private BottomiumVector CalculateppPopulationsBeforeMuonDecay()
{
BottomiumVector ppDimuonDecays = GetNormalizedProtonProtonDimuonDecays();
BottomiumCascadeMatrix inverseDMatrix = CalculateInverseDimuonDecayMatrix();
return(inverseDMatrix * ppDimuonDecays);
}
public BottomiumVector CalculateInitialQQPopulations()
{
BottomiumCascadeMatrix inverseCMatrix = CalculateInverseCumulativeMatrix();
BottomiumVector popsBeforeMuonDecay = CalculateppPopulationsBeforeMuonDecay();
return(inverseCMatrix * popsBeforeMuonDecay);
}
/********************************************************************************************
* Public static members, functions and properties
********************************************************************************************/
public static BottomiumCascadeMatrix CreateUnitMatrix()
{
BottomiumCascadeMatrix matrix = new BottomiumCascadeMatrix();
foreach (BottomiumState s in Enum.GetValues(typeof(BottomiumState)))
{
matrix[s, s] = 1;
}
return(matrix);
}
private BottomiumVector CalculateReducedInitialQQPopulations(
BottomiumVector qgpSuppressionFactors
)
{
BottomiumVector initialPops = CalculateInitialQQPopulations();
BottomiumCascadeMatrix qgpSuppressionMatrix
= BottomiumCascadeMatrix.CreateDiagonalMatrix(qgpSuppressionFactors);
return(qgpSuppressionMatrix * initialPops);
}
public static BottomiumCascadeMatrix CreateDiagonalMatrix(
BottomiumVector diagonalElements
)
{
BottomiumCascadeMatrix matrix = new BottomiumCascadeMatrix();
foreach (BottomiumState s in Enum.GetValues(typeof(BottomiumState)))
{
matrix[s, s] = diagonalElements[s];
}
return(matrix);
}
public BottomiumVector CalculateDimuonDecays(
BottomiumVector qgpSuppressionFactors
)
{
BottomiumCascadeMatrix cMatrix = CalculateCumulativeMatrix();
BottomiumVector reducedPops = CalculateReducedInitialQQPopulations(qgpSuppressionFactors);
BottomiumVector tmpPop = cMatrix * reducedPops;
BottomiumCascadeMatrix dMatrix = CalculateDimuonDecayMatrix();
return(dMatrix * tmpPop);
}
public static BottomiumCascadeMatrix CalculateDimuonDecayMatrix()
{
BottomiumCascadeMatrix dMatrix = new BottomiumCascadeMatrix();
dMatrix[BottomiumState.Y1S, BottomiumState.Y1S] = Constants.B1Smu;
dMatrix[BottomiumState.x1P, BottomiumState.x1P] = Constants.B1Smu * Constants.B1P1S;
dMatrix[BottomiumState.Y2S, BottomiumState.Y2S] = Constants.B2Smu;
dMatrix[BottomiumState.x2P, BottomiumState.x2P] = Constants.B1Smu * Constants.B2P1S;
dMatrix[BottomiumState.Y3S, BottomiumState.Y3S] = Constants.B3Smu;
dMatrix[BottomiumState.x3P, BottomiumState.x3P] = Constants.B1Smu * Constants.B3P1S;
return(dMatrix);
}
public BottomiumVector CalculateY1SFeedDownFractions()
{
BottomiumVector initialPops = CalculateInitialQQPopulations();
BottomiumCascadeMatrix cMatrix = CalculateCumulativeMatrix();
BottomiumVector tmpPops = cMatrix * initialPops;
BottomiumCascadeMatrix bMatrix = CalculateBranchingRatioMatrix();
foreach (BottomiumState i in Enum.GetValues(typeof(BottomiumState)))
{
tmpPops[i] *= Constants.B1Smu * bMatrix[BottomiumState.Y1S, i];
}
tmpPops[BottomiumState.Y1S] = Constants.B1Smu * initialPops[BottomiumState.Y1S];
return(tmpPops);
}
public static BottomiumCascadeMatrix CalculateInverseDimuonDecayMatrix()
{
BottomiumCascadeMatrix inverseDMatrix = new BottomiumCascadeMatrix();
inverseDMatrix[BottomiumState.Y1S, BottomiumState.Y1S]
= 1.0 / Constants.B1Smu;
inverseDMatrix[BottomiumState.x1P, BottomiumState.x1P]
= 1.0 / (Constants.B1Smu * Constants.B1P1S);
inverseDMatrix[BottomiumState.Y2S, BottomiumState.Y2S]
= 1.0 / Constants.B2Smu;
inverseDMatrix[BottomiumState.x2P, BottomiumState.x2P]
= 1.0 / (Constants.B1Smu * Constants.B2P1S);
inverseDMatrix[BottomiumState.Y3S, BottomiumState.Y3S]
= 1.0 / Constants.B3Smu;
inverseDMatrix[BottomiumState.x3P, BottomiumState.x3P]
= 1.0 / (Constants.B1Smu * Constants.B3P1S);
return(inverseDMatrix);
}
public static BottomiumCascadeMatrix operator *(
BottomiumCascadeMatrix left,
BottomiumCascadeMatrix right
)
{
BottomiumCascadeMatrix result = new BottomiumCascadeMatrix();
foreach (BottomiumState s in Enum.GetValues(typeof(BottomiumState)))
{
foreach (BottomiumState t in Enum.GetValues(typeof(BottomiumState)))
{
foreach (BottomiumState u in Enum.GetValues(typeof(BottomiumState)))
{
result[s, t] += left[s, u] * right[u, t];
}
}
}
return(result);
}
public static BottomiumCascadeMatrix CalculateCumulativeMatrix()
{
BottomiumCascadeMatrix cMatrix = BottomiumCascadeMatrix.CreateUnitMatrix();
BottomiumCascadeMatrix bMatrix = CalculateBranchingRatioMatrix();
for (int j = 0; j < BottomiumStatesCount; j++)
{
for (int i = BottomiumStatesCount - 1; i >= 0; i--)
{
for (int k = BottomiumStatesCount - 1; k >= 0; k--)
{
var iState = (BottomiumState)i;
var jState = (BottomiumState)j;
var kState = (BottomiumState)k;
cMatrix[iState, jState] += bMatrix[iState, kState] * cMatrix[kState, jState];
}
}
}
return(cMatrix);
}
public static BottomiumCascadeMatrix CalculateInverseCumulativeMatrix()
{
BottomiumCascadeMatrix inverseCMatrix = new BottomiumCascadeMatrix();
BottomiumCascadeMatrix bMatrix = CalculateBranchingRatioMatrix();
foreach (BottomiumState i in Enum.GetValues(typeof(BottomiumState)))
{
foreach (BottomiumState j in Enum.GetValues(typeof(BottomiumState)))
{
if (i == j)
{
inverseCMatrix[i, j] = 1 - bMatrix[i, j];
}
else
{
inverseCMatrix[i, j] = -bMatrix[i, j];
}
}
}
return(inverseCMatrix);
}
/********************************************************************************************
* Public static members, functions and properties
********************************************************************************************/
public static BottomiumCascadeMatrix CalculateBranchingRatioMatrix()
{
// Branching ratio B(X->Y) have non-zero values if the masses X,Y satisfy X > Y.
BottomiumCascadeMatrix bMatrix = new BottomiumCascadeMatrix();
bMatrix[BottomiumState.Y1S, BottomiumState.x1P] = Constants.B1P1S;
bMatrix[BottomiumState.Y1S, BottomiumState.Y2S] = Constants.B2S1S;
bMatrix[BottomiumState.Y1S, BottomiumState.x2P] = Constants.B2P1S;
bMatrix[BottomiumState.Y1S, BottomiumState.Y3S] = Constants.B3S1S;
bMatrix[BottomiumState.Y1S, BottomiumState.x3P] = Constants.B3P1S;
bMatrix[BottomiumState.x1P, BottomiumState.Y2S] = Constants.B2S1P;
bMatrix[BottomiumState.x1P, BottomiumState.x2P] = Constants.B2P1P;
bMatrix[BottomiumState.x1P, BottomiumState.Y3S] = Constants.B3S1P;
bMatrix[BottomiumState.x1P, BottomiumState.x3P] = Constants.B3P1P;
bMatrix[BottomiumState.Y2S, BottomiumState.x2P] = Constants.B2P2S;
bMatrix[BottomiumState.Y2S, BottomiumState.Y3S] = Constants.B3S2S;
bMatrix[BottomiumState.Y2S, BottomiumState.x3P] = Constants.B3P2S;
bMatrix[BottomiumState.x2P, BottomiumState.Y3S] = Constants.B3S2P;
bMatrix[BottomiumState.x2P, BottomiumState.x3P] = Constants.B3P2P;
bMatrix[BottomiumState.Y3S, BottomiumState.x3P] = Constants.B3P3S;
return(bMatrix);
}
