暗黒物質模型の解析で ニューラルネットワークを使った話

Transcript

1. ҉ࠇ෺࣭໛ܕͷղੳͰ χϡʔϥϧωοτϫʔΫΛ࢖ͬͨ࿩ ༄ܓ༞
   ౦ژେֶ
   ૉཻࢠཧ࿦ݚڀࣨ
   % Based on Bae, Jinno, Kamada, KY [arXiv: 1906.09141] Feb. 10, 2020 @Machine Learning and Physics Bridge vol.1
2. ࣗݾ঺հ • ༄ܓ༞ (@yana_phys) • ૉཻࢠݱ৅࿦ͷݚڀΛ͍ͯ͠·͢ - ඪ४໛ܕΛ௒͑Δ෺ཧ໛ܕͷ୳ࡧ - ࣮ࡍͷ࣮ݧ΍؍ଌʹؔΘΔྔΛܭࢉ͢Δ • Particle astrophysics తͳݚڀ͕ଟ͍Ͱ͢ - தੑࢠ੕Λ࢖ͬͨ৽෺ཧ୳ࡧ(D࿦ͷςʔϚ) - ҉ࠇ෺࣭ͱӉ஦ͷߏ଄ܗ੒
3. ࣗݾ঺հ • ༄ܓ༞ (@yana_phys) • ૉཻࢠݱ৅࿦ͷݚڀΛ͍ͯ͠·͢ - ඪ४໛ܕΛ௒͑Δ෺ཧ໛ܕͷ୳ࡧ - ࣮ࡍͷ࣮ݧ΍؍ଌʹؔΘΔྔΛܭࢉ͢Δ • Particle astrophysics తͳݚڀ͕ଟ͍Ͱ͢ - தੑࢠ੕Λ࢖ͬͨ৽෺ཧ୳ࡧ(D࿦ͷςʔϚ) - ҉ࠇ෺࣭ͱӉ஦ͷߏ଄ܗ੒ ͜͜ͰػցֶशΛ࢖ͬͨ࿩Λ͠·͢
4. • ͍ܰ҉ࠇ෺࣭ (m ~ keV): Ӊ஦ͷߏ଄ܗ੒͔ΒϞσϧʹڧ੍͍ݶ͕ͭ͘ - ܰ͗͢Δͱີ౓ͷภΓ͕ͳΒ͞Εͯ͠·͍ɺ؍ଌ͞Εͨߏ଄͕࡞Εͳ͍ (hot/warm dark matter ʹͳΔ) ɹ → ࣭ྔʹԼݶ • ͦͷΑ͏ͳϞσϧͷղੳ͸ඇৗʹେม • ޙͷਓʑ(ओʹকདྷͷࣗ෼ୡ)ͷղੳʹศརͳΑ͏ʹɺ͜͜ͷؔ܎ΛNNͰϑΟοτͯ͠༩͑Δ [Our work] Overview Particle model ℒSM + ℒDM ඇৗʹେมͳ (਺஋)ܭࢉ/γϛϡϨʔγϣϯ ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) NN ػցֶशͷԠ༻ͱͯ͠͸ too trivial…
5. • ༷ʑͳ؍ଌతূڌ͔Βɺ҉ࠇ෺࣭ͷଘࡏ͕ࣔ͞Ε͍ͯΔ • ۜՏஂͷ࣭ྔͱޫ౓ • ۜՏͷճసۂઢ • ॏྗϨϯζ • CMB • DMʹٻΊΒΕΔੑ࣭ • ిؾతʹதੑ • ҆ఆʢण໋ >> Ӊ஦೥ྸʣ • ؍ଌ͞ΕͨӉ஦ͷେن໛ߏ଄Λ࠶ݱͰ͖Δ ҉ࠇ෺࣭ 1939LicOB..19...41B ΞϯυϩϝμۜՏ [Babcock (1939)] Fig 2.1.1: The velocities of 21 Sc galaxies. The flatness beyond 5 kpc suggests the non-luminous matter in the galaxy. Figure is taken from [35]. [Rubin, Ford., Thonnard (1980)] [Zwicky (1937)]
6. FIMP DM TeV GeV MeV keV ~10-22 eV ʙ ʙ ʙ ʙ meV WIMP (weakly interacting massive particle) • e.g., SUSY model ͷχϡʔτϥϦʔϊ FIMP (feebly interacting massive particle) • εςϥΠϧɾχϡʔτϦϊ • Axino • e.t.c. QCD Axion Fuzzy DM Mass
7. • ඪ४໛ܕͷऑ͍૬ޓ࡞༻Λ͢Δཻࢠ • ཧ࿦తʹ͸ਓؾ͕͋Γਫ਼ྗతʹ୳ࡧ͞Ε͖ͯ ͕ͨະͩݟ͔ͭΒͣ FIMP DM TeV GeV MeV keV ~10-22 eV ʙ ʙ ʙ ʙ meV QCD Axion Fuzzy DM Mass WIMP (weakly interacting massive particle) • e.g., SUSY model ͷχϡʔτϥϦʔϊ FIMP (feebly interacting massive particle) • εςϥΠϧɾχϡʔτϦϊ • Axino • e.t.c.
8. FIMP DM TeV GeV MeV keV ~10-22 eV ʙ ʙ ʙ ʙ meV QCD Axion Fuzzy DM • ඪ४໛ܕཻࢠͱͷ݁߹͕ඇৗʹখ͍͞ (feeble) • WIMP ͷਰୀʹΑΓ࠷ۙΑ͘ݚڀ͞Ε͍ͯΔ • Hot/warm dark matter Mass WIMP (weakly interacting massive particle) • e.g., SUSY model ͷχϡʔτϥϦʔϊ FIMP (feebly interacting massive particle) • εςϥΠϧɾχϡʔτϦϊ • Axino • e.t.c.
9. FIMP DM TeV GeV MeV keV ~10-22 eV ʙ ʙ ʙ ʙ meV QCD Axion Fuzzy DM 5 6 7 Flux (cnts s-1 keV-1 ) -0.2 -0.1 0 0.1 0.2 0.3 Residuals 3 3.2 3.4 3.6 3.8 4 Energy (keV) 300 305 310 315 Eff. Area (cm2 ) XMM - MOS Perseus (with core) 317 ks 10 12 14 16 Flux (cnts s-1 keV-1 ) -0.8 -0.4 0 0.4 0.8 Residuals 3 3.2 690 700 710 720 Eff. Area (cm2 ) Xઢ؍ଌ͔Βͷώϯτʁ 3.5 keV ෇ۙʹexcess → decay of 7 keV DM?? • keV ෇ۙͰͷDMϞσϧ΁ͷ੍ݶΛ͖ͪΜͱௐ΂Δඞཁ͕͋Δ • ͜ͷྖҬ͸Ӊ஦ͷߏ଄ܗ੒ͱໃ६͠ͳ͍͔͕ॏཁ Mass 7 keV WIMP (weakly interacting massive particle) • e.g., SUSY model ͷχϡʔτϥϦʔϊ FIMP (feebly interacting massive particle) • εςϥΠϧɾχϡʔτϦϊ • Axino • e.t.c.
10. Ӊ஦ͷߏ଄ܗ੒ ॳظӉ஦ͷඍখͳີ౓༳Β͕͗ॏྗʹΑͬͯ੒௕ͯ͠ݱࡏͷߏ଄Λ࡞Δ DM production [NASA]
11. Ӊ஦ͷߏ଄ܗ੒ͷܭࢉ Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation)
12. Ӊ஦ͷߏ଄ܗ੒ͷܭࢉ Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) • ҉ࠇ෺࣭ͷ࢒ଘྔͷܭࢉ • ҉ࠇ෺࣭ͷԹ౓ͷܭࢉ • ҉ࠇ෺࣭ͷ଎౓෼෍ͷܭࢉ ρDM TDM f(v) DM͕Cold͔Hot͔ΛܾΊΔ ͍ܰDMͷ৔߹ʹಛʹॏཁ }
13. Ӊ஦ͷߏ଄ܗ੒ͷܭࢉ Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) • ඇҰ༷ɾඇ౳ํੑͷܭࢉ • Ұ༷౳ํӉ஦͔ΒͷζϨͷҰ࣍·ͰͰΞϯ γϡλΠϯํఔࣜΛղ͘ ρ = ¯ ρ + δρ
14. Ӊ஦ͷߏ଄ܗ੒ͷܭࢉ Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) • • ॏྗ૬ޓ࡞༻͢ΔNݸͷ࣭఺ͷӡಈΛ࣮ࡍʹ ௥͏ • ࠷ۙ͸όϦΦϯΛೖΕͨhydro simulation ΋ δρ ≳ ¯ ρ
15. Ӊ஦ͷߏ଄ܗ੒ͷܭࢉ Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) 3124 A. Schneider lines) are all plotted in Fig. 4. For the case of CDM (black), the sharp-k mass function closely follows both the simulation measure- ments and the Sheth–Tormen model. For the case of WDM (red, cyan, purple, pink), MDM (green, magenta, blue), and WIMP DM (brown, orange), the sharp-k mass function gives a reasonably good match to simulations, while the Sheth–Tormen approach fails to match the flattening or the turnaround visible in simulations. In Schneider et al. (2013), the sharp-k model has been reported to underestimate the halo abundance when the suppression scale lies in the exponential tail of the halo mass function (i.e. for ν 1), which generally happens at very high redshift. It turns out, however, that this discrepancy between the sharp-k model and the data is greatly reduced for haloes defined by a spherical overdensity instead of a friends-of-friends linking criterion (see Watson et al. 2013, for a comparison of the two). We therefore do not use the correction model proposed by Schneider et al. (2013). 4.3 Conditional mass function Another important application of the EPS model is the conditional Downloaded from https://academic.oup • ఱͷ઒ۜՏ಺ͷ؍ଌ͞ΕͨαςϥΠτۜՏͷ਺: • ͍ܰ҉ࠇ෺࣭͸free-streaming ʹΑΓখن໛ͳߏ଄ΛݮΒͯ͠͠·͏ ɹˠ Λ༧ݴ͢ΔΑ͏ͳཧ࿦͸غ٫ Nsat ≃ 63 Nsat ≪ 63 [Murgia et al. (2017)] [Schneider (2015)] ఱͷ઒ۜՏ಺ʹ͍ΔΑΓখ͍ۜ͞Տ
16. ͜ͷҰ࿈ͷܭࢉ͸େม యܕతͳݱ৅࿦ݚڀɿ؍ଌ΍γϛϡϨʔγϣϯ͕Ξοϓσʔτ͞ΕͨΒ ͷύϥϝʔλۭؒશମΛௐ΂௚͢ →ຖճ͜ͷҰ࿈ͷܭࢉΛ΍Γ௚͢ͷ͸ਏ͍… ℒDM Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) • DMͷ଎౓෼෍ˠϘϧπϚϯํఔࣜͷੵ෼ J 2-body s-ch t-ch 3-body Fermi-Dirac
        
    
    
    
    
    
    
    
    
    
    ()
    
    
    () fDM (tf , p) = ∫ tf ti dt 1 EDM C t, a (tf) a(t) p gDM EDM C (t, pDM) = 1 2EDM ∫ ∏ i≠DM d3pi (2π)32Ei (2π)4δ4 (Pi − Pf) × ∑ spin ℳ 2 f1 f2 ⋯(1 ∓ f3) (1 ∓ f4)⋯ 4. Einstein Equations and Energy-Momentum Conservation For a homogeneous Friedmann-Robertson-Walker universe with energy density ¯ ρ(τ) and pressure ¯ P(τ), the Einstein equations give the following evolution equations for the expansion factor a(τ): ˙ a a 2 = 8π 3 Ga2 ¯ ρ − κ , (19) d dτ ˙ a a = − 4π 3 Ga2(¯ ρ + 3 ¯ P) , (20) where the dots denote derivatives with respect to τ, and κ is positive, zero, or negative for a closed, flat, or open universe, respectively. We consider only models with total Ω = 1 in this paper, so we set κ = 0. A cosmological constant is allowed through its inclusion in ¯ ρ and ¯ P: ¯ ρΛ = Λ/8πG = − ¯ PΛ. This is the only place that Λ enters in the entire set of calculations. It follows from equation (19) with κ = 0 that the expansion factor scales as a ∝ τ in the radiation-dominated era, a ∝ τ2 in the matter-dominated era, and a ∝ (τ∞ −τ)−1 in a cosmological constant-dominated era (in the latter case, τ∞ is the radius of the de Sitter event horizon). We find it most convenient to solve the linearized Einstein equations in the two gauges in the Fourier space k. In the synchronous gauge, the scalar perturbations are characterized by h(k, τ) and η(k, τ) in equation (4). In terms of h and η, the time-time, longitudinal time-space, trace space-space, and longitudinal traceless space-space parts of the Einstein equations give the following four equations to linear order in k-space: Synchronous gauge — k2η − 1 2 ˙ a a ˙ h = 4πGa2δT0 0(Syn) , (21a) k2 ˙ η = 4πGa2(¯ ρ + ¯ P)θ(Syn) , (21b) ¨ h + 2 ˙ a a ˙ h − 2k2η = −8πGa2δTi i(Syn) , (21c) ¨ h + 6¨ η + 2 ˙ a a ˙ h + 6 ˙ η − 2k2η = −24πGa2(¯ ρ + ¯ P)σ(Syn) . (21d) The label “Syn” is used to distinguish the components of the energy-momentum tensor in the synchronous gauge from those in the conformal Newtonian gauge. The variables θ and σ are defined as (¯ ρ + ¯ P)θ ≡ ikjδT0 j , (¯ ρ + ¯ P)σ ≡ −(ˆ ki ˆ kj − 1 3 δij)Σi j , (22) and Σi j ≡ Ti j − δi jTk k/3 denotes the traceless component of Ti j. Kodama & Sasaki (1984) define the anisotropic stress perturbation Π, related to our σ by σ = 2Π ¯ P/3(¯ ρ + ¯ P). When the different • ΞΠϯγϡλΠϯํఔࣜΛઢܗۙࣅͰղ͘ → Linear matter power spectrum CDM 2.0 keV 5.3 keV
    
    
    
    
    
    
    
    
     
    
    
    
    -
     
    -
    
    
    - 
    -
    
    
    () • N-body simulation ͨ͘͞Μͷ࣌ؒͱܭࢉࢿݯ͕ඞཁ
17. NNͰϑΟοςΟϯάؔ਺Λ༩͑Α͏ Nsat = f(P(k)) P(k) = f(ℒDM ) 3124 A. Schneider lines) are all plotted in Fig. 4. For the case of CDM (black), the sharp-k mass function closely follows both the simulation measure- ments and the Sheth–Tormen model. For the case of WDM (red, cyan, purple, pink), MDM (green, magenta, blue), and WIMP DM (brown, orange), the sharp-k mass function gives a reasonably good match to simulations, while the Sheth–Tormen approach fails to match the flattening or the turnaround visible in simulations. In Schneider et al. (2013), the sharp-k model has been reported to underestimate the halo abundance when the suppression scale lies in the exponential tail of the halo mass function (i.e. for ν 1), which generally happens at very high redshift. It turns out, however, that this discrepancy between the sharp-k model and the data is greatly reduced for haloes defined by a spherical overdensity instead of a friends-of-friends linking criterion (see Watson et al. 2013, for a comparison of the two). We therefore do not use the correction model proposed by Schneider et al. (2013). 4.3 Conditional mass function Another important application of the EPS model is the conditional mass function, which gives the abundance of haloes per mass and look-back redshift z1 , eventually ending up in a single host halo at redshift z0 . As the conditional mass function provides a connection between haloes at different redshifts, it acts as the starting point of more evolved quantities such as the halo collapse redshift, the number of satellites, and halo merger trees. The conditional mass function is given by dN(M|M0 ) d ln M = − M0 M Sf (δc, S|δc,0, S0 ) d ln S d ln M (13) (Lacey & Cole 1993). For the sharp-k model this can be simplified to dNSK (M|M0 ) d ln M = 1 6π2 M0 M f (δc, S|δc,0, S0 ) P(1/R) R3 , (14) where the filter scale R and the mass M are related by equation (12). The conditional first-crossing distribution again depends on the assumed model for non-linear collapse. The case of spherical col- lapse is given by f (δc, S|δc,0, S0 ) = δc − δc,0 √ 2π(S − S0 ) exp − (δc − δc,0 )2 2(S − S0 ) , (15) Figure 5. Conditional mass functions for a M0 = 1013 h−1 M host and a look-back redshift of z = 1.1. Coloured symbols refer to simulation outputs (with circumjacent shaded regions representing the uncertainty due to arte- fact subtraction), while the solid and dotted lines represent the sharp-k model and the standard Press–Schechter model, respectively. The colour-coding is the same as in the previous plots. 4.4 Estimating the number of dwarf satellites Each DM scenario has to produce a sufficient amount of substruc- tures to account for the observed MW satellites. While some (or most) of the substructures could be dark due to inefficient star for- mation, fewer substructures than observed means the failure of the DM scenario. In the case of WDM, comparing numbers of simulated substructures with observed satellites has led to tight constraints on the thermal particle mass ruling out masses below 2 keV (Polisen- sky & Ricotti 2011; Kennedy et al. 2014). The EPS approach can be used to estimate the average number of dwarf galaxies orbiting a galaxy like the MW. This means it is possible to check whether a certain DM scenario is likely to be in agreement with observations without running expensive numerical zoom-simulations of an MW halo. In principle, finding the number CDM 2.0 keV 5.3 keV
    
    
    
    
    
    
    
    
     
    
    
    
    -
     
    -
    
    
    - 
    -
    
    
    [/]
    () Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) P(k): linear matter power spectrum ֤εέʔϧͰͷߏ଄ͷଟ͞Λද͢ྔ
18. • Pros: • ෳ਺ͷม਺ؒͷඇઢܗͳؔ܎Λ؆୯ʹදݱͰ͖ΔʢϑΟοςϯάެࣜΛ explicit ʹߟ͑Δඞཁ͕ͳ͍ʣ • ܭࢉͷ(్த)݁ՌΛNNͰڞ༗͢Δ͜ͱͰɺকདྷͷ؍ଌ౳ͷΞοϓσʔτʹָʹରԠͰ͖Δ • ΠϯϓοτɾΞ΢τϓοτύϥϝʔλͷ਺Λ૿΍ͯ͠΋ɺڞ༗͢΂͖σʔλ͸ͦΜͳʹ૿͑ͳ͍ • Cons: • NNͷ܇࿅ͷͨΊʹɺ্ͷҰ࿈ͷܭࢉΛҰճ͸΍Δඞཁ͕͋Δʢैདྷͷख๏͕ෆཁʹͳΔΘ͚Ͱ͸ͳ͍ʣ NNͰϑΟοςΟϯάؔ਺Λ༩͑Α͏ Nsat = f(P(k)) P(k) = f(ℒDM ) 3124 A. Schneider lines) are all plotted in Fig. 4. For the case of CDM (black), the sharp-k mass function closely follows both the simulation measure- ments and the Sheth–Tormen model. For the case of WDM (red, cyan, purple, pink), MDM (green, magenta, blue), and WIMP DM (brown, orange), the sharp-k mass function gives a reasonably good match to simulations, while the Sheth–Tormen approach fails to match the flattening or the turnaround visible in simulations. In Schneider et al. (2013), the sharp-k model has been reported to underestimate the halo abundance when the suppression scale lies in the exponential tail of the halo mass function (i.e. for ν 1), which generally happens at very high redshift. It turns out, however, that this discrepancy between the sharp-k model and the data is greatly reduced for haloes defined by a spherical overdensity instead of a friends-of-friends linking criterion (see Watson et al. 2013, for a comparison of the two). We therefore do not use the correction model proposed by Schneider et al. (2013). 4.3 Conditional mass function Another important application of the EPS model is the conditional mass function, which gives the abundance of haloes per mass and look-back redshift z1 , eventually ending up in a single host halo at redshift z0 . As the conditional mass function provides a connection between haloes at different redshifts, it acts as the starting point of more evolved quantities such as the halo collapse redshift, the number of satellites, and halo merger trees. The conditional mass function is given by dN(M|M0 ) d ln M = − M0 M Sf (δc, S|δc,0, S0 ) d ln S d ln M (13) (Lacey & Cole 1993). For the sharp-k model this can be simplified to dNSK (M|M0 ) d ln M = 1 6π2 M0 M f (δc, S|δc,0, S0 ) P(1/R) R3 , (14) where the filter scale R and the mass M are related by equation (12). The conditional first-crossing distribution again depends on the assumed model for non-linear collapse. The case of spherical col- lapse is given by f (δc, S|δc,0, S0 ) = δc − δc,0 √ 2π(S − S0 ) exp − (δc − δc,0 )2 2(S − S0 ) , (15) Figure 5. Conditional mass functions for a M0 = 1013 h−1 M host and a look-back redshift of z = 1.1. Coloured symbols refer to simulation outputs (with circumjacent shaded regions representing the uncertainty due to arte- fact subtraction), while the solid and dotted lines represent the sharp-k model and the standard Press–Schechter model, respectively. The colour-coding is the same as in the previous plots. 4.4 Estimating the number of dwarf satellites Each DM scenario has to produce a sufficient amount of substruc- tures to account for the observed MW satellites. While some (or most) of the substructures could be dark due to inefficient star for- mation, fewer substructures than observed means the failure of the DM scenario. In the case of WDM, comparing numbers of simulated substructures with observed satellites has led to tight constraints on the thermal particle mass ruling out masses below 2 keV (Polisen- sky & Ricotti 2011; Kennedy et al. 2014). The EPS approach can be used to estimate the average number of dwarf galaxies orbiting a galaxy like the MW. This means it is possible to check whether a certain DM scenario is likely to be in agreement with observations without running expensive numerical zoom-simulations of an MW halo. In principle, finding the number CDM 2.0 keV 5.3 keV
    
    
    
    
    
    
    
    
     
    
    
    
    -
     
    -
    
    
    - 
    -
    
    
    [/]
    () Particle model ℒSM + ℒDM Linear perturbation ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) Non-linear growth (e.g., N-body simulation) P(k): linear matter power spectrum ֤εέʔϧͰͷߏ଄ͷଟ͞Λද͢ྔ
19. ࣮ࡍʹ΍ͬͨ͜ͱ ҰൠతͳFIMP DM Ϟσϧͱͯ͠ɺDM͕೤ཋཻࢠͷ่յͱࢄཚͰ࡞ΒΕΔ৔߹Λߟ͑ͨ JCAP11(2019)029 2 Setup 2.1 Benchmark FIMP model We consider Majorana fermion DM , which feebly interacts with a Dirac fermion and a complex scalar . also couples to a Dirac fermion f. We discuss the correspondence to prominent FIMP models in section 3.3. The Lagrangian relevant to freeze-in production of is LF.I. = y ¯ yf ¯ ff + h.c. , (2.1) where y and yf are Yukawa couplings. We assume that and f are in equilibrium with the thermal plasma. In the following, we consider the mass spectrum of m , mf ⌧ m < m .4 Due to the feeble interaction with the other particles, y ⌧ 1, is not in equilibrium with the thermal plasma. Meanwhile is produced by freeze-in processes: • 2-body decay: ! , ¯ ! ⇤ • t-channel scattering: f ! f, ¯ f ! ¯ f, ¯ f ! f, ¯ ¯ f ! ¯ f • s-channel scattering: f ¯ f ! , f ¯ f ! ¯ The scattering processes are mediated by . The freeze-in production is most e cient when the heaviest particle in the process, i.e., , becomes non-relativistic. After that the pro- duction is suppressed by the Boltzmann factor. Thus we define the decoupling temperature Tdec = m . Model Parameters (mχ , mΨ /mϕ , yf , Δ) T2(k) = P(k) PCDM (k) ∼ (1 + (αk)β)2γ Nsat DM Transfer function ΛύϥϝτϥΠζ αςϥΠτۜՏͷ਺ (α, β, γ) ରԠ͢Δ۩ମతͳϞσϧͷྫ • εςϥΠϧɾχϡʔτϦϊ • Axino in DFSZ SUSY model χ = χ = Figure 4: Schematic diagram of the neural network. Partly taken from Ref. [196]. Figure 4: Schematic diagram of the neural network. Partly taken from Ref. [196]. ਖ਼نͷखଓ͖Ͱ܇࿅σʔλΛ࡞Δ → Hidden layer ೋͭͷ (shallow) neural network Λ܇࿅
20. ൺֱ 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 m2/m1 Y scat /Y total mDM=5keV 4keV 3keV mDM[keV] 2 3 4 5 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 m2/m1 Y scat /Y total mDM=5keV 4keV 3keV mDM[keV] 2 3 4 5 mDM contour ͷࠨ্Ͱ͸ → excluded Nsat < Nobs sat = 63 Original NN
21. 7 keV FIMP DM ͸ੜ͖͍ͯΔ͔ʁ • Lyman-alpha forest ͷσʔλΛ࢖͏ͱ͞Βʹڧ੍͍ݶ͕ͭ͘ • 7 keV FIMP DM ͕؍ଌͱໃ६͠ͳ͍ͷ͸ಛผͳ৔߹ͷΈʢ਌ཻࢠୡͷ࣭ྔ͕ॖୀɾΤϯτϩϐʔੜ੒϶͕͋Δ৔߹ʣ 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 m2/m1 Y scat /Y total mDM=7keV 6keV 5keV 4keV 3keV mDM[keV] 3 4 5 6 7 0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20 m2/m1 mDM[keV]
    =0.1
    =1
    =10
    0.1 0.2 0.5 1 2 5 10
22. • ͍ܰ҉ࠇ෺࣭ (m ~ keV): Ӊ஦ͷߏ଄ܗ੒͔ΒϞσϧʹڧ੍͍ݶ͕ͭ͘ - ܰ͗͢Δͱີ౓ͷภΓ͕ͳΒ͞Εͯ͠·͍ɺ؍ଌ͞Εͨߏ଄͕࡞Εͳ͍ (hot/warm dark matter ʹͳΔ) ɹ → ࣭ྔʹԼݶ • ͦͷΑ͏ͳϞσϧͷղੳ͸ඇৗʹେม • ޙͷਓʑ(ओʹকདྷͷࣗ෼ୡ)ͷղੳʹศརͳΑ͏ʹɺ͜͜ͷؔ܎ΛNNͰϑΟοτͯ͠༩͑Δ [Our work] ·ͱΊ Particle model ℒSM + ℒDM ඇৗʹେมͳ (਺஋)ܭࢉ/γϛϡϨʔγϣϯ ؍ଌྔ (ྫ:αςϥΠτۜՏͷ਺) NN