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Summary

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.)
  • Δm
    Sunda: p=2
    = Accepted name by KEW: 7.59.
  • Δm
    Sunda: p=2
    ≈ Δm
    Sunda: 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:
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.

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current18:23, 26 August 2011Thumbnail for version as of 18:23, 26 August 2011450 × 303 (367 KB)StraitI made this myself.

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