File:Oscillations electron long.svg

 

W3C-validity not checked.

Summary[edit]

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.)
• 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[edit]

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 = 1;
maxLE = 38000;
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[edit]

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