Atmospheric Neutrino Fluxes: The use of muon fluxes to Improve the - PowerPoint PPT Presentation

Atmospheric Neutrino Fluxes: The use of muon fluxes to Improve the Accuracy in Low Energies. May, 28, 2018 M. Honda @ PANE 2018 1. Over view of the calculation of atmospheric neutrino and the Muon Calibration of Atmospheric Neutrino. 2. Analytic formalism of the calculation of atmospheric neutrino flux and extension of the muon calibration to lower energies. a. ONLY with Meson production variation in Hadronic Interactions. b. With Nucleus/Nucleon propagation variations

Gaisser Formula for the illustration (by T.K.Gaisser at Takayama, 1998) Φ ν = Φ primary ⊗ R cut ⊗ Y ν Φ μ = Φ primary ⊗ R cut ⊗ Y μ Where : Cosmic Ray Flux Φ primary : Geomagnetic fjeld R cut = R cut ( R cr ,latt. , long. , θ , ϕ) : Hadronic Interaction Model, Y ν = Yield ν ( h , θ) Air Profjle, and meson-muon decay : Hadronic Interaction Model, Y μ = Yield μ ( h , θ) Air Profjle, and meson decay

Full 3D-Calculation Simulation Sphere (Rs = 10 x Re) Cosmic ray go out this sphere are Re = 6378km discarded. Cosmic rays go beyond are pass the rigidity cutofg test Injection Sphere (Re +100lm) Cosmic Rays are sampled and injected here Virtual Detector The neutrino flux is calculated from the number of neutrinos path through with virtual detector correction.

Direct Observation Balloon Borne (BESS) Satellite (ISS, AMS02)

Cosmic Ray Spectra Model Based on AMS02 Observation (2017 1ry model) Looking forward to hearing from CALET and ISS-CREAM

Atmosphere model (NRLMSISE-00) and seasonal variations INO site Kamioka South Pole Near North Pole (Physalmi)

IGRF10 Geomagnetic Horizontal Field Strength

We use Modefied DPMJET3 as the Hadronic interactio model Modefied DPMJET3 = parameter fitting of the out put of DMPMJET3 Quick, Easy to modify, but conseration rules are statistical. Note, we have tried other interaction models, and they give a similar results when they are modified in our method to reproduce the observed muon fluxes.

Muon Observations Balloon Altitude L3(+C) BESS Mt Norikura Tsukuba (KEK)

Muon data used here L3+C at Cern BESS-TeV at Tsukuba Mutron at Tanashi

Muon Calibration of Interaction Model Quick 3D Calculation for Muon flux. As the muon flux is a “local quantity” ( γ c t 〜 60km at10 GeV ), We can calculate it in a quick calculation method: 1. Inject cosmic rays just above the observation point, 2. Analyze all muons reach the surface of Earth.

Comparison of Quick 3D and Full 3D calculations + − μ μ Full 3D Quick 3D This method works above 0.2 GeV/c.

Responsible 1ry CR energy and Interaction Energy for Vertical Muon P=10 GeV/c P=1 GeV/c P=100 GeV/c P=1 TeV/c

Responsible 1ry CR energy and Interaction Energy for Horizontal Muon P=10 GeV/c P=1 GeV/c P=100 GeV/c P=1 TeV/c

Median Energy of the Responsible 1ry and Interaction Energy for Muons

Responsible 1ry CR energy and Interaction Energy for Vertical Neutrino P=10 GeV/c P=1 GeV/c P=100 GeV/c P=1 TeV/c

Responsible 1ry CR energy and Interaction Energy for Horizontal Neutrino P=10 GeV/c P=1 GeV/c P=100 GeV/c P=1 TeV/c

Median Energy of the Responsible 1ry and Interaction Energy for Neutrinos

Contribution of Kaon for atmospheric muons and neutrinos

Observation / Calculation ratio with 2004 peimey cosmic ray model and 2006 interaction model

Muon Calibration of inclusive DPMJET-III Data are larger by ~0.05 Data are larger by ~15% ~15% scatter ? Data are smaller by ~0.05 ==> DPMJET-III Should be Modifjed

Modification of DPMJET3 in 2006

Cosmic Ray Spectra Model Based on AMS02 Observation (2017 1ry model) Looking forward to hearing from CALET and ISS-CREAM

Observation / Calculation ratio with 2017 primary cosmic ray moddel and 2006 interaction model

Observation / Calculation ratio with 2017 primary cosmic ray model and 2017 interaction model A (Studied without MUTRON)

Observation / Calculation ratio with 2017 primary cosmic ray model and 2017 interaction model B (Studied with MUTRON)

Based On AMS02 Obervation (Preliminary)

2. Analytic expression of the Calculation of the Atmospheric Lepton Flux obs , x obs )= ∑ N CR ∑ N int ∑ M brn ∑ M dcy ∑ L brn ∫∫ ⋅ ⋅ ∫ Φ L obs ( p L brn , p L brn , x obs , p L obs , x brn → L obs ) P L-prp ( L dcy , p M brn , p L dcy → L brn ) × P M-dcy ( M brn , p M brn , x dcy , p M dcy , x int → M dcy ) × P M-prp ( M int , p N brn , p M int → M brn ) × P H-int ( N in , x int , p N int , x in → N int ) × P N-prp ( N CR , p CR in , x in ) × Φ CR ( N CR , p CR brn dp M dcy dx dcy dp M brn dp N int dx int dp CR in dx in dp L 0 , x 0 , p 1 , p 0 → L 1 , x 1 ) P L-prp ( L 0 0 1 1 : The probablility of a -lepton with momentum at propagates to as -lepton with momentum . 0 1 L p L p x x 0 , x 0 , p 1 , x 1 , p 0 → M 1 ) P M-prp ( M 1 0 0 0 1 1 : The probablility of a -meson with momentum at propagates to as -meson with momentum . p p M x M x 0, x 0 , p 1 ,x 1 , p 0 → N 1 ) P N-prp ( N 0 1 1 1 : The probablility of a -nucleus with momentum at propagates to as -nucleus with momentum . 0 0 p N p x N x p M : The probablility of a N -nucleus with momentum produces M -mesion with momentum . in a p N P N-int ( N , p N → M , p M ) hadronic interaction with air. P M-dcy ( M , p M → L , p L ) : The probablility of a M -meson with momentum produces L -lepton with momentum in its decay. p L p M

2. The Variation of Lepton Fluxes caused by the “Variation” of the Nucleus Hadronic Interactions ~ obs , x obs )= ∑ N CR ∑ N int ∑ M brn ∑ M dcy ∑ L brn ∫∫ ⋅ ⋅ ∫ Φ L obs ( p L brn , p L brn , x obs , p L obs , x P L-prp ( L brn → L obs ) dcy , p M brn , p L × P M-dcy ( M dcy → L brn ) brn , p M brn , x dcy , p M dcy , x × P M-prp ( M int → M dcy ) int , p N brn , p M int , p N int , M brn , p M ⋅ ( 1 +δ H-int ( N brn ) ) int → M brn ) × P H-int ( N in , x int , p N int , x ⋅ ( 1 +δ N-prp ( N CR , p CR , x in , N int , p N int , x int ) ) × P N-prp ( N CR , p CR in → N int ) in , x in ) × Φ CR ( N CR , p CR brn dp M dcy dx brn dp N int dx int dp CR in dx dcy dp M in dp L 0 , x 0 , p 1 , p 0 → L 1 , x 1 ) P L-prp ( L 0 0 1 1 : The probablility of a -lepton with momentum at propagates to as -lepton with momentum . 0 1 L p L p x x 0 , x 0 , p 1 , x 1 , p 0 → M 1 ) P M-prp ( M 1 0 0 0 1 1 : The probablility of a -meson with momentum at propagates to as -meson with momentum . p p M x M x 0, x 0 , p 1 ,x 1 , p 0 → N 1 ) P N-prp ( N 0 1 1 1 : The probablility of a -nucleus with momentum at propagates to as -nucleus with momentum . 0 0 p N p x N x p M : The probablility of a N -nucleus with momentum produces M -mesion with momentum . in a p N P N-int ( N , p N → M , p M ) hadronic interaction with air. P M-dcy ( M , p M → L , p L ) : The probablility of a M -meson with momentum produces L -lepton with momentum in its decay. p L p M

Simplified Expression with the result of Monte Carlo Simulation obs , x int , p N int , M brn , p M brn , L obs , p L brn dp N obs )= ∑ N int ∑ M brn ∫∫ DD ( N Φ L obs ( p L obs ) dp M int obs , x Where int , M , p M brn , L obs , p L obs )≡ ∑ N CR ∑ M dcy ∑ L brn ∫∫ ⋅ ∫ DD ( N , p N ⋅ obs , x brn , p L brn , x obs , p L obs , x P L-prp ( L brn → L obs ) dcy , p M brn , p L × P M-dcy ( M dcy → L brn ) brn , p M brn , x dcy , p M dcy , x × P M-prp ( M int → M dcy ) int , p N brn , p M × P H-int ( N int → M brn ) in , x int , p N int , x × P N-prp ( N CR , p CR in → N int ) in , x × Φ CR ( N CR , p CR in ) brn dp M dcy dx dcy dx int dp CR in dx in dp L Note, the DD function is calculated in Monte Carlo Simulation is the usual calculation.

int , p N int , M brn , p M brn , L obs , p L in the Simulation for vertical Neutrino DD ( N obs ) obs , x at Kamioka at 1 GeV

in the Simulation for vertical Muon int , p N int , M brn , p M brn , L obs , p L obs ) DD ( N obs , x at Kamioka at 1 GeV/c and 10 GeV/c

int , p N int , M brn , p M brn , L obs , p L DD ( N obs ) obs , x Site dependence for Muon at 0.1 GeV. ~0 m A.S.L ~3000 m A.S.L

int , p N int , M brn , p M brn , L obs , p L DD ( N obs ) obs , x Site dependence for Muon at 0.1 GeV. ~5000 m A.S.L ~30k m A.S.L (Balloon)