino Oscillation in Dark Matter

P.-Y. Tseng and Y.-M. Yeh, ``Phenomenology of neutrino-dark matter interaction in DSNB and AGN'', JCAP 08 (2025) 038, http://arxiv.org/abs/2412.08537 arXiv:2412.08537.

The saturation density $ρ_sat$ depends on the $ϕϕ^∗$ annihilation, and the cross section is proportional to $y_α^2y^2_β$ [ref] . supports this paper p 0.80 · load-bearing 0.64 · Active Galactic Nuclei

P.~F. de~Salas, R.~A. Lineros, and M.~T\'ortola, ``Neutrino propagation in the galactic dark matter halo'', Phys. Rev. D 94 (2016), no.~12, 123001, http://arxiv.org/abs/1601.05798 arXiv:1601.05798.

We denote the initial flavor ratio by $f_0=(f_0e,f_0μ,f_0τ)$, then after propagating a distance that is far longer than the oscillation length, the final average flavor ratio is given by [ref] [equation] where $r_0$ is the distance to the source. supports this paper p 0.61 · load-bearing 0.62 · Neutrino Oscillation in Dark Matter

P.-Y. Tseng and Y.-M. Yeh, ``Phenomenology of neutrino-dark matter interaction in DSNB and AGN'', JCAP 08 (2025) 038, http://arxiv.org/abs/2412.08537 arXiv:2412.08537.

We fix $m_ϕ$ to this value and $m_F$ to $0.1 GeV$, then use the exact $σ_νϕ$ [ref] to compute the neutrino mean free path. method or tool p 0.69 · load-bearing 0.61 · Diffuse Supernova Neutrino Background

S.~Horiuchi, J.~F. Beacom, and E.~Dwek, ``The Diffuse Supernova Neutrino Background is detectable in Super-Kamiokande'', Phys. Rev. D 79 (2009) 083013, http://arxiv.org/abs/0812.3157 arXiv:0812.3157.

The diffuse differential neutrino flux is given by [equation] The core-collapse supernova rate $R_CCSN$ and the star-formation rate are parameterized as [ref] data used p 0.59 · load-bearing 0.60 · Diffuse Supernova Neutrino Background

S.~K. Agarwalla, M.~Bustamante, S.~Das, and A.~Narang, ``Present and future constraints on flavor-dependent long-range interactions of high-energy astrophysical neutrinos'', JHEP 08 (2023) 113, http://arxiv.org/abs/2305.03675 arXiv:2305.036

We included the Single-Power Law (SPL) best fitting of IceCube MESE data with 68% and 95% confidence level [ref] and the combined limit using 15 years of IceCube plus 10 years of IceCube-Gen2 and the future neutrino telescopes [ref] in our plots. comparison p 0.56 · load-bearing 0.55 · AGN Neutrino Flavor Ratio in IceCube

J.~F. Beacom, ``The Diffuse Supernova Neutrino Background'', Ann. Rev. Nucl. Part. Sci. 60 (2010) 439--462, http://arxiv.org/abs/1004.3311 arXiv:1004.3311.

The neutrino spectrum emitted from a supernova is given by [ref] [equation] where $E_tot=3×10^53 erg$ is the total emitted energy, the factor $1/6$ factor stands for energy of one of $ν_e$, $ν_e̅$, $ν_μ$, $ν_μ̅$, $ν_τ$, $ν_τ̅$, and $T$ is the neutrino temperature. background p 0.45 · load-bearing 0.55 · Diffuse Supernova Neutrino Background

IceCube Collaboration, M.~G. Aartsen et~al., ``Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert'', Science 361 (2018), no.~6398, 147--151, http://arxiv.org/abs/1807.08794 arXiv:1807.08794.

The IceCube collaboration has identified high energy neutrinos from two distinct AGNs, the NGC 1068 and TXS 0506+056, with energy $E∈[1.5,15] TeV$ and $[40,4000] TeV$, respectively [ref] . data used p 0.75 · load-bearing 0.54 · Introduction

G.~Herrera and K.~Murase, ``Probing light dark matter through cosmic-ray cooling in active galactic nuclei'', Phys. Rev. D 110 (2024), no.~1, L011701, http://arxiv.org/abs/2307.09460 arXiv:2307.09460.

The total contributions to annihilation cross section is $∑_α,βσ_ϕϕ^∗→ν_αν̅_β$. $ρ_sp$ is the spike density around the central supermassive black hole and is given by [ref] [equation] where $R_sp$ indicates the size of the spike. supports this paper p 0.42 · load-bearing 0.53 · Active Galactic Nuclei

G.~J. Mathews, J.~Hidaka, T.~Kajino, and J.~Suzuki, ``Supernova Relic Neutrinos and the Supernova Rate Problem: Analysis of Uncertainties and Detectability of ONeMg and Failed Supernovae'', Astrophys. J. 790 (2014) 115, http://arxiv.org/abs

The neutrino temperature can be obtained by the core-collapse simulation of neutrino emissions [ref] . data used p 0.50 · load-bearing 0.51 · Diffuse Supernova Neutrino Background

S.~Horiuchi, J.~F. Beacom, and E.~Dwek, ``The Diffuse Supernova Neutrino Background is detectable in Super-Kamiokande'', Phys. Rev. D 79 (2009) 083013, http://arxiv.org/abs/0812.3157 arXiv:0812.3157.

The neutrino temperature can be obtained by the core-collapse simulation of neutrino emissions [ref] . data used p 0.52 · load-bearing 0.50 · Diffuse Supernova Neutrino Background

IceCube Collaboration, A.~Balagopal~V. et~al., ``Measurement of the Three-Flavor Composition of Astrophysical Neutrinos with Contained IceCube Events'', PoS ICRC2025 (2025) 983, http://arxiv.org/abs/2507.07212 arXiv:2507.07212.

We included the Single-Power Law (SPL) best fitting of IceCube MESE data with 68% and 95% confidence level [ref] and the combined limit using 15 years of IceCube plus 10 years of IceCube-Gen2 and the future neutrino telescopes [ref] in our plots. data used p 0.52 · load-bearing 0.50 · AGN Neutrino Flavor Ratio in IceCube

Particle Data Group Collaboration, S. Navas et al., “Review of particle physics”, Phys. Rev. D 110 (2024), no. 3, 030001.

The differences of mass square for Normal Ordering (Inverse Ordering) are given by [ref] data used p 0.98 · load-bearing 0.50 · Neutrino Oscillation in Dark Matter

J.~M. Cline, S.~Gao, F.~Guo, Z.~Lin, S.~Liu, M.~Puel, P.~Todd, and T.~Xiao, ``Blazar Constraints on Neutrino-Dark Matter Scattering'', Phys. Rev. Lett. 130 (2023), no.~9, 091402, http://arxiv.org/abs/2209.02713 arXiv:2209.02713.

The first range is $[10^2,10^5]R_s$, where $10^5R_s$ is the influence radius of TXS 0506+056 [ref] . data used p 0.93 · load-bearing 0.50 · AGN Neutrino Flavor Ratio in IceCube

J.~M. Cline and M.~Puel, ``NGC 1068 constraints on neutrino-dark matter scattering'', JCAP 06 (2023) 004, http://arxiv.org/abs/2301.08756 arXiv:2301.08756.

Active Galactic Nuclei (AGNs) are point-like sources of neutrinos with energy scale $𝒪(TeV)$, and the DM density around the central supermassive black hole has been proposed to be a spiked-like distribution [ref] . supports this paper p 0.49 · load-bearing 0.49 · Introduction

C.~Blanco, D.~Hooper, T.~Linden, and E.~Pinetti, ``Neutrino and gamma-ray emissions from NGC 1068'', Phys. Rev. D 112 (2025), no.~12, 123016, http://arxiv.org/abs/2307.03259 arXiv:2307.03259.

We assume neutrinos from NGC are produced within the corona, which possess radius $R∈[10,10^2]R_s$[NGC's corona radius is estimated by $R∈[3,100]R_s$ [ref] . data used p 0.75 · load-bearing 0.46 · Active Galactic Nuclei

D.~F.~G. Fiorillo, F.~Testagrossa, M.~Petropoulou, and W.~Winter, ``Can the Neutrinos from TXS 0506+056 Have a Coronal Origin?'', Astrophys. J. 986 (2025), no.~1, 104, http://arxiv.org/abs/2502.01738 arXiv:2502.01738.

Ref. [ref] states that the TXS's neutrino flux from corona isn't sufficient enough to produce IceCube observed neutrino.]. supports this paper p 0.90 · load-bearing 0.46 · Active Galactic Nuclei

P.~F. de~Salas, R.~A. Lineros, and M.~T\'ortola, ``Neutrino propagation in the galactic dark matter halo'', Phys. Rev. D 94 (2016), no.~12, 123001, http://arxiv.org/abs/1601.05798 arXiv:1601.05798.

Following Ref. [ref] , we obtain the average flavor ratio method or tool p 0.52 · load-bearing 0.44 · AGN Neutrino Flavor Ratio in IceCube

Z.~Tabrizi and S.~Horiuchi, ``Flavor Triangle of the Diffuse Supernova Neutrino Background'', JCAP 05 (2021) 011, http://arxiv.org/abs/2011.10933 arXiv:2011.10933.

The combined limit from HK, DUNE, and JUNO [ref] is included in Fig. [ref]. comparison p 0.51 · load-bearing 0.44 · DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO

S.~K. Agarwalla, M.~Bustamante, S.~Das, and A.~Narang, ``Present and future constraints on flavor-dependent long-range interactions of high-energy astrophysical neutrinos'', JHEP 08 (2023) 113, http://arxiv.org/abs/2305.03675 arXiv:2305.036

Combining IceCube MESE, IceCube-Gen2, and additional contributions from future neutrino telescopes [ref] , supports this paper p 0.54 · load-bearing 0.41 · Introduction

IceCube-Gen2 Collaboration, N.~Lad et~al., ``Sensitivity of IceCube-Gen2 to measure flavor composition of Astrophysical neutrinos'', PoS ICRC2023 (2023) 1123, http://arxiv.org/abs/2308.15220 arXiv:2308.15220.

The future IceCube-Gen2 [ref] background p 0.49 · load-bearing 0.41 · Introduction

IceCube Collaboration, R.~Abbasi et~al., ``Evidence for neutrino emission from the nearby active galaxy NGC 1068'', Science 378 (2022), no.~6619, 538--543, http://arxiv.org/abs/2211.09972 arXiv:2211.09972.

The neutrino spectrum from AGN can be expressed by the power law $Φ(E)∝E^-γ$ [ref] . supports this paper p 0.52 · load-bearing 0.40 · Active Galactic Nuclei

P.~Gondolo and J.~Silk, ``Dark matter annihilation at the galactic center'', Phys. Rev. Lett. 83 (1999) 1719--1722, http://arxiv.org/abs/astro-ph/9906391 astro-ph/9906391.

Active Galactic Nuclei (AGNs) are point-like sources of neutrinos with energy scale $𝒪(TeV)$, and the DM density around the central supermassive black hole has been proposed to be a spiked-like distribution [ref] . supports this paper p 0.77 · load-bearing 0.40 · Introduction

Super-Kamiokande Collaboration, K.~Abe et~al., ``Diffuse supernova neutrino background search at Super-Kamiokande'', Phys. Rev. D 104 (2021), no.~12, 122002, http://arxiv.org/abs/2109.11174 arXiv:2109.11174.

Detectors such as Super-Kamiokande/Hyper-Kamiokande (SK/HK) [ref] , Deep Underground Neutrino Experiment (DUNE) [ref] , and Jiangmen Underground Neutrino Observatory (JUNO) [ref] are aimed to detect the DSNB flux and their flavor ratio. background p 0.49 · load-bearing 0.38 · Introduction

C.~D\"oring and S.~Vogl, ``Testing secret interaction with astrophysical neutrino point sources'', JCAP 07 (2024) 015, http://arxiv.org/abs/2304.08533 arXiv:2304.08533.

The neutrino spectrum from AGN can be expressed by the power law $Φ(E)∝E^-γ$ [ref] . background p 0.55 · load-bearing 0.36 · Active Galactic Nuclei

E. E. Salpeter, “The luminosity function and stellar evolution”, Astrophys. J. 121 (1955) 161–167.

The initial mass function $ψ(M)$ is proportional to $M^-2.35$ [ref] . data used p 0.85 · load-bearing 0.35 · Diffuse Supernova Neutrino Background

H.~Yuksel, M.~D. Kistler, J.~F. Beacom, and A.~M. Hopkins, ``Revealing the High-Redshift Star Formation Rate with Gamma-Ray Bursts'', Astrophys. J. Lett. 683 (2008) L5--L8, http://arxiv.org/abs/0804.4008 arXiv:0804.4008.

The diffuse differential neutrino flux is given by [equation] The core-collapse supernova rate $R_CCSN$ and the star-formation rate are parameterized as [ref] data used p 0.90 · load-bearing 0.34 · Diffuse Supernova Neutrino Background

G.~Herrera and K.~Murase, ``Probing light dark matter through cosmic-ray cooling in active galactic nuclei'', Phys. Rev. D 110 (2024), no.~1, L011701, http://arxiv.org/abs/2307.09460 arXiv:2307.09460.

Active Galactic Nuclei (AGNs) are point-like sources of neutrinos with energy scale $𝒪(TeV)$, and the DM density around the central supermassive black hole has been proposed to be a spiked-like distribution [ref] . supports this paper p 0.63 · load-bearing 0.33 · Introduction

JUNO Collaboration, F.~An et~al., ``Neutrino Physics with JUNO'', J. Phys. G 43 (2016), no.~3, 030401, http://arxiv.org/abs/1507.05613 arXiv:1507.05613.

Detectors such as Super-Kamiokande/Hyper-Kamiokande (SK/HK) [ref] , Deep Underground Neutrino Experiment (DUNE) [ref] , and Jiangmen Underground Neutrino Observatory (JUNO) [ref] are aimed to detect the DSNB flux and their flavor ratio. background p 0.46 · load-bearing 0.33 · Introduction

DUNE Collaboration, B.~Abi et~al., ``Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report, Volume II: DUNE Physics'', http://arxiv.org/abs/2002.03005 arXiv:2002.03005.

Detectors such as Super-Kamiokande/Hyper-Kamiokande (SK/HK) [ref] , Deep Underground Neutrino Experiment (DUNE) [ref] , and Jiangmen Underground Neutrino Observatory (JUNO) [ref] are aimed to detect the DSNB flux and their flavor ratio. background p 0.46 · load-bearing 0.33 · Introduction

IceCube-Gen2 Collaboration, M.~G. Aartsen et~al., ``IceCube-Gen2: the window to the extreme Universe'', J. Phys. G 48 (2021), no.~6, 060501, http://arxiv.org/abs/2008.04323 arXiv:2008.04323.

The future IceCube-Gen2 [ref] background p 0.70 · load-bearing 0.29 · Introduction

P-ONE Collaboration, M.~Agostini et~al., ``The Pacific Ocean Neutrino Experiment'', Nature Astron. 4 (2020), no.~10, 913--915, http://arxiv.org/abs/2005.09493 arXiv:2005.09493.

In addition to IceCube observations, KM3NeT [ref] , Baikal-GVD [ref] , P-ONE [ref] , and TAMBO [ref] have the potential to detect high energy neutrinos and contribute to the flavor ratio constraints. supports this paper p 0.41 · load-bearing 0.29 · Introduction

DUNE Collaboration, B.~Abi et~al., ``Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report, Volume I Introduction to DUNE'', JINST 15 (2020) a, no.~08, T08008, http://arxiv.org/abs/2002.02967 arXiv:2002.02967.

Detectors such as Super-Kamiokande/Hyper-Kamiokande (SK/HK) [ref] , Deep Underground Neutrino Experiment (DUNE) [ref] , and Jiangmen Underground Neutrino Observatory (JUNO) [ref] are aimed to detect the DSNB flux and their flavor ratio. background p 0.46 · load-bearing 0.29 · Introduction

KM3Net Collaboration, S.~Adrian-Martinez et~al., ``Letter of intent for KM3NeT 2.0'', J. Phys. G 43 (2016), no.~8, 084001, http://arxiv.org/abs/1601.07459 arXiv:1601.07459.

In addition to IceCube observations, KM3NeT [ref] , Baikal-GVD [ref] , P-ONE [ref] , and TAMBO [ref] have the potential to detect high energy neutrinos and contribute to the flavor ratio constraints. supports this paper p 0.37 · load-bearing 0.27 · Introduction

A.~Romero-Wolf et~al., ``An Andean Deep-Valley Detector for High-Energy Tau Neutrinos'', in ``Latin American Strategy Forum for Research Infrastructure''. 2 2020. http://arxiv.org/abs/2002.06475 arXiv:2002.06475.

In addition to IceCube observations, KM3NeT [ref] , Baikal-GVD [ref] , P-ONE [ref] , and TAMBO [ref] have the potential to detect high energy neutrinos and contribute to the flavor ratio constraints. supports this paper p 0.34 · load-bearing 0.27 · Introduction

Hyper-Kamiokande Collaboration, J.~Bian et~al., ``Hyper-Kamiokande Experiment: A Snowmass White Paper'', in ``Snowmass 2021''. 3 2022. http://arxiv.org/abs/2203.02029 arXiv:2203.02029.

Detectors such as Super-Kamiokande/Hyper-Kamiokande (SK/HK) [ref] , Deep Underground Neutrino Experiment (DUNE) [ref] , and Jiangmen Underground Neutrino Observatory (JUNO) [ref] are aimed to detect the DSNB flux and their flavor ratio. background p 0.49 · load-bearing 0.27 · Introduction

Baikal-GVD Collaboration, A.~D. Avrorin et~al., ``The Baikal-GVD neutrino telescope: First results of multi-messenger study'', PoS ICRC2019 (2020) 1013, http://arxiv.org/abs/1908.05450 arXiv:1908.05450.

In addition to IceCube observations, KM3NeT [ref] , Baikal-GVD [ref] , P-ONE [ref] , and TAMBO [ref] have the potential to detect high energy neutrinos and contribute to the flavor ratio constraints. supports this paper p 0.40 · load-bearing 0.26 · Introduction

What was examined, and what was not

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T body sentences
C citations

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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

References

Works cited (17)

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D. F. G. Fiorillo, F. Testagrossa, M. Petropoulou, and W. Winter, “Can the Neutrinos from TXS 0506+056 Have a Coronal Origin?”, Astrophys. J.986(2025), no. 1, 104, arXiv:2502.01738

View on Pith Pith review arXiv 2025
[1]

P. Gondolo and J. Silk, “Dark matter annihilation at the galactic center”, Phys. Rev. Lett. 83(1999) 1719–1722,astro-ph/9906391

View on Pith Pith review arXiv 1999
[2]

G. Herrera and K. Murase, “Probing light dark matter through cosmic-ray cooling in active galactic nuclei”, Phys. Rev. D110(2024), no. 1, L011701,arXiv:2307.09460

View on Pith Pith review arXiv 2024
[3]

J. M. Cline and M. Puel, “NGC 1068 constraints on neutrino-dark matter scattering”, JCAP 06(2023) 004,arXiv:2301.08756. [4]IceCubeCollaboration, R. Abbasi et al., “Evidence for neutrino emission from the nearby active galaxy NGC 1068”, Science378(2022), no. 6619, 538–543,arXiv:2211.09972. [5]IceCubeCollaboration, M. G. Aartsen et al., “Neutrino emission f...

View on Pith Pith review arXiv 2023
[6]

P.-Y. Tseng and Y.-M. Yeh, “Phenomenology of neutrino-dark matter interaction in DSNB and AGN”, JCAP08(2025) 038,arXiv:2412.08537. [7]IceCubeCollaboration, A. Balagopal V. et al., “Measurement of the Three-Flavor Composition of Astrophysical Neutrinos with Contained IceCube Events”, PoSICRC2025 (2025) 983,arXiv:2507.07212. [8]IceCube-Gen2Collaboration, M....

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A. Romero-Wolf et al., “An Andean Deep-Valley Detector for High-Energy Tau Neutrinos”, in “Latin American Strategy Forum for Research Infrastructure”. 2 2020. arXiv:2002.06475

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[14]

S. K. Agarwalla, M. Bustamante, S. Das, and A. Narang, “Present and future constraints on flavor-dependent long-range interactions of high-energy astrophysical neutrinos”, JHEP08 (2023) 113,arXiv:2305.03675. [15]Super-KamiokandeCollaboration, K. Abe et al., “Diffuse supernova neutrino background search at Super-Kamiokande”, Phys. Rev. D104(2021), no. 12, ...

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[21]

P. F. de Salas, R. A. Lineros, and M. T´ ortola, “Neutrino propagation in the galactic dark matter halo”, Phys. Rev. D94(2016), no. 12, 123001,arXiv:1601.05798

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[22]

C. D¨ oring and S. Vogl, “Testing secret interaction with astrophysical neutrino point sources”, JCAP07(2024) 015,arXiv:2304.08533

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[23]

C. Blanco, D. Hooper, T. Linden, and E. Pinetti, “Neutrino and gamma-ray emissions from NGC 1068”, Phys. Rev. D112(2025), no. 12, 123016,arXiv:2307.03259

View on Pith Pith review arXiv 2025
[25]

J. F. Beacom, “The Diffuse Supernova Neutrino Background”, Ann. Rev. Nucl. Part. Sci.60 (2010) 439–462,arXiv:1004.3311

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[26]

S. Horiuchi, J. F. Beacom, and E. Dwek, “The Diffuse Supernova Neutrino Background is detectable in Super-Kamiokande”, Phys. Rev. D79(2009) 083013,arXiv:0812.3157

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[27]

H. Yuksel, M. D. Kistler, J. F. Beacom, and A. M. Hopkins, “Revealing the High-Redshift Star Formation Rate with Gamma-Ray Bursts”, Astrophys. J. Lett.683(2008) L5–L8, arXiv:0804.4008

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[28]

E. E. Salpeter, “The luminosity function and stellar evolution”, Astrophys. J.121(1955) 161–167

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[29]

G. J. Mathews, J. Hidaka, T. Kajino, and J. Suzuki, “Supernova Relic Neutrinos and the Supernova Rate Problem: Analysis of Uncertainties and Detectability of ONeMg and Failed Supernovae”, Astrophys. J.790(2014) 115,arXiv:1405.0458

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[30]

Z. Tabrizi and S. Horiuchi, “Flavor Triangle of the Diffuse Supernova Neutrino Background”, JCAP05(2021) 011,arXiv:2011.10933

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[31]

J. M. Cline, S. Gao, F. Guo, Z. Lin, S. Liu, M. Puel, P. Todd, and T. Xiao, “Blazar Constraints on Neutrino-Dark Matter Scattering”, Phys. Rev. Lett.130(2023), no. 9, 091402,arXiv:2209.02713. – 21 –

View on Pith Pith review arXiv 2023

Forward citations

Cited by 2 Pith papers

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

Probing flavor-dependent neutrino-dark matter interactions with the flavor composition of high-energy cosmic neutrinos
hep-ph 2026-11 conditional novelty 5.0 of 10

Strong flavor-dependent neutrino-dark matter interactions isolate one mass eigenstate inside a dark matter spike, leaving two eigenstates unabsorbed and relaxing IceCube cross-section bounds by up to a few orders of m...
Resonant neutrino flavor conversion within dark matter spikes
hep-ph 2026-09 conditional novelty 5.0 of 10

Neutrino-dark matter forward scattering inside AGN black hole spikes alters the flavor composition at Earth, and in the strong-coupling limit the pγ muon-damped prediction falls outside IceCube's 95% flavor contour.

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]

D. F. G. Fiorillo, F. Testagrossa, M. Petropoulou, and W. Winter, “Can the Neutrinos from TXS 0506+056 Have a Coronal Origin?”, Astrophys. J.986(2025), no. 1, 104, arXiv:2502.01738

View on Pith Pith review arXiv 2025

[2] [1]

P. Gondolo and J. Silk, “Dark matter annihilation at the galactic center”, Phys. Rev. Lett. 83(1999) 1719–1722,astro-ph/9906391

View on Pith Pith review arXiv 1999

[3] [2]

G. Herrera and K. Murase, “Probing light dark matter through cosmic-ray cooling in active galactic nuclei”, Phys. Rev. D110(2024), no. 1, L011701,arXiv:2307.09460

View on Pith Pith review arXiv 2024

[4] [3]

J. M. Cline and M. Puel, “NGC 1068 constraints on neutrino-dark matter scattering”, JCAP 06(2023) 004,arXiv:2301.08756. [4]IceCubeCollaboration, R. Abbasi et al., “Evidence for neutrino emission from the nearby active galaxy NGC 1068”, Science378(2022), no. 6619, 538–543,arXiv:2211.09972. [5]IceCubeCollaboration, M. G. Aartsen et al., “Neutrino emission f...

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