File:Oscillations tau short.svg
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Summary
Vacuum oscillation probabilities for electron (black), muon (blue) and tau (red) neutrinos for the following parameter values:
- sin22θ13 = 0.10 (If it turns out to be much smaller or zero, the small wiggles shown here will be much smaller or non-existent, respectively.)
- sin22θ23 = 0.97 (It may turn out to be exactly one.)
- sin22θ12 = 0.861.
- δ = 0 (If it is actually large, these probabilities will be somewhat distorted and different for neutrinos and antineutrinos.)
- ΔmSunda: p=2= Accepted name by KEW: 7.59.
- ΔmSunda: p=2≈ ΔmSunda: p=2= Accepted name by KEW: 2.32.
- Normal mass hierarchy.
Mathematica source code
CS[z_] = Re[z]^2 + Im[z]^2; c12 := Cos[\[Theta]12]; c13 := Cos[\[Theta]13]; c23 := Cos[\[Theta]23]; s12 := Sin[\[Theta]12]; s13 := Sin[\[Theta]13]; s23 := Sin[\[Theta]23]; P[\[Alpha]_, \[Beta]_, LoverE_, \[Delta]_, \[Theta]12_, \[Theta]23_, \[Theta]13_, \ \[CapitalDelta]ms12_, \[CapitalDelta]ms23_, inverted_] = Block[{U, ms1, ms2, ms3}, ms1 = If[inverted, \[CapitalDelta]ms23 - \[CapitalDelta]ms12, 0]; (* Absolute mass does not matter, so put the lightest at zero *) ms2 = If[inverted, \[CapitalDelta]ms23, \[CapitalDelta]ms12]; ms3 = If[inverted, 0, \[CapitalDelta]ms12 + \[CapitalDelta]ms23]; U[a_, b_] := If[a == 1, If[b == 1, c13 c12, If[b == 2, c13 s12, If[b == 3, s13 E^(-I \[Delta])]]], If[a == 2, If[b == 1, -c23 s12 - s13 s23 c12 E^(I \[Delta]), If[b == 2, c23 c12 - s13 s23 s12 E^(I \[Delta]), If[b == 3, c13 s23]]], If[a == 3, If[b == 1, s23 s12 - s13 c23 c12 E^(I \[Delta]), If[b == 2, -s23 c12 - s13 c23 s12 E^(I \[Delta]), If[b == 3, c13 c23]]]]]]; CS[Sum[Conjugate[U[\[Alpha], i]] U[\[Beta], i] E^(-2 I ots If[i == 1, ms1, If[i == 2, ms2, If[i == 3, ms3, -1]]] LoverE), {i, 1, 3}]]]; (*********************************) ots = 1.2669327621645516; (* constant *) (* Neutrino parameters *) \ \[Theta]23 = ArcSin[Sqrt[0.97`]]/2; \[Theta]12 = ArcSin[Sqrt[0.861`]]/2; \[Theta]13 = ArcSin[Sqrt[0.1]]/2; \[Delta] = 0; \[CapitalDelta]ms23 = 0.00232`; \[CapitalDelta]ms12 = 0.0000759`; (* Initial neutrino and max L/E for plot *) initial = 3; maxLE = 4000; Plot[{ P[initial, 1, LoverE, \[Delta], \[Theta]12, \[Theta]23, \[Theta]13, \ \[CapitalDelta]ms12, \[CapitalDelta]ms23, False], P[initial, 2, LoverE, \[Delta], \[Theta]12, \[Theta]23, \[Theta]13, \ \[CapitalDelta]ms12, \[CapitalDelta]ms23, False], P[initial, 3, LoverE, \[Delta], \[Theta]12, \[Theta]23, \[Theta]13, \ \[CapitalDelta]ms12, \[CapitalDelta]ms23, False]}, {LoverE, 0, maxLE}, PlotRange -> {0, 1}, PlotPoints -> 500, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}}, Frame -> True, FrameLabel -> {{"Probability", ""}, {"L/E (km/GeV)", "Initial " <> If[initial == 1, "Electron", If[initial == 2, "Muon", "Tau"]] <> " Neutrino"}}, BaseStyle -> {FontSize -> 18}, ImageSize -> 500]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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current | 18:23, 26 August 2011 | ![]() | 450 × 303 (367 KB) | Strait | I made this myself. |
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