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Summary

Description
English: Vacuum oscillation probabilities for electron (black), muon (blue) and tau (red) neutrinos for the following parameter values:
  • sin213 = 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.)
  • sin223 = 0.97 (It may turn out to be exactly one.)
  • sin212 = 0.861.
  • δ = 0 (If it is actually large, these probabilities will be somewhat distorted and different for neutrinos and antineutrinos.)
  • Δm2
    12
    = 7.59×10−5 eV2.
  • Δm2
    32
    ≈ Δm2
    13
    = 2.32×10−3 eV2.
  • 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 = 2;
 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]
Date 26 August 2011 (original upload date)
Source Own work
Author Strait at English Wikipedia

Licensing

Strait at English Wikipedia, the copyright holder of this work, hereby publishes it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2011-08-26 17:13 363×250× (382354 bytes) Strait Fix bounding box.
2011-08-26 17:05 450×303× (382354 bytes) Strait New version of Muon_neutrino_oscillation_short.png that is an SVG and has thicker lines and bigger text relative to the image size.

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Date/TimeThumbnailDimensionsUserComment
current00:32, 20 July 2018Thumbnail for version as of 00:32, 20 July 2018363 × 250 (373 KB)OgreBot(BOT): Reverting to most recent version before archival
00:32, 20 July 2018Thumbnail for version as of 00:32, 20 July 2018450 × 303 (373 KB)OgreBot(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2011-08-26 17:05:27 by Strait
10:57, 18 July 2018Thumbnail for version as of 10:57, 18 July 2018363 × 250 (373 KB)ТибериумTransferred from en.wikipedia via #commonshelper

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