Movatterモバイル変換

[0]ホーム
URL:

Skip to content

Navigation Menu

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly

 Sign up

Neutrino oscillation probability calculator

License

NotificationsYou must be signed in to change notification settings

KM3NeT/Neurthino.jl

Repository files navigation

StableDevBuild StatusCodecovDOI

Neurthino.jl

Neurthino.jl is a package for calculating neutrino oscillation probabilities.The main focus of the package lies on atmospheric neutrino flux and the neutrinopropagation through earth.

Basic Usage

First of all the basic vacuum properties have to be defined by creating aOscillationParameters struct with fixed number of neutrino flavours of theconsidered model:

julia>using Neurthinojulia> osc=OscillationParameters(3);

The values of the mixing angles (setθ!), mass squared differences (setΔm²)and CP phases (setδ!) are initialised to 0 and have to be set individually:

julia> setθ!(osc, 1=>2, 0.59);julia> setθ!(osc, 1=>3, 0.15);julia> setθ!(osc, 2=>3, 0.84);julia> setδ!(osc, 1=>3, 3.86);

The mass squared differences are defined as andwithin the package the convention is kept.

julia> setΔm²!(osc, 2=>3, -2.523e-3);julia> setΔm²!(osc, 1=>2, -7.39e-5);

These oscillation parameters can now be used to calculate the oscillationprobabilities between the flavour states:

julia> p = Pνν(osc, 1, 10000)4-dimensional AxisArray{Float64,4,...} with axes:    :Energy, [1.0]    :Baseline, [10000.0]    :InitFlav, NeutrinoFlavour[Electron, Muon, Tau]    :FinalFlav, NeutrinoFlavour[Electron, Muon, Tau]And data, a 1×1×3×3 Array{Float64,4}:[:, :, 1, 1] = 0.40280077905806266[:, :, 2, 1] = 0.24823028034134093[:, :, 3, 1] = 0.348968940600596[:, :, 1, 2] = 0.10025499082597984[:, :, 2, 2] = 0.49250415138072934[:, :, 3, 2] = 0.4072408577932906[:, :, 1, 3] = 0.49694423011595723[:, :, 2, 3] = 0.2592655682779296[:, :, 3, 3] = 0.24379020160611306

The output is anAxisArray which provides intuitive indexing, e.g.for P(νμ→ντ) at the given energy and baseline:

julia> p[Energy=1, Baseline=1, InitFlav=Muon, FinalFlav=Tau]0.2592655682779296

The probabilities are calculated based on the transition matrix(the so-called PMNS-Matrix) between flavour and mass eigenstates,as well as the Hamiltonian in the mass eigenbasis. In order to calculating thesejust once, thePνν function can be utilised in the following way:

julia> U = PMNSMatrix(osc)3×3 Array{Complex{Float64},2}:   0.82161+0.0im         0.550114+0.0im        -0.112505+0.0983582im -0.301737+0.0608595im   0.601232+0.0407488im   0.736282+0.0im  0.476688+0.0545516im  -0.576975+0.0365253im   0.659968+0.0imjulia> H = Hamiltonian(osc)3-element Array{Complex{Float64},1}: -0.0008902666666666667 + 0.0im -0.0008163666666666667 + 0.0im  0.0017066333333333333 + 0.0imjulia> Pνν(U, H, 1, 10000)4-dimensional AxisArray{Float64,4,...} with axes:    :Energy, [1.0]    :Baseline, [10000.0]    :InitFlav, NeutrinoFlavour[Electron, Muon, Tau]    :FinalFlav, NeutrinoFlavour[Electron, Muon, Tau]And data, a 1×1×3×3 Array{Float64,4}:[:, :, 1, 1] = 0.40280077905806266[:, :, 2, 1] = 0.24823028034134093[:, :, 3, 1] = 0.348968940600596[:, :, 1, 2] = 0.10025499082597984[:, :, 2, 2] = 0.49250415138072934[:, :, 3, 2] = 0.4072408577932906[:, :, 1, 3] = 0.49694423011595723[:, :, 2, 3] = 0.2592655682779296[:, :, 3, 3] = 0.24379020160611306

Oscillations in Vacuum

Forhomogeneous matter with a fixed density, a modified PMNS-Matrixand Hamiltonian can be determined and passed intoPνν, just like foroscillations in vacuum. In order to determine the modified PMNS-Matrix andHamiltonian the neutrino energy and the matter density are required:

julia> U_mat, H_mat = MatterOscillationMatrices(U, H, 1, 13);julia> H_mat3-element Array{Complex{Float64},1}: -0.0008404901318507502 - 2.5459232191294903e-20im   9.078126149399635e-5 - 1.75151351027943e-20im  0.0017419062876598283 - 1.8741859435908039e-19imjulia> U_mat3×3 Array{Complex{Float64},2}:  0.0358018-0.000158113im  0.970863+0.0im       -0.178275+0.156083im -0.662778+0.00661213im    0.157174+0.116074im   0.722845+0.0im  0.74793+0.0im            0.0917808+0.104043im  0.649115-0.00104331im

The oscillation probabilities using thePνν function, as described above:

julia> Pνν(U_mat, H_mat, 1, 10000)4-dimensional AxisArray{Float64,4,...} with axes:    :Energy, [1]    :Baseline, [10000]    :InitFlav, NeutrinoFlavour[Electron, Muon, Tau]    :FinalFlav, NeutrinoFlavour[Electron, Muon, Tau]And data, a 1×1×3×3 Array{Float64,4}:[:, :, 1, 1] = 0.8340722296308641[:, :, 2, 1] = 0.08290502782120308[:, :, 3, 1] = 0.08302274254793415[:, :, 1, 2] = 0.10825570726818898[:, :, 2, 2] = 0.052976635020068[:, :, 3, 2] = 0.8387676577117485[:, :, 1, 3] = 0.05767206310094823[:, :, 2, 3] = 0.8641183371587345[:, :, 3, 3] = 0.07820959974032213

The second option is suitable for scenarios with morecomplex paths withsections of different densities. An example is shown in the next chapter, wherewe propagate neutrinos through the earth.

Neutrino Propagation through the Earth

TheNeurthino.jl package also includes features for the neutrino oscillation probabilitiesthrough the Earth, i.e. it contains functions for generating a neutrino path based on thePREM model. In the following example a neutrino oscillogram with a resolution of 200x200 binsis determined. The zenith angles for up going neutrinos (cos(θ)ϵ[-1,0]) andsubsequently the neutrino paths are generated first:

julia> zenith = acos.(range(-1,stop=0,length=200));julia> paths = Neurthino.prempath(zenith, 2.5, samples=100, discrete_densities=0:0.1:14);

The detector is assumed to be 2.5km under the earth's surface (a typical KM3NeTdetector block in the Mediterranean), which is a realistic scenario forWater-Cherenkov-Detectors in sea or ice. Each path consists of 100 sections ofequal lengths while the matter density is taken from the PREM model.If a vector of densities is passed asdiscrete_densities, the values areclipped to the closest value.

julia> energies = 10 .^ range(0, stop=2, length=200);julia> prob = Pνν(U, H, energies, paths);

The returned arrayprob is again of typeAxisArray with an axisPath for the path index (instead of theBaseline axis).P(νe→νe) is determined byprob[InitFlav=Electron, FinalFlav=Electron], which can be visualised by aheatmap:

and for P(νμ→νμ) orprob[InitFlav=Muon, FinalFlav=Muon]:

[8]ページ先頭
©2009-2025 Movatter.jp