{"body":{"source":"LaTeX source","sections":["Introduction","Introduction","Neutrino Oscillation in Dark Matter","Active Galactic Nuclei","Diffuse Supernova Neutrino Background","AGN Neutrino Flavor Ratio in IceCube","DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","Summary","Acknowledgment","TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","The Coupling Constants Excluded by Combined $ν$ Telescopes"],"sentences":[{"id":"b00.000.00","role":"background","text":"The neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum.","cites":[],"own_p":0.15,"role_p":0.62,"quant_p":0.07,"section":"Introduction","condition_p":0.26,"main_claim_p":0.09},{"id":"b00.000.01","role":"setup","text":"In this work we consider neutrinos interact with ultra-light scalar dark matters $ϕ$ ($m_ϕ≪1 eV$).","cites":[],"own_p":0.65,"role_p":1.0,"quant_p":0.79,"section":"Introduction","condition_p":0.87,"main_claim_p":0.06},{"id":"b00.000.02","role":"setup","text":"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.","cites":[],"own_p":0.31,"role_p":0.99,"quant_p":0.05,"section":"Introduction","condition_p":0.82,"main_claim_p":0.08},{"id":"b00.000.03","role":"setup","text":"Two types of neutrino sources are adopted in our calculations.","cites":[],"own_p":0.83,"role_p":0.68,"quant_p":0.31,"section":"Introduction","condition_p":0.42,"main_claim_p":0.04},{"id":"b00.000.04","role":"setup","text":"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 ($ν_e,ν_μ,ν_τ$)=($1:2:0$).","cites":[],"own_p":0.31,"role_p":0.96,"quant_p":0.82,"section":"Introduction","condition_p":0.47,"main_claim_p":0.05},{"id":"b00.000.05","role":"setup","text":"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.","cites":[],"own_p":0.77,"role_p":0.91,"quant_p":0.89,"section":"Introduction","condition_p":0.88,"main_claim_p":0.04},{"id":"b00.001.00","role":"method","text":"We consider the range of $νϕ$ coupling constant such that the adiabatic condition and mean free path can be satisfied.","cites":[],"own_p":0.67,"role_p":0.54,"quant_p":0.06,"section":"Introduction","condition_p":0.95,"main_claim_p":0.06},{"id":"b00.001.01","role":"method","text":"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.","cites":[],"own_p":0.93,"role_p":1.0,"quant_p":0.58,"section":"Introduction","condition_p":0.94,"main_claim_p":0.12},{"id":"b00.001.02","role":"setup","text":"The second source considered is the Diffuse Supernova Neutrino Background (DSNB), it is an isotropic neutrino source with energy $𝒪(MeV)$.","cites":[],"own_p":0.43,"role_p":0.86,"quant_p":0.51,"section":"Introduction","condition_p":0.39,"main_claim_p":0.06},{"id":"b00.001.03","role":"method","text":"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.","cites":[],"own_p":0.89,"role_p":0.9,"quant_p":0.78,"section":"Introduction","condition_p":0.8,"main_claim_p":0.18},{"id":"b01.000.00","role":"background","text":"Neutrinos are known to oscillate between different flavor eigenstates while propagating in vacuum due to their tiny but non-negligible mass differences.","cites":[],"own_p":0.05,"role_p":1.0,"quant_p":0.16,"section":"Introduction","condition_p":0.11,"main_claim_p":0.04},{"id":"b01.000.01","role":"background","text":"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.","cites":[],"own_p":0.05,"role_p":1.0,"quant_p":0.04,"section":"Introduction","condition_p":0.1,"main_claim_p":0.03},{"id":"b01.000.02","role":"background","text":"The neutrino-matter interaction will change the averaged flavor ratio between different flavor eigenstates in the vacuum.","cites":[],"own_p":0.1,"role_p":0.98,"quant_p":0.05,"section":"Introduction","condition_p":0.16,"main_claim_p":0.13},{"id":"b01.000.03","role":"setup","text":"In this work, we consider neutrinos interacting with ultra-light scalar dark matter (DM) $ϕ$","cites":[],"own_p":0.8,"role_p":0.98,"quant_p":0.04,"section":"Introduction","condition_p":0.76,"main_claim_p":0.04},{"id":"b01.001.00","role":"background","text":"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] .","cites":["Gondolo:1999ef","Herrera:2023nww","Cline:2023tkp"],"own_p":0.14,"role_p":0.76,"quant_p":0.27,"section":"Introduction","condition_p":0.49,"main_claim_p":0.06},{"id":"b01.001.01","role":"background","text":"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] .","cites":["IceCube:2022der","IceCube:2018cha"],"own_p":0.09,"role_p":0.99,"quant_p":0.95,"section":"Introduction","condition_p":0.12,"main_claim_p":0.05},{"id":"b01.001.02","role":"method","text":"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.","cites":["Tseng:2024akh"],"own_p":0.86,"role_p":0.92,"quant_p":0.12,"section":"Introduction","condition_p":0.93,"main_claim_p":0.11},{"id":"b01.002.00","role":"background","text":"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] .","cites":["IceCube:2025uyt"],"own_p":0.12,"role_p":0.97,"quant_p":0.9,"section":"Introduction","condition_p":0.21,"main_claim_p":0.05},{"id":"b01.002.01","role":"method","text":"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.","cites":[],"own_p":0.82,"role_p":0.83,"quant_p":0.78,"section":"Introduction","condition_p":0.27,"main_claim_p":0.11},{"id":"b01.002.02","role":"future_work","text":"The future IceCube-Gen2 [ref]","cites":["IceCube-Gen2:2020qha","IceCube-Gen2:2023rds"],"own_p":0.15,"role_p":0.64,"quant_p":0.05,"section":"Introduction","condition_p":0.11,"main_claim_p":0.03},{"id":"b01.003.00","role":"background","text":"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.","cites":["KM3Net:2016zxf","Baikal-GVD:2019fko","P-ONE:2020ljt","Romero-Wolf:2020pzh"],"own_p":0.09,"role_p":0.79,"quant_p":0.06,"section":"Introduction","condition_p":0.08,"main_claim_p":0.04},{"id":"b01.003.01","role":"background","text":"Combining IceCube MESE, IceCube-Gen2, and additional contributions from future neutrino telescopes [ref] ,","cites":["Agarwalla:2023sng"],"own_p":0.15,"role_p":0.45,"quant_p":0.05,"section":"Introduction","condition_p":0.16,"main_claim_p":0.03},{"id":"b01.004.00","role":"result","text":"we are able to distinguish the flavor ratio signal from different DM mass","cites":[],"own_p":0.77,"role_p":0.71,"quant_p":0.11,"section":"Introduction","condition_p":0.28,"main_claim_p":0.45},{"id":"b01.005.00","role":"other","text":"and from different production sources.","cites":[],"own_p":0.13,"role_p":0.57,"quant_p":0.03,"section":"Introduction","condition_p":0.19,"main_claim_p":0.04},{"id":"b01.005.01","role":"interpretation","text":"Furthermore, the couplings of the neutrino-DM interactions would be constrained by these experimental limits.","cites":[],"own_p":0.17,"role_p":0.78,"quant_p":0.04,"section":"Introduction","condition_p":0.18,"main_claim_p":0.18},{"id":"b01.006.00","role":"setup","text":"The Diffuse Supernova Neutrino Background (DSNB) is an alternative neutrino source considered in this work, with energy scale $𝒪(10 MeV)$.","cites":[],"own_p":0.48,"role_p":0.8,"quant_p":0.71,"section":"Introduction","condition_p":0.36,"main_claim_p":0.05},{"id":"b01.006.01","role":"background","text":"The neutrino fluxes with certain flavor structure are produced by core-collapse supernovae that have occurred throughout the cosmic history and are nearly isotropic.","cites":[],"own_p":0.1,"role_p":0.78,"quant_p":0.08,"section":"Introduction","condition_p":0.41,"main_claim_p":0.05},{"id":"b01.006.02","role":"background","text":"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.","cites":["Super-Kamiokande:2021jaq","Hyper-Kamiokande:2022smq","DUNE:2020lwj","DUNE:2020ypp","JUNO:2015zny"],"own_p":0.11,"role_p":0.81,"quant_p":0.05,"section":"Introduction","condition_p":0.09,"main_claim_p":0.04},{"id":"b01.006.03","role":"background","text":"The detection of DSNB from these experiments relies on different neutrino interactions.","cites":[],"own_p":0.13,"role_p":0.51,"quant_p":0.04,"section":"Introduction","condition_p":0.13,"main_claim_p":0.05},{"id":"b01.006.04","role":"background","text":"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 $ν̅_e$.","cites":[],"own_p":0.1,"role_p":0.5,"quant_p":0.06,"section":"Introduction","condition_p":0.13,"main_claim_p":0.04},{"id":"b01.006.05","role":"setup","text":"On the other hand, the muon and tau neutrinos can be detected from neutrino-electron elastic scattering.","cites":[],"own_p":0.12,"role_p":0.54,"quant_p":0.04,"section":"Introduction","condition_p":0.23,"main_claim_p":0.04},{"id":"b01.006.06","role":"method","text":"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.","cites":[],"own_p":0.91,"role_p":0.77,"quant_p":0.26,"section":"Introduction","condition_p":0.29,"main_claim_p":0.29},{"id":"b01.007.00","role":"other","text":"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.","cites":[],"own_p":0.43,"role_p":0.94,"quant_p":0.05,"section":"Introduction","condition_p":0.17,"main_claim_p":0.03},{"id":"b01.007.01","role":"method","text":"Then we compute the average flavor ratio by taking the oscillation length and the adiabatic condition into account.","cites":[],"own_p":0.88,"role_p":0.92,"quant_p":0.08,"section":"Introduction","condition_p":0.77,"main_claim_p":0.04},{"id":"b01.007.02","role":"method","text":"We set our analysis upper limit on coupling constant with the neutrino mean free path.","cites":[],"own_p":0.9,"role_p":0.74,"quant_p":0.09,"section":"Introduction","condition_p":0.51,"main_claim_p":0.19},{"id":"b01.007.03","role":"other","text":"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.","cites":[],"own_p":0.86,"role_p":0.52,"quant_p":0.43,"section":"Introduction","condition_p":0.56,"main_claim_p":0.12},{"id":"b01.007.04","role":"method","text":"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 $10^-22 eV$.","cites":[],"own_p":0.87,"role_p":0.8,"quant_p":0.83,"section":"Introduction","condition_p":0.9,"main_claim_p":0.06},{"id":"b01.007.05","role":"other","text":"We summarize our work in Section [ref].","cites":[],"own_p":0.25,"role_p":1.0,"quant_p":0.03,"section":"Introduction","condition_p":0.06,"main_claim_p":0.03},{"id":"b02.000.00","role":"setup","text":"We assume neutrinos are Majorana fermions and couple to hypothetical dark scalar $ϕ$ through a fermionic mediator $F$.","cites":[],"own_p":0.45,"role_p":1.0,"quant_p":0.04,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.96,"main_claim_p":0.04},{"id":"b02.000.01","role":"setup","text":"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.","cites":["Tseng:2024akh"],"own_p":0.51,"role_p":1.0,"quant_p":0.05,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.45,"main_claim_p":0.03},{"id":"b02.000.02","role":"setup","text":"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.","cites":[],"own_p":0.59,"role_p":0.99,"quant_p":0.04,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.31,"main_claim_p":0.04},{"id":"b02.000.03","role":"setup","text":"The differences of mass square for Normal Ordering (Inverse Ordering) are given by [ref]","cites":["ParticleDataGroup:2024cfk"],"own_p":0.25,"role_p":0.51,"quant_p":0.06,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.16,"main_claim_p":0.03},{"id":"b02.001.00","role":"setup","text":"[equation] From ([ref]), we can write down the components of $V$: [equation] The Feynman diagram of $νϕ$ scattering is shown in Fig. [ref].","cites":[],"own_p":0.49,"role_p":0.89,"quant_p":0.05,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.1,"main_claim_p":0.03},{"id":"b02.002.00","role":"setup","text":"The effective mass squared is given by [equation] where $U'$ is the mixing matrix that diagonalized the flavor basis total Hamiltonian Eq.([ref]).","cites":[],"own_p":0.65,"role_p":0.94,"quant_p":0.05,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.17,"main_claim_p":0.03},{"id":"b02.002.01","role":"setup","text":"Then oscillation length is [equation] where the Latin alphabets $i,j$ are the mass eigenstate label.","cites":[],"own_p":0.6,"role_p":0.96,"quant_p":0.06,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.19,"main_claim_p":0.03},{"id":"b02.003.00","role":"setup","text":"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.","cites":["deSalas:2016svi"],"own_p":0.48,"role_p":0.59,"quant_p":0.14,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.88,"main_claim_p":0.06},{"id":"b02.003.01","role":"method","text":"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.","cites":[],"own_p":0.78,"role_p":0.82,"quant_p":0.14,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.9,"main_claim_p":0.07},{"id":"b02.003.02","role":"setup","text":"The adiabatic parameter is defined by [equation] where $I$ is the $3×3$ identity matrix.","cites":[],"own_p":0.65,"role_p":0.96,"quant_p":0.06,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.38,"main_claim_p":0.04},{"id":"b02.003.03","role":"setup","text":"The $⟨...⟩$ denotes the average over all the matrix elements.","cites":[],"own_p":0.39,"role_p":0.97,"quant_p":0.04,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.17,"main_claim_p":0.03},{"id":"b02.003.04","role":"setup","text":"The propagation of neutrinos is adiabatic if $η≪1$.","cites":[],"own_p":0.43,"role_p":0.94,"quant_p":0.86,"section":"Neutrino Oscillation in Dark Matter","condition_p":0.93,"main_claim_p":0.09},{"id":"b03.000.00","role":"setup","text":"The neutrino spectrum from AGN can be expressed by the power law $Φ(E)∝E^-γ$ [ref] .","cites":["IceCube:2022der","Doring:2023vmk"],"own_p":0.18,"role_p":0.58,"quant_p":0.07,"section":"Active Galactic Nuclei","condition_p":0.45,"main_claim_p":0.04},{"id":"b03.000.01","role":"setup","text":"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.","cites":[],"own_p":0.52,"role_p":0.54,"quant_p":0.08,"section":"Active Galactic Nuclei","condition_p":0.74,"main_claim_p":0.03},{"id":"b03.001.00","role":"setup","text":"The DM density around AGN is given by the spike-profile, [equation] where $R_s$ is the Schwarzschild radius.","cites":[],"own_p":0.4,"role_p":0.98,"quant_p":0.05,"section":"Active Galactic Nuclei","condition_p":0.53,"main_claim_p":0.04},{"id":"b03.001.01","role":"setup","text":"The saturation density $ρ_sat$ depends on the $ϕϕ^∗$ annihilation, and the cross section is proportional to $y_α^2y^2_β$ [ref] .","cites":["Tseng:2024akh"],"own_p":0.26,"role_p":0.8,"quant_p":0.05,"section":"Active Galactic Nuclei","condition_p":0.41,"main_claim_p":0.04},{"id":"b03.001.02","role":"setup","text":"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.","cites":["Herrera:2023nww"],"own_p":0.28,"role_p":0.94,"quant_p":0.05,"section":"Active Galactic Nuclei","condition_p":0.18,"main_claim_p":0.04},{"id":"b03.001.03","role":"setup","text":"For $r≥R_sp$ the spike density is replace by the Navarro-Frenk-White (NFW) profile.","cites":[],"own_p":0.37,"role_p":0.97,"quant_p":0.07,"section":"Active Galactic Nuclei","condition_p":0.83,"main_claim_p":0.03},{"id":"b03.002.00","role":"result","text":"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.","cites":[],"own_p":0.87,"role_p":0.92,"quant_p":0.99,"section":"Active Galactic Nuclei","condition_p":0.52,"main_claim_p":0.14},{"id":"b03.002.01","role":"result","text":"The maximum of adiabatic parameter $η$ is below $10^-10$, which means neutrinos propagates extremely adiabatically.","cites":[],"own_p":0.89,"role_p":0.63,"quant_p":0.98,"section":"Active Galactic Nuclei","condition_p":0.69,"main_claim_p":0.15},{"id":"b03.002.02","role":"method","text":"Therefore, we can simply consider the DM density at the source location and around the Earth.","cites":[],"own_p":0.79,"role_p":0.5,"quant_p":0.06,"section":"Active Galactic Nuclei","condition_p":0.89,"main_claim_p":0.13},{"id":"b03.002.03","role":"setup","text":"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] .","cites":["Blanco:2023dfp"],"own_p":0.71,"role_p":0.98,"quant_p":0.9,"section":"Active Galactic Nuclei","condition_p":0.95,"main_claim_p":0.06},{"id":"b03.002.04","role":"background","text":"Ref. [ref] states that the TXS's neutrino flux from corona isn't sufficient enough to produce IceCube observed neutrino.].","cites":["Fiorillo:2025cgm"],"own_p":0.1,"role_p":0.93,"quant_p":0.52,"section":"Active Galactic Nuclei","condition_p":0.2,"main_claim_p":0.09},{"id":"b03.003.00","role":"setup","text":"The DM density around the Earth is taken to be $ρ^⊕_DM=0.4 GeV/cm^3$.","cites":[],"own_p":0.49,"role_p":0.99,"quant_p":0.94,"section":"Active Galactic Nuclei","condition_p":0.9,"main_claim_p":0.03},{"id":"b03.003.01","role":"setup","text":"The relevant parameters for TXS 0506+056 are $η≃6×10^-11$ and averaged $L_ij ∼10^-4 pc$.","cites":[],"own_p":0.68,"role_p":0.88,"quant_p":0.97,"section":"Active Galactic Nuclei","condition_p":0.51,"main_claim_p":0.04},{"id":"b03.004.00","role":"setup","text":"The $νϕ$ scattering may affect the direction of propagation.","cites":[],"own_p":0.24,"role_p":0.48,"quant_p":0.03,"section":"Active Galactic Nuclei","condition_p":0.24,"main_claim_p":0.08},{"id":"b03.004.01","role":"setup","text":"For detection on Earth, we require that the neutrinos be forward-scattered through their path.","cites":[],"own_p":0.35,"role_p":0.75,"quant_p":0.04,"section":"Active Galactic Nuclei","condition_p":0.93,"main_claim_p":0.09},{"id":"b03.004.02","role":"setup","text":"So the mean free path should be longer than the distance between AGN and Earth.","cites":[],"own_p":0.39,"role_p":0.73,"quant_p":0.82,"section":"Active Galactic Nuclei","condition_p":0.93,"main_claim_p":0.11},{"id":"b03.004.03","role":"setup","text":"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 $m_F^2≫m_ϕE$.","cites":[],"own_p":0.53,"role_p":0.8,"quant_p":0.59,"section":"Active Galactic Nuclei","condition_p":0.94,"main_claim_p":0.05},{"id":"b03.004.04","role":"method","text":"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.","cites":[],"own_p":0.67,"role_p":0.31,"quant_p":0.11,"section":"Active Galactic Nuclei","condition_p":0.92,"main_claim_p":0.1},{"id":"b03.004.05","role":"setup","text":"For the analysis of AGNs, $m_F$ is fixed to $1 TeV$.","cites":[],"own_p":0.84,"role_p":0.95,"quant_p":0.69,"section":"Active Galactic Nuclei","condition_p":0.95,"main_claim_p":0.04},{"id":"b03.004.06","role":"result","text":"For a given $y_α,β$, $l$ reaches its minimum when (i) $ρ_DM$ is maximum, i.e., the peaked spike density, and (ii) $E=E_max$.","cites":[],"own_p":0.86,"role_p":0.59,"quant_p":0.14,"section":"Active Galactic Nuclei","condition_p":0.84,"main_claim_p":0.1},{"id":"b03.004.07","role":"result","text":"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 $y_α,β=10$.","cites":[],"own_p":0.96,"role_p":1.0,"quant_p":0.98,"section":"Active Galactic Nuclei","condition_p":0.92,"main_claim_p":0.07},{"id":"b03.004.08","role":"result","text":"In terms of Schwarzschild radius, $l_min/R_s∼190$ ($l_min/R_s∼6$) for NGC 1068 (TXS 0506+056).","cites":[],"own_p":0.93,"role_p":1.0,"quant_p":0.99,"section":"Active Galactic Nuclei","condition_p":0.34,"main_claim_p":0.09},{"id":"b03.004.09","role":"interpretation","text":"As neutrinos propagate outward, $l$ increases because $ρ_DM$ gets lower.","cites":[],"own_p":0.78,"role_p":0.47,"quant_p":0.06,"section":"Active Galactic Nuclei","condition_p":0.46,"main_claim_p":0.1},{"id":"b03.004.10","role":"interpretation","text":"Therefore, neutrinos produced in the direction forward to Earth are rarely deflected by DM.","cites":[],"own_p":0.85,"role_p":0.8,"quant_p":0.1,"section":"Active Galactic Nuclei","condition_p":0.39,"main_claim_p":0.15},{"id":"b04.000.00","role":"setup","text":"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.","cites":["Beacom:2010kk"],"own_p":0.25,"role_p":0.88,"quant_p":0.89,"section":"Diffuse Supernova Neutrino Background","condition_p":0.35,"main_claim_p":0.03},{"id":"b04.000.01","role":"setup","text":"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]","cites":["Horiuchi:2008jz","Yuksel:2008cu"],"own_p":0.3,"role_p":0.82,"quant_p":0.06,"section":"Diffuse Supernova Neutrino Background","condition_p":0.13,"main_claim_p":0.03},{"id":"b04.001.00","role":"setup","text":"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 $α=3.4±0.2$, $β=-0.3±0.2$, $γ=-3.5±1$.","cites":[],"own_p":0.43,"role_p":0.91,"quant_p":0.97,"section":"Diffuse Supernova Neutrino Background","condition_p":0.27,"main_claim_p":0.03},{"id":"b04.001.01","role":"setup","text":"The initial mass function $ψ(M)$ is proportional to $M^-2.35$ [ref] .","cites":["Salpeter1955"],"own_p":0.22,"role_p":0.66,"quant_p":0.68,"section":"Diffuse Supernova Neutrino Background","condition_p":0.36,"main_claim_p":0.03},{"id":"b04.001.02","role":"setup","text":"We fixed $z_max=5$ for which there is a reasonable amount of star formation.","cites":[],"own_p":0.88,"role_p":0.93,"quant_p":0.74,"section":"Diffuse Supernova Neutrino Background","condition_p":0.93,"main_claim_p":0.03},{"id":"b04.001.03","role":"method","text":"The neutrino temperature can be obtained by the core-collapse simulation of neutrino emissions [ref] .","cites":["Horiuchi:2008jz","Mathews:2014qba"],"own_p":0.28,"role_p":0.4,"quant_p":0.08,"section":"Diffuse Supernova Neutrino Background","condition_p":0.37,"main_claim_p":0.04},{"id":"b04.001.04","role":"background","text":"The simulations predict the temperature hierarchy $T_ν_e<T_ν̅_e<T_ν_x$.","cites":[],"own_p":0.15,"role_p":0.67,"quant_p":0.97,"section":"Diffuse Supernova Neutrino Background","condition_p":0.34,"main_claim_p":0.09},{"id":"b04.001.05","role":"setup","text":"We adopt $T_ν_e=5 MeV$, $T_ν̅_e=6 MeV$, and $T_ν_x=7 MeV$ in our calculations.","cites":[],"own_p":0.87,"role_p":0.92,"quant_p":0.96,"section":"Diffuse Supernova Neutrino Background","condition_p":0.89,"main_claim_p":0.04},{"id":"b04.002.00","role":"setup","text":"where $ν_x$ is the collective notation of $ν_μ,ν̅_μ,ν_τ,ν̅_τ$.","cites":[],"own_p":0.33,"role_p":1.0,"quant_p":0.06,"section":"Diffuse Supernova Neutrino Background","condition_p":0.21,"main_claim_p":0.03},{"id":"b04.002.01","role":"setup","text":"Eq.([ref]a) indicates the initial flavor ratio of the DSNB flux, while Eq.([ref]b) is the initial ratio for each energy bin.","cites":[],"own_p":0.43,"role_p":0.96,"quant_p":0.08,"section":"Diffuse Supernova Neutrino Background","condition_p":0.17,"main_claim_p":0.04},{"id":"b04.002.02","role":"setup","text":"Since the neutrinos are propagating in the extragalactic medium, the dark matter density is far smaller than the AGN spike density.","cites":[],"own_p":0.36,"role_p":0.75,"quant_p":0.94,"section":"Diffuse Supernova Neutrino Background","condition_p":0.61,"main_claim_p":0.08},{"id":"b04.002.03","role":"setup","text":"Furthermore, the neutrino energy from DSNB scales around $𝒪(MeV)$, hence the vacuum Hamiltonian is several order larger than those of AGN neutrinos.","cites":[],"own_p":0.48,"role_p":0.55,"quant_p":0.93,"section":"Diffuse Supernova Neutrino Background","condition_p":0.46,"main_claim_p":0.07},{"id":"b04.002.04","role":"interpretation","text":"We must therefore increase the value of effective potential $V_αβ$.","cites":[],"own_p":0.42,"role_p":0.38,"quant_p":0.07,"section":"Diffuse Supernova Neutrino Background","condition_p":0.4,"main_claim_p":0.07},{"id":"b04.002.05","role":"setup","text":"The theoretical lower limit of ultra-light dark matter mass is approximately $10^-22 eV$.","cites":[],"own_p":0.22,"role_p":0.53,"quant_p":0.93,"section":"Diffuse Supernova Neutrino Background","condition_p":0.58,"main_claim_p":0.07},{"id":"b04.002.06","role":"method","text":"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.","cites":["Tseng:2024akh"],"own_p":0.88,"role_p":0.89,"quant_p":0.75,"section":"Diffuse Supernova Neutrino Background","condition_p":0.83,"main_claim_p":0.06},{"id":"b04.002.07","role":"result","text":"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.","cites":[],"own_p":0.91,"role_p":0.99,"quant_p":0.98,"section":"Diffuse Supernova Neutrino Background","condition_p":0.47,"main_claim_p":0.12},{"id":"b04.003.00","role":"result","text":"The maximum average oscillation length is $∼10^-5 pc$.","cites":[],"own_p":0.65,"role_p":0.68,"quant_p":0.97,"section":"Diffuse Supernova Neutrino Background","condition_p":0.32,"main_claim_p":0.05},{"id":"b04.003.01","role":"setup","text":"We assume the DM density between CCSN and Earth varies as a linear function of $z$, denoted by $ρ_DM(z)$.","cites":[],"own_p":0.75,"role_p":1.0,"quant_p":0.05,"section":"Diffuse Supernova Neutrino Background","condition_p":0.97,"main_claim_p":0.04},{"id":"b04.003.02","role":"setup","text":"When $z=0$, $ρ_DM(0)=ρ^⊕_DM$.","cites":[],"own_p":0.44,"role_p":1.0,"quant_p":0.16,"section":"Diffuse Supernova Neutrino Background","condition_p":0.89,"main_claim_p":0.03},{"id":"b04.003.03","role":"setup","text":"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.","cites":[],"own_p":0.37,"role_p":0.95,"quant_p":0.96,"section":"Diffuse Supernova Neutrino Background","condition_p":0.82,"main_claim_p":0.05},{"id":"b04.003.04","role":"result","text":"Then the adiabatic parameter $η∼10^-19∼10^-13$ for $z=5∼10^-5$.","cites":[],"own_p":0.79,"role_p":0.8,"quant_p":0.97,"section":"Diffuse Supernova Neutrino Background","condition_p":0.62,"main_claim_p":0.06},{"id":"b04.003.05","role":"method","text":"The contribution to the number of events from certain energy $E$ is [equation]","cites":[],"own_p":0.61,"role_p":0.86,"quant_p":0.07,"section":"Diffuse Supernova Neutrino Background","condition_p":0.15,"main_claim_p":0.04},{"id":"b05.000.00","role":"setup","text":"The neutrinos from AGN are mainly produced from the charged pion decay, which yields the initial flavor ratio $f_0=(1,2,0)/3$.","cites":[],"own_p":0.19,"role_p":0.77,"quant_p":0.71,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.3,"main_claim_p":0.06},{"id":"b05.000.01","role":"method","text":"Due to the adiabatic condition, we only need to consider the average flavor ratio at the production location and the Earth.","cites":[],"own_p":0.58,"role_p":0.78,"quant_p":0.05,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.95,"main_claim_p":0.09},{"id":"b05.000.02","role":"result","text":"Fig. [ref] shows ternary plots of the average flavor ratio emitted from NGC 1068 and detected on Earth.","cites":[],"own_p":0.86,"role_p":0.87,"quant_p":0.07,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.12,"main_claim_p":0.06},{"id":"b05.000.03","role":"method","text":"Following Ref. [ref] , we obtain the average flavor ratio","cites":["deSalas:2016svi"],"own_p":0.5,"role_p":0.43,"quant_p":0.05,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.22,"main_claim_p":0.05},{"id":"b05.001.00","role":"setup","text":"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.","cites":[],"own_p":0.47,"role_p":0.81,"quant_p":0.96,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.44,"main_claim_p":0.07},{"id":"b05.002.00","role":"setup","text":"$N$ is the total numbers of event.","cites":[],"own_p":0.39,"role_p":0.88,"quant_p":0.08,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.16,"main_claim_p":0.02},{"id":"b05.002.01","role":"setup","text":"For each event, the neutrinos are assumed to be produced within the range $[10,10^2]R_s$ randomly in logarithmic scale.","cites":[],"own_p":0.82,"role_p":0.58,"quant_p":0.48,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.95,"main_claim_p":0.03},{"id":"b05.002.02","role":"setup","text":"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.","cites":[],"own_p":0.86,"role_p":0.86,"quant_p":0.86,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.96,"main_claim_p":0.05},{"id":"b05.002.03","role":"setup","text":"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): $(y_e,y_μ,y_τ)$ ,","cites":[],"own_p":0.86,"role_p":0.89,"quant_p":0.17,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.73,"main_claim_p":0.04},{"id":"b05.003.00","role":"setup","text":"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.","cites":[],"own_p":0.77,"role_p":0.52,"quant_p":0.11,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.7,"main_claim_p":0.06},{"id":"b05.003.01","role":"result","text":"The ranges of resonance effective potential for NGC 1068 and TXS 0506+056 are given by [equation]","cites":[],"own_p":0.81,"role_p":0.59,"quant_p":0.16,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.22,"main_claim_p":0.05},{"id":"b05.004.00","role":"setup","text":"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).","cites":[],"own_p":0.86,"role_p":0.68,"quant_p":0.41,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.32,"main_claim_p":0.04},{"id":"b05.004.01","role":"result","text":"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 $V_31^r$.","cites":[],"own_p":0.84,"role_p":0.91,"quant_p":0.99,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.53,"main_claim_p":0.1},{"id":"b05.004.02","role":"interpretation","text":"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.","cites":[],"own_p":0.69,"role_p":0.75,"quant_p":0.4,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.5,"main_claim_p":0.1},{"id":"b05.004.03","role":"interpretation","text":"The distribution of the flavor ratio spreads significantly when $V^⊕$ (The matrix element of $V^⊕$ is $V^⊕_αβ$) covers the whole range of $V_31^r$.","cites":[],"own_p":0.85,"role_p":0.58,"quant_p":0.15,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.68,"main_claim_p":0.22},{"id":"b05.005.00","role":"setup","text":"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).","cites":[],"own_p":0.86,"role_p":0.54,"quant_p":0.57,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.4,"main_claim_p":0.05},{"id":"b05.005.01","role":"interpretation","text":"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 $V_31^r$.","cites":[],"own_p":0.86,"role_p":0.68,"quant_p":0.97,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.67,"main_claim_p":0.1},{"id":"b05.005.02","role":"interpretation","text":"Therefore, the Hamiltonian is dominated by $V^⊕$ and the final flavor ratio depends on the relative strength between each $V^⊕_αβ$.","cites":[],"own_p":0.84,"role_p":0.97,"quant_p":0.49,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.76,"main_claim_p":0.17},{"id":"b05.006.00","role":"result","text":"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 $f^⊕_0=(0.34,0.31,0.35)$.","cites":[],"own_p":0.9,"role_p":0.95,"quant_p":0.97,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.27,"main_claim_p":0.27},{"id":"b05.006.01","role":"method","text":"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.","cites":["IceCube:2025uyt","Agarwalla:2023sng"],"own_p":0.76,"role_p":0.57,"quant_p":0.35,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.14,"main_claim_p":0.06},{"id":"b05.006.02","role":"result","text":"Our simulations are partially overlap with the IceCube observations.","cites":[],"own_p":0.9,"role_p":0.54,"quant_p":0.26,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.16,"main_claim_p":0.16},{"id":"b05.007.00","role":"result","text":"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).","cites":[],"own_p":0.89,"role_p":0.79,"quant_p":0.1,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.13,"main_claim_p":0.05},{"id":"b05.008.00","role":"setup","text":"The color bar on the right of each panel indicates the deviation from $f^⊕_0$.","cites":[],"own_p":0.64,"role_p":0.47,"quant_p":0.12,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.09,"main_claim_p":0.04},{"id":"b05.008.01","role":"setup","text":"The darker red (darker blue) regions correspond to larger (smaller) values of $f̅^⊕_e,μ,τ$ compared with $f^⊕_0 e,0μ,0τ$.","cites":[],"own_p":0.62,"role_p":0.53,"quant_p":0.91,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.12,"main_claim_p":0.06},{"id":"b05.008.02","role":"interpretation","text":"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.","cites":[],"own_p":0.73,"role_p":0.55,"quant_p":0.07,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.14,"main_claim_p":0.04},{"id":"b05.008.03","role":"interpretation","text":"We illustrate this point by taking Fig. [ref](a) as an example.","cites":[],"own_p":0.79,"role_p":0.52,"quant_p":0.06,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.12,"main_claim_p":0.03},{"id":"b05.008.04","role":"interpretation","text":"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).","cites":[],"own_p":0.86,"role_p":0.71,"quant_p":0.56,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.24,"main_claim_p":0.05},{"id":"b05.009.00","role":"result","text":"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 $f^⊕_0$.","cites":[],"own_p":0.85,"role_p":0.52,"quant_p":0.79,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.2,"main_claim_p":0.14},{"id":"b05.010.00","role":"result","text":"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 $f̅^⊕_μ,τ$.","cites":[],"own_p":0.85,"role_p":0.63,"quant_p":0.65,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.11,"main_claim_p":0.11},{"id":"b05.010.01","role":"result","text":"Therefore, the black points in Fig. [ref](a1) form a strip extending to lower-right direction.","cites":[],"own_p":0.87,"role_p":0.77,"quant_p":0.11,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.07,"main_claim_p":0.1},{"id":"b05.011.00","role":"interpretation","text":"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.","cites":[],"own_p":0.83,"role_p":0.88,"quant_p":0.27,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.16,"main_claim_p":0.08},{"id":"b05.012.00","role":"interpretation","text":"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)).","cites":[],"own_p":0.88,"role_p":0.77,"quant_p":0.95,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.14,"main_claim_p":0.11},{"id":"b05.012.01","role":"interpretation","text":"Following the same logic, the distributions for Case-(b) and Case-(c) in Fig. [ref] can be inferred from Fig. [ref].","cites":[],"own_p":0.51,"role_p":0.77,"quant_p":0.07,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.36,"main_claim_p":0.06},{"id":"b05.013.00","role":"method","text":"For TXS 0506+056 with a higher neutrino energy, we repeated the same analysis.","cites":[],"own_p":0.89,"role_p":0.96,"quant_p":0.09,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.32,"main_claim_p":0.04},{"id":"b05.013.01","role":"limitation","text":"Since the location of neutrino production is under investigation.","cites":[],"own_p":0.12,"role_p":0.86,"quant_p":0.03,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.28,"main_claim_p":0.02},{"id":"b05.014.00","role":"setup","text":"The first range is $[10^2,10^5]R_s$, where $10^5R_s$ is the influence radius of TXS 0506+056 [ref] .","cites":["Cline:2022qld"],"own_p":0.37,"role_p":0.8,"quant_p":0.93,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.77,"main_claim_p":0.03},{"id":"b05.015.00","role":"setup","text":"The second range is chosen to be the same as NGC 1068, i.e. $[10,10^2]R_s$.","cites":[],"own_p":0.83,"role_p":0.56,"quant_p":0.86,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.82,"main_claim_p":0.03},{"id":"b05.015.01","role":"result","text":"The results of second production range are shown in Appendix [ref].","cites":[],"own_p":0.87,"role_p":0.5,"quant_p":0.07,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.2,"main_claim_p":0.04},{"id":"b05.015.02","role":"result","text":"Fig [ref] shows the correspoding flavor ratio distribution for the production range $[10^2,10^5]R_s$.","cites":[],"own_p":0.9,"role_p":0.92,"quant_p":0.42,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.57,"main_claim_p":0.05},{"id":"b05.016.00","role":"result","text":"The event-averaged deviation for Fig. [ref] is shown in Fig. [ref].","cites":[],"own_p":0.8,"role_p":0.53,"quant_p":0.08,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.1,"main_claim_p":0.07},{"id":"b05.016.01","role":"interpretation","text":"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 $f̅_τ^⊕$.","cites":[],"own_p":0.83,"role_p":0.7,"quant_p":0.47,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.5,"main_claim_p":0.29},{"id":"b05.017.00","role":"result","text":"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.","cites":[],"own_p":0.86,"role_p":0.83,"quant_p":0.06,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.62,"main_claim_p":0.26},{"id":"b05.017.01","role":"result","text":"In Fig. [ref], we demonstrate the constraints on the coupling constants for $m_ϕ=1 feV$.","cites":[],"own_p":0.88,"role_p":0.93,"quant_p":0.33,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.54,"main_claim_p":0.17},{"id":"b05.018.00","role":"method","text":"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].","cites":[],"own_p":0.87,"role_p":0.87,"quant_p":0.2,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.45,"main_claim_p":0.11},{"id":"b05.018.01","role":"setup","text":"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.","cites":[],"own_p":0.72,"role_p":0.85,"quant_p":0.06,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.89,"main_claim_p":0.06},{"id":"b05.018.02","role":"interpretation","text":"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]).","cites":[],"own_p":0.77,"role_p":0.98,"quant_p":0.29,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.28,"main_claim_p":0.08},{"id":"b05.018.03","role":"interpretation","text":"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.","cites":[],"own_p":0.83,"role_p":1.0,"quant_p":0.28,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.36,"main_claim_p":0.13},{"id":"b05.019.00","role":"setup","text":"The dark scalar mass $m_ϕ$ also affects the value of $V^⊕_αβ$ which scales as $m^-1_ϕ$ in Eq.([ref]).","cites":[],"own_p":0.63,"role_p":0.51,"quant_p":0.3,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.42,"main_claim_p":0.1},{"id":"b05.019.01","role":"method","text":"According to Fig. [ref] for $m_ϕ=1 feV$ and Fig. [ref], we can derive the boundaries for other values of $m_ϕ$.","cites":[],"own_p":0.83,"role_p":0.67,"quant_p":0.24,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.37,"main_claim_p":0.09},{"id":"b05.019.02","role":"result","text":"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].","cites":[],"own_p":0.89,"role_p":0.61,"quant_p":0.08,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.56,"main_claim_p":0.09},{"id":"b05.019.03","role":"interpretation","text":"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.","cites":[],"own_p":0.72,"role_p":0.86,"quant_p":0.33,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.22,"main_claim_p":0.22},{"id":"b05.020.00","role":"result","text":"The parameters $(y_e, y_μ , y_τ)$ of Case-(d) excluded by IceCube MESE 95% C.L. contour are shown in Fig. [ref].","cites":[],"own_p":0.86,"role_p":0.97,"quant_p":0.15,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.31,"main_claim_p":0.08},{"id":"b05.020.01","role":"interpretation","text":"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).","cites":[],"own_p":0.87,"role_p":0.52,"quant_p":0.76,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.35,"main_claim_p":0.1},{"id":"b05.020.02","role":"interpretation","text":"This patch arises from the nonzero value of the third coupling constant.","cites":[],"own_p":0.84,"role_p":0.98,"quant_p":0.08,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.31,"main_claim_p":0.07},{"id":"b05.020.03","role":"result","text":"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).","cites":[],"own_p":0.9,"role_p":0.52,"quant_p":0.92,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.3,"main_claim_p":0.11},{"id":"b05.020.04","role":"method","text":"The same calculation is repeated using the combined $ν$-telescope contour, and the results are shown in Appendix [ref].","cites":[],"own_p":0.92,"role_p":0.71,"quant_p":0.05,"section":"AGN Neutrino Flavor Ratio in IceCube","condition_p":0.23,"main_claim_p":0.04},{"id":"b06.000.00","role":"other","text":"The similar calculations for DSNB neutrinos are shown in Fig. [ref] and [ref].","cites":[],"own_p":0.83,"role_p":0.65,"quant_p":0.07,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.11,"main_claim_p":0.04},{"id":"b06.000.01","role":"method","text":"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 $(ν̅_e,ν_x,ν_e)$.","cites":[],"own_p":0.87,"role_p":0.53,"quant_p":0.17,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.74,"main_claim_p":0.05},{"id":"b06.000.02","role":"setup","text":"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 $T_ν_x=7 MeV$.","cites":[],"own_p":0.72,"role_p":0.61,"quant_p":0.98,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.7,"main_claim_p":0.06},{"id":"b06.000.03","role":"result","text":"After the propagation in vacuum, the final flavor ratio at Earth is $f^⊕_0=(0.166,0.647,0.187)$.","cites":[],"own_p":0.82,"role_p":0.93,"quant_p":0.98,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.62,"main_claim_p":0.11},{"id":"b06.000.04","role":"method","text":"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]).","cites":[],"own_p":0.89,"role_p":0.95,"quant_p":0.14,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.51,"main_claim_p":0.08},{"id":"b06.001.00","role":"result","text":"The combined limit from HK, DUNE, and JUNO [ref] is included in Fig. [ref].","cites":["Tabrizi:2020vmo"],"own_p":0.67,"role_p":0.42,"quant_p":0.09,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.13,"main_claim_p":0.07},{"id":"b06.001.01","role":"result","text":"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.","cites":[],"own_p":0.87,"role_p":0.99,"quant_p":0.82,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.25,"main_claim_p":0.28},{"id":"b06.001.02","role":"result","text":"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).","cites":[],"own_p":0.89,"role_p":0.81,"quant_p":0.8,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.22,"main_claim_p":0.13},{"id":"b06.001.03","role":"result","text":"As a result, the distribution in Fig. [ref](b) is “shorter” than others.","cites":[],"own_p":0.88,"role_p":0.72,"quant_p":0.7,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.12,"main_claim_p":0.1},{"id":"b06.001.04","role":"interpretation","text":"Overall, the neutrino dark matter interaction tends to decrease the fractions of $μ$ and $τ$ flavor, and the fraction of electron neutrino is increased.","cites":[],"own_p":0.88,"role_p":0.57,"quant_p":0.72,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.2,"main_claim_p":0.46},{"id":"b06.001.05","role":"result","text":"The anti-electron neutrino fraction is mildly shifted away from the vacuum case (red point).","cites":[],"own_p":0.87,"role_p":0.96,"quant_p":0.51,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.14,"main_claim_p":0.14},{"id":"b06.001.06","role":"method","text":"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.","cites":[],"own_p":0.86,"role_p":0.5,"quant_p":0.97,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.89,"main_claim_p":0.11},{"id":"b06.001.07","role":"interpretation","text":"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 $f^⊕_0$.","cites":[],"own_p":0.86,"role_p":0.47,"quant_p":0.92,"section":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","condition_p":0.64,"main_claim_p":0.28},{"id":"b07.000.00","role":"setup","text":"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) $(y_e,y_μ,y_τ)$.","cites":[],"own_p":0.85,"role_p":0.99,"quant_p":0.12,"section":"Summary","condition_p":0.75,"main_claim_p":0.09},{"id":"b07.000.01","role":"setup","text":"The effective potential $V_αβ$ depends on the coupling constant $y_e,μ,τ$, scalar DM mass $m_ϕ$, and the mediator mass $m_F$.","cites":[],"own_p":0.59,"role_p":1.0,"quant_p":0.04,"section":"Summary","condition_p":0.36,"main_claim_p":0.07},{"id":"b07.000.02","role":"setup","text":"We take the AGNs and the DSNB as our sources that produce neutrinos at different energy scales.","cites":[],"own_p":0.81,"role_p":0.93,"quant_p":0.12,"section":"Summary","condition_p":0.57,"main_claim_p":0.08},{"id":"b07.001.00","role":"setup","text":"The $𝒪(TeV)$ neutrinos are assumed to be produced from NGC 1068 and TXS 0506+056 via pion decay with initial flavor ratio $(ν_e:ν_μ:ν_τ)=(1:2:0)$.","cites":[],"own_p":0.68,"role_p":0.99,"quant_p":0.7,"section":"Summary","condition_p":0.94,"main_claim_p":0.08},{"id":"b07.001.01","role":"setup","text":"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.","cites":[],"own_p":0.77,"role_p":0.99,"quant_p":0.72,"section":"Summary","condition_p":0.95,"main_claim_p":0.05},{"id":"b07.001.02","role":"method","text":"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 $n=1$.","cites":[],"own_p":0.75,"role_p":0.94,"quant_p":0.78,"section":"Summary","condition_p":0.95,"main_claim_p":0.18},{"id":"b07.001.03","role":"method","text":"The coupling constant is restricted by the mean free path of neutrino, which depends on the spike density of AGN.","cites":[],"own_p":0.71,"role_p":0.51,"quant_p":0.06,"section":"Summary","condition_p":0.85,"main_claim_p":0.09},{"id":"b07.001.04","role":"setup","text":"The upper limit for $y_e,μ,τ$ is 10, and we fix the lower limit at 0.1.","cites":[],"own_p":0.86,"role_p":0.8,"quant_p":0.89,"section":"Summary","condition_p":0.93,"main_claim_p":0.05},{"id":"b07.002.00","role":"method","text":"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.","cites":[],"own_p":0.92,"role_p":0.86,"quant_p":0.53,"section":"Summary","condition_p":0.95,"main_claim_p":0.13},{"id":"b07.003.00","role":"result","text":"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 $f^⊕_0μ$.","cites":[],"own_p":0.93,"role_p":0.97,"quant_p":0.9,"section":"Summary","condition_p":0.17,"main_claim_p":0.44},{"id":"b07.003.01","role":"result","text":"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.","cites":[],"own_p":0.75,"role_p":0.85,"quant_p":0.3,"section":"Summary","condition_p":0.22,"main_claim_p":0.22},{"id":"b07.003.02","role":"method","text":"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].","cites":[],"own_p":0.93,"role_p":0.51,"quant_p":0.17,"section":"Summary","condition_p":0.48,"main_claim_p":0.34},{"id":"b07.003.03","role":"interpretation","text":"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.","cites":[],"own_p":0.93,"role_p":0.8,"quant_p":0.66,"section":"Summary","condition_p":0.47,"main_claim_p":0.19},{"id":"b07.004.00","role":"method","text":"We also define the deviation parameters $R̅_e,μ,τ$ and generate their color maps for the distributions in the ternary plots.","cites":[],"own_p":0.93,"role_p":0.68,"quant_p":0.07,"section":"Summary","condition_p":0.11,"main_claim_p":0.07},{"id":"b07.004.01","role":"interpretation","text":"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.","cites":[],"own_p":0.86,"role_p":0.67,"quant_p":0.37,"section":"Summary","condition_p":0.27,"main_claim_p":0.14},{"id":"b07.004.02","role":"interpretation","text":"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.","cites":[],"own_p":0.84,"role_p":0.85,"quant_p":0.12,"section":"Summary","condition_p":0.65,"main_claim_p":0.15},{"id":"b07.005.00","role":"setup","text":"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.","cites":[],"own_p":0.55,"role_p":0.46,"quant_p":0.95,"section":"Summary","condition_p":0.36,"main_claim_p":0.11},{"id":"b07.005.01","role":"setup","text":"Furthermore, the neutrinos from CCSN propagate in the extragalactic medium, where the DM density is extremely low.","cites":[],"own_p":0.32,"role_p":0.73,"quant_p":0.33,"section":"Summary","condition_p":0.79,"main_claim_p":0.07},{"id":"b07.005.02","role":"setup","text":"The effective potential should then be enhanced to make significant change in flavor ratio.","cites":[],"own_p":0.44,"role_p":0.43,"quant_p":0.07,"section":"Summary","condition_p":0.69,"main_claim_p":0.18},{"id":"b07.005.03","role":"method","text":"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.","cites":[],"own_p":0.91,"role_p":0.63,"quant_p":0.9,"section":"Summary","condition_p":0.93,"main_claim_p":0.08},{"id":"b07.005.04","role":"method","text":"Given the temperature of $ν_e$, $ν̅_e$, and $ν_x$, we may compute the DSNB flux and the initial flavor ratio.","cites":[],"own_p":0.66,"role_p":0.95,"quant_p":0.07,"section":"Summary","condition_p":0.45,"main_claim_p":0.06},{"id":"b07.005.05","role":"result","text":"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 $f̅_ν_e^⊕$.","cites":[],"own_p":0.93,"role_p":0.98,"quant_p":0.86,"section":"Summary","condition_p":0.18,"main_claim_p":0.2},{"id":"b07.005.06","role":"result","text":"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.","cites":[],"own_p":0.93,"role_p":0.88,"quant_p":0.77,"section":"Summary","condition_p":0.27,"main_claim_p":0.14},{"id":"b07.005.07","role":"interpretation","text":"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.","cites":[],"own_p":0.88,"role_p":0.88,"quant_p":0.56,"section":"Summary","condition_p":0.15,"main_claim_p":0.08},{"id":"b07.005.08","role":"result","text":"We include the combined constraint from HK/DUNE/JUNO and find that all the points stay inside the sensitivity contour.","cites":[],"own_p":0.91,"role_p":0.8,"quant_p":0.45,"section":"Summary","condition_p":0.42,"main_claim_p":0.21},{"id":"b08.000.00","role":"other","text":"We acknowledge the kind support of the National Science and Technology Council of Taiwan, with grant number NSTC 115-2112-M-007-010-.","cites":[],"own_p":0.09,"role_p":1.0,"quant_p":0.6,"section":"Acknowledgment","condition_p":0.04,"main_claim_p":0.01},{"id":"b08.000.01","role":"other","text":"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.","cites":[],"own_p":0.18,"role_p":1.0,"quant_p":0.44,"section":"Acknowledgment","condition_p":0.04,"main_claim_p":0.01},{"id":"b08.000.02","role":"other","text":"Y.M.Y. is supported in part by NSTC Grant No. 115B0061I4.","cites":[],"own_p":0.11,"role_p":1.0,"quant_p":0.42,"section":"Acknowledgment","condition_p":0.04,"main_claim_p":0.01},{"id":"b09.000.00","role":"setup","text":"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].","cites":[],"own_p":0.81,"role_p":0.63,"quant_p":0.35,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.9,"main_claim_p":0.04},{"id":"b09.000.01","role":"limitation","text":"Unfortunately, the $m_ϕ=0.1 peV$ and $m_ϕ=1 peV$ distributions nearly completely overlap.","cites":[],"own_p":0.91,"role_p":0.59,"quant_p":0.86,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.26,"main_claim_p":0.07},{"id":"b09.000.02","role":"method","text":"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).","cites":[],"own_p":0.94,"role_p":0.93,"quant_p":0.79,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.46,"main_claim_p":0.07},{"id":"b09.001.00","role":"result","text":"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.","cites":[],"own_p":0.91,"role_p":0.53,"quant_p":0.68,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.33,"main_claim_p":0.24},{"id":"b09.002.00","role":"result","text":"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).","cites":[],"own_p":0.88,"role_p":0.31,"quant_p":0.64,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.15,"main_claim_p":0.05},{"id":"b09.002.01","role":"result","text":"The red squares in Fig. [ref] (a3,b3,c3) depicts the range of $V^⊕$ of $m_ϕ=100 peV$ distributions.","cites":[],"own_p":0.85,"role_p":0.4,"quant_p":0.18,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.16,"main_claim_p":0.05},{"id":"b09.002.02","role":"result","text":"The regions enclosed by these squares are very lightly colored.","cites":[],"own_p":0.84,"role_p":0.91,"quant_p":0.13,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.09,"main_claim_p":0.04},{"id":"b09.002.03","role":"result","text":"Comparing to the black squares in Fig. [ref] (a3,b3,c3), they contains small amount of darker-blue areas.","cites":[],"own_p":0.86,"role_p":0.61,"quant_p":0.74,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.12,"main_claim_p":0.07},{"id":"b09.002.04","role":"result","text":"Therefore, the $m_ϕ=10 peV$ case of Fig. [ref] have more points with $f̅^⊕_τ≤f̅^⊕_0τ$ than the $m_ϕ=100 peV$.","cites":[],"own_p":0.89,"role_p":0.51,"quant_p":0.95,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.14,"main_claim_p":0.11},{"id":"b09.003.00","role":"interpretation","text":"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).","cites":[],"own_p":0.78,"role_p":0.66,"quant_p":0.42,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.16,"main_claim_p":0.07},{"id":"b09.003.01","role":"interpretation","text":"So, the $m_ϕ=10 peV$ distributions (blue) in Fig. [ref] have similar shapes to those (black) in Fig. [ref].","cites":[],"own_p":0.82,"role_p":0.64,"quant_p":0.59,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.12,"main_claim_p":0.1},{"id":"b09.004.00","role":"interpretation","text":"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.","cites":[],"own_p":0.81,"role_p":0.9,"quant_p":0.34,"section":"TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","condition_p":0.4,"main_claim_p":0.22},{"id":"b10.000.00","role":"result","text":"Fig. [ref] shows the constraint on the coupling constants of Case-(d), which is obtained from the combined $ν$ telescopes sensitivities.","cites":[],"own_p":0.86,"role_p":0.94,"quant_p":0.14,"section":"The Coupling Constants Excluded by Combined $ν$ Telescopes","condition_p":0.33,"main_claim_p":0.16},{"id":"b10.000.01","role":"interpretation","text":"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].","cites":[],"own_p":0.82,"role_p":0.92,"quant_p":0.94,"section":"The Coupling Constants Excluded by Combined $ν$ Telescopes","condition_p":0.23,"main_claim_p":0.2}]},"paper":{"title":"AGN and DSNB Neutrino Oscillation in Dark Matter Background","authors":["Po-Yan Tseng","Yu-Min Yeh"],"primary":"hep-ph","arxiv_id":"2609.21768","published":"2026-09-18T13:36:36Z","primary_cat":"hep-ph","submitted_at":"2026-09-18T13:36:36Z","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv abstract and full text. Labels and probabilities are the outputs of classifier-1.13.0 on the question banks abstract-p1-20260923 + fulltext-p1-20260923, exactly as returned. Measurements are the authors' numbers, located and checked by code. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","results":[{"p":0.96,"kind":"derivation","role":"result","text":"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 $y_α,β=10$.","unit":"b03.004.07","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.22,"locations":["Active Galactic Nuclei"]},{"p":0.93,"kind":"derivation","role":"result","text":"In terms of Schwarzschild radius, $l_min/R_s∼190$ ($l_min/R_s∼6$) for NGC 1068 (TXS 0506+056).","unit":"b03.004.08","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.06,"locations":["Active Galactic Nuclei"]},{"p":0.911,"kind":"simulation","role":"result","text":"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 $f̅_ν_e^⊕$.","unit":"b07.005.05","hedge":{"p":0.99,"label":"asserted"},"causal_p":0.1,"locations":["Summary"]},{"p":0.902,"kind":"observation","role":"result","text":"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 $f^⊕_0μ$.","unit":"b07.003.00","hedge":{"p":0.91,"label":"asserted"},"causal_p":0.71,"locations":["Summary"]},{"p":0.901,"kind":"derivation","role":"result","text":"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.","unit":"b04.002.07","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.17,"locations":["Diffuse Supernova Neutrino Background"]},{"p":0.861,"kind":"observation","role":"result","text":"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.","unit":"b06.001.01","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.06,"locations":["DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO"]},{"p":0.855,"kind":"simulation","role":"result","text":"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 $f^⊕_0=(0.34,0.31,0.35)$.","unit":"b05.006.00","hedge":{"p":0.8,"label":"asserted"},"causal_p":0.2,"locations":["AGN Neutrino Flavor Ratio in IceCube"]},{"p":0.835,"kind":"observation","role":"result","text":"The anti-electron neutrino fraction is mildly shifted away from the vacuum case (red point).","unit":"b06.001.05","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.13,"locations":["DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO"]},{"p":0.834,"kind":"measurement","role":"result","text":"The parameters $(y_e, y_μ , y_τ)$ of Case-(d) excluded by IceCube MESE 95% C.L. contour are shown in Fig. [ref].","unit":"b05.020.00","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.09,"locations":["AGN Neutrino Flavor Ratio in IceCube"]},{"p":0.83,"kind":"interpretation","role":"interpretation","text":"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.","unit":"b05.018.03","hedge":{"p":0.5,"label":"asserted"},"causal_p":0.93,"locations":["AGN Neutrino Flavor Ratio in IceCube"]},{"p":0.828,"kind":"simulation","role":"result","text":"Fig [ref] shows the correspoding flavor ratio distribution for the production range $[10^2,10^5]R_s$.","unit":"b05.015.02","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.22,"locations":["AGN Neutrino Flavor Ratio in IceCube"]},{"p":0.823,"kind":"interpretation","role":"interpretation","text":"This patch arises from the nonzero value of the third coupling constant.","unit":"b05.020.02","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.97,"locations":["AGN Neutrino Flavor Ratio in IceCube"]},{"p":0.818,"kind":"derivation","role":"result","text":"In Fig. [ref], we demonstrate the constraints on the coupling constants for $m_ϕ=1 feV$.","unit":"b05.017.01","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.12,"locations":["AGN Neutrino Flavor Ratio in IceCube"]},{"p":0.818,"kind":"simulation","role":"result","text":"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.","unit":"b07.005.06","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.1,"locations":["Summary"]},{"p":0.815,"kind":"interpretation","role":"interpretation","text":"Therefore, the Hamiltonian is dominated by $V^⊕$ and the final flavor ratio depends on the relative strength between each $V^⊕_αβ$.","unit":"b05.005.02","hedge":{"p":1.0,"label":"asserted"},"causal_p":0.85,"locations":["AGN Neutrino Flavor Ratio in IceCube"]}],"abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"The neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.07,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.84,"id":"s1","own":false,"role":"contribution","text":"In this work we consider neutrinos interact with ultra-light scalar dark matters $φ$ ($m_φ\\ll 1\\,{\\rm eV}$).","hedge":{"p":0.87,"label":"asserted"},"own_p":0.48,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.91,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.84,"interpretation":0.0}},{"i":2,"p":0.89,"id":"s2","own":false,"role":"method","text":"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.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.23,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.89,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.08,"interpretation":0.0}},{"i":3,"p":0.9,"id":"s3","own":true,"role":"method","text":"Two types of neutrino sources are adopted in our calculations.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.77,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.57,"role_probabilities":{"gap":0.0,"method":0.9,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.1,"interpretation":0.0}},{"i":4,"p":0.88,"id":"s4","own":false,"role":"method","text":"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 ($ν_e,ν_μ,ν_τ$)=($1:2:0$).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.24,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.93,"role_probabilities":{"gap":0.0,"method":0.88,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.0}},{"i":5,"p":0.82,"id":"s5","own":true,"role":"method","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.68,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.91,"role_probabilities":{"gap":0.0,"method":0.82,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.17,"interpretation":0.0}},{"i":6,"p":0.96,"id":"s6","own":true,"role":"method","text":"We consider the range of $νφ$ coupling constant such that the adiabatic condition and mean free path can be satisfied.","hedge":{"p":0.76,"label":"asserted"},"own_p":0.64,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.96,"result":0.0,"background":0.0,"limitation":0.02,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":7,"p":0.95,"id":"s7","own":true,"role":"method","text":"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.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":true,"quantitative_p":0.96,"role_probabilities":{"gap":0.0,"method":0.95,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.0}},{"i":8,"p":0.54,"id":"s8","own":false,"role":"method","text":"The second source considered is the Diffuse Supernova Neutrino Background (DSNB), it is an isotropic neutrino source with energy $\\mathcal{O}({\\rm MeV})$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.31,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.73,"role_probabilities":{"gap":0.0,"method":0.54,"result":0.0,"background":0.11,"limitation":0.0,"future_work":0.0,"contribution":0.34,"interpretation":0.0}},{"i":9,"p":0.4,"id":"s9","own":true,"role":"method","text":"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.","hedge":{"p":0.88,"label":"asserted"},"own_p":0.91,"main_claim_p":0.17,"quantitative":true,"quantitative_p":0.8,"role_probabilities":{"gap":0.0,"method":0.4,"result":0.25,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.34,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":0.67,"text":"The neutrino-matter interaction cause the final flavor compositions deviating from those expected in vacuum.","location":"abstract s0","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"abstract: one request per paper; body: one sentence per request","requests":274,"input_tokens":363210,"cost_usd_reported":0.0,"cost_usd_at_list_price":0.015255},"compiled_at":"2026-09-24","bank_version":"abstract-p1-20260923 + fulltext-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.03,"states_limitation":0.2,"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},"abstract_vs_body":{"stronger_p":0.63,"supported_p":0.87},"evidential_basis":{"p":1.0,"value":"simulation or computation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":1.0}},"contribution_type":{"p":0.76,"value":"simulation study","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.76,"theoretical_result":0.24,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.48,"text":"In this work we consider neutrinos interact with ultra-light scalar dark matters $φ$ ($m_φ\\ll 1\\,{\\rm eV}$).","location":"abstract s1"}},"coverage":{"tier":"full_text","levels_run":["P abstract","S sections","T body sentences","C citations"],"not_examined":["figures and tables","equation content","supplementary material","relations to other papers"],"sources_read":["arXiv listing abstract v1","arXiv full text v1, LaTeX source: 11 sections, 207 body sentences"],"levels_not_run":["R cross-paper relations"],"references_parsed":31,"sentences_in_body":207,"sentences_examined":207,"citation_contexts_examined":40},"conditions":[{"p":0.97,"key":"assumption or scope","text":"We assume the DM density between CCSN and Earth varies as a linear function of $z$, denoted by $ρ_DM(z)$.","unit":"b04.003.01","location":"Diffuse Supernova Neutrino Background"},{"p":0.96,"key":"assumption or scope","text":"We assume neutrinos are Majorana fermions and couple to hypothetical dark scalar $ϕ$ through a fermionic mediator $F$.","unit":"b02.000.00","location":"Neutrino Oscillation in Dark Matter"},{"p":0.96,"key":"assumption or scope","text":"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.","unit":"b05.002.02","location":"AGN Neutrino Flavor Ratio in IceCube"},{"p":0.95,"key":"assumption or scope","text":"We consider the range of $νϕ$ coupling constant such that the adiabatic condition and mean free path can be satisfied.","unit":"b00.001.00","location":"Introduction"},{"p":0.95,"key":"assumption or scope","text":"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] .","unit":"b03.002.03","location":"Active Galactic Nuclei"},{"p":0.95,"key":"assumption or scope","text":"For the analysis of AGNs, $m_F$ is fixed to $1 TeV$.","unit":"b03.004.05","location":"Active Galactic Nuclei"},{"p":0.95,"key":"assumption or scope","text":"Due to the adiabatic condition, we only need to consider the average flavor ratio at the production location and the Earth.","unit":"b05.000.01","location":"AGN Neutrino Flavor Ratio in IceCube"},{"p":0.95,"key":"assumption or scope","text":"For each event, the neutrinos are assumed to be produced within the range $[10,10^2]R_s$ randomly in logarithmic scale.","unit":"b05.002.01","location":"AGN Neutrino Flavor Ratio in IceCube"},{"p":0.95,"key":"assumption or scope","text":"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.","unit":"b07.001.01","location":"Summary"},{"p":0.95,"key":"assumption or scope","text":"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 $n=1$.","unit":"b07.001.02","location":"Summary"},{"p":0.95,"key":"assumption or scope","text":"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.","unit":"b07.002.00","location":"Summary"},{"p":0.94,"key":"assumption or scope","text":"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.","unit":"b00.001.01","location":"Introduction"},{"p":0.94,"key":"assumption or scope","text":"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 $m_F^2≫m_ϕE$.","unit":"b03.004.03","location":"Active Galactic Nuclei"},{"p":0.94,"key":"assumption or scope","text":"The $𝒪(TeV)$ neutrinos are assumed to be produced from NGC 1068 and TXS 0506+056 via pion decay with initial flavor ratio $(ν_e:ν_μ:ν_τ)=(1:2:0)$.","unit":"b07.001.00","location":"Summary"},{"p":0.93,"key":"assumption or scope","text":"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.","unit":"b01.001.02","location":"Introduction"},{"p":0.93,"key":"assumption or scope","text":"The propagation of neutrinos is adiabatic if $η≪1$.","unit":"b02.003.04","location":"Neutrino Oscillation in Dark Matter"},{"p":0.93,"key":"assumption or scope","text":"For detection on Earth, we require that the neutrinos be forward-scattered through their path.","unit":"b03.004.01","location":"Active Galactic Nuclei"},{"p":0.93,"key":"assumption or scope","text":"So the mean free path should be longer than the distance between AGN and Earth.","unit":"b03.004.02","location":"Active Galactic Nuclei"},{"p":0.93,"key":"assumption or scope","text":"We fixed $z_max=5$ for which there is a reasonable amount of star formation.","unit":"b04.001.02","location":"Diffuse Supernova Neutrino Background"},{"p":0.93,"key":"assumption or scope","text":"The upper limit for $y_e,μ,τ$ is 10, and we fix the lower limit at 0.1.","unit":"b07.001.04","location":"Summary"}],"measurements":[{"p":0.79,"kind":"value unit","text":"In this work we consider neutrinos interact with ultra-light scalar dark matters $ϕ$ ($m_ϕ≪1 eV$).","unit":"b00.000.01","group":"","value":"1 eV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Introduction","quantity":"interact with ultra-light scalar dark matters ϕ (m_ϕ≪"},{"p":0.78,"kind":"value unit","text":"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.","unit":"b00.001.03","group":"","value":"-22 eV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction","status":"consistent"}],"location":"Introduction","quantity":"the similar analysis for the DSNB with m_ϕ=10^"},{"p":0.83,"kind":"value unit","text":"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 $10^-22 eV$.","unit":"b01.007.04","group":"","value":"-22 eV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction","status":"consistent"}],"location":"Introduction","quantity":"and the DM mass is fixed at 10^"},{"p":0.99,"kind":"value unit","text":"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.","unit":"b03.002.00","group":"","value":"-6 pc","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Active Galactic Nuclei","quantity":"over energy and coupling constant is around 10^"},{"p":0.97,"kind":"scientific","text":"The relevant parameters for TXS 0506+056 are $η≃6×10^-11$ and averaged $L_ij ∼10^-4 pc$.","unit":"b03.003.01","group":"","value":"6×10^-11","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"Acknowledgment","status":"consistent"}],"location":"Active Galactic Nuclei","quantity":"The relevant parameters for TXS 0506+056 are η≃"},{"p":0.97,"kind":"value unit","text":"The relevant parameters for TXS 0506+056 are $η≃6×10^-11$ and averaged $L_ij ∼10^-4 pc$.","unit":"b03.003.01","group":"","value":"-4 pc","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Active Galactic Nuclei","quantity":"TXS 0506+056 are η≃6×10^-11 and averaged L_ij ∼10^"},{"p":0.59,"kind":"value unit","text":"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 $m_F^2≫m_ϕE$.","unit":"b03.004.03","group":"","value":"1 TeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Active Galactic Nuclei","quantity":"σ_νϕ=y^2_αy^2_βm_ϕE/(32πm_F^4) under the heavy mediator limit, i.e. m_F≥"},{"p":0.69,"kind":"value unit","text":"For the analysis of AGNs, $m_F$ is fixed to $1 TeV$.","unit":"b03.004.05","group":"","value":"1 TeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Active Galactic Nuclei","quantity":"the analysis of AGNs, m_F is fixed to"},{"p":0.98,"kind":"scientific","text":"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 $y_α,β=10$.","unit":"b03.004.07","group":"","value":"1.81×10^-4 pc","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"stated once","status":"not repeated"}],"location":"Active Galactic Nuclei","quantity":"Concerning this extreme case, we find l_min∼"},{"p":0.98,"kind":"scientific","text":"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 $y_α,β=10$.","unit":"b03.004.07","group":"","value":"1.85×10^-4 pc","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"stated once","status":"not repeated"}],"location":"Active Galactic Nuclei","quantity":"this extreme case, we find l_min∼1.81×10^-4 pc (l_min∼"},{"p":0.96,"kind":"value unit","text":"We adopt $T_ν_e=5 MeV$, $T_ν̅_e=6 MeV$, and $T_ν_x=7 MeV$ in our calculations.","unit":"b04.001.05","group":"","value":"5 MeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"We adopt T_ν_e="},{"p":0.96,"kind":"value unit","text":"We adopt $T_ν_e=5 MeV$, $T_ν̅_e=6 MeV$, and $T_ν_x=7 MeV$ in our calculations.","unit":"b04.001.05","group":"","value":"6 MeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"We adopt T_ν_e=5 MeV, T_ν̅_e="},{"p":0.96,"kind":"value unit","text":"We adopt $T_ν_e=5 MeV$, $T_ν̅_e=6 MeV$, and $T_ν_x=7 MeV$ in our calculations.","unit":"b04.001.05","group":"","value":"7 MeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"We adopt T_ν_e=5 MeV, T_ν̅_e=6 MeV, and T_ν_x="},{"p":0.75,"kind":"value unit","text":"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.","unit":"b04.002.06","group":"","value":"0.1 GeV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"AGN Neutrino Flavor Ratio in IceCube, DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Introduction","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"fix m_ϕ to this value and m_F to"},{"p":0.98,"kind":"value unit","text":"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.","unit":"b04.002.07","group":"","value":"400 kpc","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"Introduction","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"It turns out l∼"},{"p":0.98,"kind":"value unit","text":"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.","unit":"b04.002.07","group":"","value":"0.4 GeV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"AGN Neutrino Flavor Ratio in IceCube, Active Galactic Nuclei","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"around Earth (the maximum DM density is ρ^⊕_DM="},{"p":0.97,"kind":"value unit","text":"The maximum average oscillation length is $∼10^-5 pc$.","unit":"b04.003.00","group":"","value":"-5 pc","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Diffuse Supernova Neutrino Background","quantity":"The maximum average oscillation length is ∼10^"},{"p":0.99,"kind":"scientific","text":"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 $V_31^r$.","unit":"b05.004.01","group":"","value":"3.1×10^-21","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"stated once","status":"not repeated"}],"location":"AGN Neutrino Flavor Ratio in IceCube","quantity":"potentials at Earth lie within the range ["},{"p":0.99,"kind":"scientific","text":"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 $V_31^r$.","unit":"b05.004.01","group":"","value":"3.1×10^-17","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"stated once","status":"not repeated"}],"location":"AGN Neutrino Flavor Ratio in IceCube","quantity":"at Earth lie within the range [3.1×10^-21"},{"p":0.98,"kind":"value unit","text":"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 $T_ν_x=7 MeV$.","unit":"b06.000.02","group":"","value":"5 MeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","quantity":"is obtained from Eq.([ref]a) with the temperature T_ν_e="},{"p":0.98,"kind":"value unit","text":"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 $T_ν_x=7 MeV$.","unit":"b06.000.02","group":"","value":"6 MeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","quantity":"from Eq.([ref]a) with the temperature T_ν_e=5 MeV, T_ν̅_e="},{"p":0.98,"kind":"value unit","text":"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 $T_ν_x=7 MeV$.","unit":"b06.000.02","group":"","value":"7 MeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","quantity":"the temperature T_ν_e=5 MeV, T_ν̅_e=6 MeV, and T_ν_x="},{"p":0.97,"kind":"value unit","text":"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.","unit":"b06.001.06","group":"","value":"-22 eV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction","status":"consistent"}],"location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","quantity":"order smaller than AGN neutrino, we consider m_ϕ=10^"},{"p":0.97,"kind":"value unit","text":"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.","unit":"b06.001.06","group":"","value":"0.1 GeV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"AGN Neutrino Flavor Ratio in IceCube, DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background","status":"consistent"}],"location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","quantity":"AGN neutrino, we consider m_ϕ=10^-22 eV and m_F="},{"p":0.92,"kind":"value unit","text":"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 $f^⊕_0$.","unit":"b06.001.07","group":"","value":"-22 eV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction","status":"consistent"}],"location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","quantity":"Even though, the m_ϕ=10^"},{"p":0.53,"kind":"value unit","text":"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.","unit":"b07.002.00","group":"","value":"1 TeV","checks":[{"check":"number matches the authors' source text","status":"consistent"}],"location":"Summary","quantity":"feV, with the mediator mass fixed at m_F="},{"p":0.9,"kind":"value unit","text":"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.","unit":"b07.005.03","group":"","value":"-22 eV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background, Introduction","status":"consistent"}],"location":"Summary","quantity":"We adopt the lower limit of m_ϕ=10^"},{"p":0.9,"kind":"value unit","text":"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.","unit":"b07.005.03","group":"","value":"0.1 GeV","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"AGN Neutrino Flavor Ratio in IceCube, DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO, Diffuse Supernova Neutrino Background","status":"consistent"}],"location":"Summary","quantity":"eV and fix the mediator mass m_F to"},{"p":0.94,"kind":"percent","text":"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].","unit":"b10.000.01","group":"","value":"95%","checks":[{"check":"number matches the authors' source text","status":"consistent"},{"check":"same number stated elsewhere in the paper","detail":"AGN Neutrino Flavor Ratio in IceCube, TXS 0506+056 Analysis with Neutrino Production Region $[10,10^2]R_s$","status":"consistent"}],"location":"The Coupling Constants Excluded by Combined $ν$ Telescopes","quantity":"sensitivities is much smaller than the IceCube MESE"}],"citations_out":{"count":31,"shown":[{"p":0.81,"key":"Tseng:2024akh","ref":"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.","unit":"b01.001.02","intent":"method or tool","location":"Introduction","citing_text":"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.","load_bearing_p":0.77},{"p":0.78,"key":"IceCube:2025uyt","ref":"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.","unit":"b01.002.00","intent":"data used","location":"Introduction","citing_text":"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] .","load_bearing_p":0.74},{"p":0.72,"key":"IceCube:2022der","ref":"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.","unit":"b01.001.01","intent":"data used","location":"Introduction","citing_text":"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] .","load_bearing_p":0.67},{"p":0.41,"key":"Tseng:2024akh","ref":"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.","unit":"b02.000.01","intent":"supports this paper","location":"Neutrino Oscillation in Dark Matter","citing_text":"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.","load_bearing_p":0.65},{"p":0.8,"key":"Tseng:2024akh","ref":"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.","unit":"b03.001.01","intent":"supports this paper","location":"Active Galactic Nuclei","citing_text":"The saturation density $ρ_sat$ depends on the $ϕϕ^∗$ annihilation, and the cross section is proportional to $y_α^2y^2_β$ [ref] .","load_bearing_p":0.64},{"p":0.61,"key":"deSalas:2016svi","ref":"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.","unit":"b02.003.00","intent":"supports this paper","location":"Neutrino Oscillation in Dark Matter","citing_text":"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.","load_bearing_p":0.62},{"p":0.69,"key":"Tseng:2024akh","ref":"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.","unit":"b04.002.06","intent":"method or tool","location":"Diffuse Supernova Neutrino Background","citing_text":"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.","load_bearing_p":0.61},{"p":0.59,"key":"Horiuchi:2008jz","ref":"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.","unit":"b04.000.01","intent":"data used","location":"Diffuse Supernova Neutrino Background","citing_text":"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]","load_bearing_p":0.6},{"p":0.56,"key":"Agarwalla:2023sng","ref":"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","unit":"b05.006.01","intent":"comparison","location":"AGN Neutrino Flavor Ratio in IceCube","citing_text":"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.","load_bearing_p":0.55},{"p":0.45,"key":"Beacom:2010kk","ref":"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.","unit":"b04.000.00","intent":"background","location":"Diffuse Supernova Neutrino Background","citing_text":"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.","load_bearing_p":0.55},{"p":0.75,"key":"IceCube:2018cha","ref":"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.","unit":"b01.001.01","intent":"data used","location":"Introduction","citing_text":"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] .","load_bearing_p":0.54},{"p":0.42,"key":"Herrera:2023nww","ref":"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.","unit":"b03.001.02","intent":"supports this paper","location":"Active Galactic Nuclei","citing_text":"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.","load_bearing_p":0.53},{"p":0.5,"key":"Mathews:2014qba","ref":"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","unit":"b04.001.03","intent":"data used","location":"Diffuse Supernova Neutrino Background","citing_text":"The neutrino temperature can be obtained by the core-collapse simulation of neutrino emissions [ref] .","load_bearing_p":0.51},{"p":0.52,"key":"Horiuchi:2008jz","ref":"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.","unit":"b04.001.03","intent":"data used","location":"Diffuse Supernova Neutrino Background","citing_text":"The neutrino temperature can be obtained by the core-collapse simulation of neutrino emissions [ref] .","load_bearing_p":0.5},{"p":0.52,"key":"IceCube:2025uyt","ref":"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.","unit":"b05.006.01","intent":"data used","location":"AGN Neutrino Flavor Ratio in IceCube","citing_text":"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.","load_bearing_p":0.5},{"p":0.98,"key":"ParticleDataGroup:2024cfk","ref":"Particle Data Group Collaboration, S. Navas et al., “Review of particle physics”, Phys. Rev. D 110 (2024), no. 3, 030001.","unit":"b02.000.03","intent":"data used","location":"Neutrino Oscillation in Dark Matter","citing_text":"The differences of mass square for Normal Ordering (Inverse Ordering) are given by [ref]","load_bearing_p":0.5},{"p":0.93,"key":"Cline:2022qld","ref":"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.","unit":"b05.014.00","intent":"data used","location":"AGN Neutrino Flavor Ratio in IceCube","citing_text":"The first range is $[10^2,10^5]R_s$, where $10^5R_s$ is the influence radius of TXS 0506+056 [ref] .","load_bearing_p":0.5},{"p":0.49,"key":"Cline:2023tkp","ref":"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.","unit":"b01.001.00","intent":"supports this paper","location":"Introduction","citing_text":"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] .","load_bearing_p":0.49},{"p":0.75,"key":"Blanco:2023dfp","ref":"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.","unit":"b03.002.03","intent":"data used","location":"Active Galactic Nuclei","citing_text":"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] .","load_bearing_p":0.46},{"p":0.9,"key":"Fiorillo:2025cgm","ref":"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.","unit":"b03.002.04","intent":"supports this paper","location":"Active Galactic Nuclei","citing_text":"Ref. [ref] states that the TXS's neutrino flux from corona isn't sufficient enough to produce IceCube observed neutrino.].","load_bearing_p":0.46},{"p":0.52,"key":"deSalas:2016svi","ref":"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.","unit":"b05.000.03","intent":"method or tool","location":"AGN Neutrino Flavor Ratio in IceCube","citing_text":"Following Ref. [ref] , we obtain the average flavor ratio","load_bearing_p":0.44},{"p":0.51,"key":"Tabrizi:2020vmo","ref":"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.","unit":"b06.001.00","intent":"comparison","location":"DSNB Neutrino Flavor Ratio in Hyper-K, DUNE, and JUNO","citing_text":"The combined limit from HK, DUNE, and JUNO [ref] is included in Fig. [ref].","load_bearing_p":0.44},{"p":0.54,"key":"Agarwalla:2023sng","ref":"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","unit":"b01.003.01","intent":"supports this paper","location":"Introduction","citing_text":"Combining IceCube MESE, IceCube-Gen2, and additional contributions from future neutrino telescopes [ref] ,","load_bearing_p":0.41},{"p":0.49,"key":"IceCube-Gen2:2023rds","ref":"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.","unit":"b01.002.02","intent":"background","location":"Introduction","citing_text":"The future IceCube-Gen2 [ref]","load_bearing_p":0.41},{"p":0.52,"key":"IceCube:2022der","ref":"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.","unit":"b03.000.00","intent":"supports this paper","location":"Active Galactic Nuclei","citing_text":"The neutrino spectrum from AGN can be expressed by the power law $Φ(E)∝E^-γ$ [ref] .","load_bearing_p":0.4},{"p":0.77,"key":"Gondolo:1999ef","ref":"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.","unit":"b01.001.00","intent":"supports this paper","location":"Introduction","citing_text":"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] .","load_bearing_p":0.4},{"p":0.49,"key":"Super-Kamiokande:2021jaq","ref":"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.","unit":"b01.006.02","intent":"background","location":"Introduction","citing_text":"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.","load_bearing_p":0.38},{"p":0.55,"key":"Doring:2023vmk","ref":"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.","unit":"b03.000.00","intent":"background","location":"Active Galactic Nuclei","citing_text":"The neutrino spectrum from AGN can be expressed by the power law $Φ(E)∝E^-γ$ [ref] .","load_bearing_p":0.36},{"p":0.85,"key":"Salpeter1955","ref":"E. E. Salpeter, “The luminosity function and stellar evolution”, Astrophys. J. 121 (1955) 161–167.","unit":"b04.001.01","intent":"data used","location":"Diffuse Supernova Neutrino Background","citing_text":"The initial mass function $ψ(M)$ is proportional to $M^-2.35$ [ref] .","load_bearing_p":0.35},{"p":0.9,"key":"Yuksel:2008cu","ref":"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.","unit":"b04.000.01","intent":"data used","location":"Diffuse Supernova Neutrino Background","citing_text":"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]","load_bearing_p":0.34},{"p":0.63,"key":"Herrera:2023nww","ref":"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.","unit":"b01.001.00","intent":"supports this paper","location":"Introduction","citing_text":"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] .","load_bearing_p":0.33},{"p":0.46,"key":"JUNO:2015zny","ref":"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.","unit":"b01.006.02","intent":"background","location":"Introduction","citing_text":"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.","load_bearing_p":0.33},{"p":0.46,"key":"DUNE:2020ypp","ref":"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.","unit":"b01.006.02","intent":"background","location":"Introduction","citing_text":"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.","load_bearing_p":0.33},{"p":0.7,"key":"IceCube-Gen2:2020qha","ref":"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.","unit":"b01.002.02","intent":"background","location":"Introduction","citing_text":"The future IceCube-Gen2 [ref]","load_bearing_p":0.29},{"p":0.41,"key":"P-ONE:2020ljt","ref":"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.","unit":"b01.003.00","intent":"supports this paper","location":"Introduction","citing_text":"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.","load_bearing_p":0.29},{"p":0.46,"key":"DUNE:2020lwj","ref":"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.","unit":"b01.006.02","intent":"background","location":"Introduction","citing_text":"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.","load_bearing_p":0.29},{"p":0.37,"key":"KM3Net:2016zxf","ref":"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.","unit":"b01.003.00","intent":"supports this paper","location":"Introduction","citing_text":"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.","load_bearing_p":0.27},{"p":0.34,"key":"Romero-Wolf:2020pzh","ref":"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.","unit":"b01.003.00","intent":"supports this paper","location":"Introduction","citing_text":"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.","load_bearing_p":0.27},{"p":0.49,"key":"Hyper-Kamiokande:2022smq","ref":"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.","unit":"b01.006.02","intent":"background","location":"Introduction","citing_text":"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.","load_bearing_p":0.27},{"p":0.4,"key":"Baikal-GVD:2019fko","ref":"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.","unit":"b01.003.00","intent":"supports this paper","location":"Introduction","citing_text":"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.","load_bearing_p":0.26}]},"limitations_stated":[{"p":0.86,"kind":[],"text":"Since the location of neutrino production is under investigation.","unit":"b05.013.01","location":"AGN Neutrino Flavor Ratio in IceCube"}],"methods_and_resources":{},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}