double LegendreMomentShape::Moment(const int l, const int i, const int k, const int j, const double mKK_mapped, const double phi, const double ctheta_1, const double ctheta_2)
{
if(j < k)
return 0;
if(std::abs(mKK_mapped) > 1)
return 0;
double Q_l = gsl_sf_legendre_Pl (l, mKK_mapped );
double P_i = gsl_sf_legendre_Pl (i, ctheta_2 );
double Y_jk = gsl_sf_legendre_sphPlm (j, k, ctheta_1);
if(k != 0)
Y_jk *= sqrt(2) * cos(k * phi);
return Q_l * P_i * Y_jk;
}
double Bd2JpsiKstar_sWave_Fs_withAcc::angularFactor( )
{
return 1;
double returnValue(0.);
#ifdef __RAPIDFIT_USE_GSL
double P_i(0.);
double Y_jk(0.);
for ( int i = 0; i < i_max+1; i++ )
{
for ( int k = 0; k < k_max; k+=2) // limiting the loop here to only look at terms we need
{
for ( int j = 0; j < j_max; j+=2 ) // must have l >= k
{
if (j < k) continue;
P_i = gsl_sf_legendre_Pl (i, cosPsi);
// only consider case where k >= 0
// these are the real valued spherical harmonics
if ( k == 0 ) Y_jk = gsl_sf_legendre_sphPlm (j, k, cosTheta);
else Y_jk = sqrt(2) * gsl_sf_legendre_sphPlm (j, k, cosTheta) * cos(k*phi);
returnValue += c[i][k][j]*(P_i * Y_jk);
}
}
}
#endif
return returnValue;
}
//Calculate the function value
double DPBackground::Evaluate(DataPoint * measurement)
{
// Observables
m23 = measurement->GetObservable( m23Name )->GetValue();
cosTheta1 = measurement->GetObservable( cosTheta1Name )->GetValue();
cosTheta2 = measurement->GetObservable( cosTheta2Name )->GetValue();
phi = measurement->GetObservable( phiName )->GetValue();
double m23_mapped = (m23 - 0.64)/(1.59 - 0.64)*2. + (-1); // should really do this in a generic way
#ifdef __RAPIDFIT_USE_GSL
double returnable_value(0.);
double Q_l(0.);
double P_i(0.);
double Y_jk(0.);
for ( int l = 0; l < l_max+1; l++ )
{
for ( int i = 0; i < i_max+1; i++ )
{
for ( int k = 0; k < 3; k++)
{
for ( int j = 0; j < 3; j+=2 ) // limiting the loop here to only look at terms we need
{
//cout << "likj" << l << " " << i << " " << k << " " << j << endl;
if (j < k) continue; // must have l >= k
Q_l = gsl_sf_legendre_Pl (l, m23_mapped);
P_i = gsl_sf_legendre_Pl (i, cosTheta2);
// only consider case where k >= 0
// these are the real valued spherical harmonics
if ( k == 0 ) Y_jk = gsl_sf_legendre_sphPlm (j, k, cosTheta1);
else Y_jk = sqrt(2) * gsl_sf_legendre_sphPlm (j, k, cosTheta1) * cos(k*phi);
returnable_value += c[l][i][k][j]*(Q_l * P_i * Y_jk);
}
}
}
}
if( std::isnan(returnable_value) || returnable_value < 0 ) return 0.;
else return returnable_value;
#endif
return 0 ;
}
double Bd2JpsiKstar_sWave_Fscopy::angularFactor( )
{
double returnValue(0.);
#ifdef __RAPIDFIT_USE_GSL
double _cosPsi(0.);
double _cosTheta(0.);
double _phi(0.);
if( useHelicityBasis() ) {
_cosTheta = helcosthetaL;
_phi = helphi;
_cosPsi = helcosthetaK;
}
else {
_cosTheta = cosTheta;
_phi = phi;
_cosPsi = cosPsi;
}
double P_i(0.);
double Y_jk(0.);
for ( int i = 0; i < i_max+1; i++ )
{
for ( int k = 0; k < k_max; k+=2) // limiting the loop here to only look at terms we need
{
for ( int j = 0; j < j_max; j+=2 ) // must have l >= k
{
if (j < k) continue;
P_i = gsl_sf_legendre_Pl (i, _cosPsi);
// only consider case where k >= 0
// these are the real valued spherical harmonics
if ( k == 0 ) Y_jk = gsl_sf_legendre_sphPlm (j, k, _cosTheta);
else Y_jk = sqrt(2) * gsl_sf_legendre_sphPlm (j, k, _cosTheta) * cos(k*_phi);
returnValue += c[i][k][j]*(P_i * Y_jk);
}
}
}
#endif
return returnValue;
}
//------------------------------------------------------------------------------
/// Legendre Polynomial \f$ P_l(x) \f$
inline double legendrePl(const int l, const double x)
{
return gsl_sf_legendre_Pl(l, x);
}
//Calculate the function value
double DPTotalAmplitudePDF_withAcc_withBkg::Evaluate(DataPoint * measurement)
{
// Observables
m23 = measurement->GetObservable( m23Name )->GetValue();
cosTheta1 = measurement->GetObservable( cosTheta1Name )->GetValue();
cosTheta2 = measurement->GetObservable( cosTheta2Name )->GetValue();
phi = measurement->GetObservable( phiName )->GetValue();
//m13 = measurement->GetObservable( m13Name )->GetValue();
//cosZ = measurement->GetObservable( cosZName )->GetValue();
//cosPsiZ = measurement->GetObservable( cosPsiZName )->GetValue();
//phiZ = measurement->GetObservable( phiZName )->GetValue();
//alpha = measurement->GetObservable( alphaName )->GetValue();
pionID = measurement->GetObservable( pionIDName )->GetValue();
double m23_mapped = (m23 - 0.64)/(1.59 - 0.64)*2. + (-1); // should really do this in a generic way
//double m23_mapped = (m23 - 0.64)/(1.68 - 0.64)*2. + (-1); // should really do this in a generic way
#ifdef __RAPIDFIT_USE_GSL
double angularAcc(0.);
double Q_l(0.);
double P_i(0.);
double Y_jk(0.);
if ( useAngularAcceptance )
{
for ( int l = 0; l < l_max+1; l++ )
{
for ( int i = 0; i < i_max+1; i++ )
{
for ( int k = 0; k < 3; k++ )
{
for ( int j = 0; j < 3; j+=2 ) // limiting the loop here to only look at terms we need
{
if (j < k) continue; // must have l >= k
Q_l = gsl_sf_legendre_Pl (l, m23_mapped);
P_i = gsl_sf_legendre_Pl (i, cosTheta2);
// only consider case where k >= 0
// these are the real valued spherical harmonics
if ( k == 0 ) Y_jk = gsl_sf_legendre_sphPlm (j, k, cosTheta1);
else Y_jk = sqrt(2) * gsl_sf_legendre_sphPlm (j, k, cosTheta1) * cos(k*phi);
angularAcc += c[l][i][k][j]*(Q_l * P_i * Y_jk);
}
}
}
}
}
else {
angularAcc = 1.;//0.0195;
}
//if (angularAcc <= 0.) cout << "angular acc " << angularAcc << " " << m23 << " " << m23_mapped << " " << cosTheta1 << " " << phi << " " << cosTheta2 << endl;
// Calculate the Z angles
//DPHelpers::calculateFinalStateMomenta(massB, m23, massPsi,
//cosTheta1, cosTheta2, phi, pionID, 0.1056583715, 0.1056583715, 0.13957018, 0.493677,
//pMuPlus, pMuMinus, pPi, pK);
DPHelpers::calculateFinalStateMomentaBelle(massB, m23, massPsi,
cosTheta1, cosTheta2, phi,
0.1056583715, 0.139570, 0.493677,
pMuPlus, pMuMinus, pPi, pK);
double belle_m23(0.);
double belle_cosKPi(0.);
double belle_cosPsi(0.);
double belle_phiKPiPsi(0.);
double belle_m13(0.);
double belle_cosZ(0.);
double belle_cosPsi_Z(0.);
double belle_phiPsiZ(0.);
double belle_phiZPsiPsi(0.);
const TLorentzVector myMuPlus(pMuPlus);
const TLorentzVector myMuMinus(pMuMinus);
const TLorentzVector myPi(pPi);
const TLorentzVector myK(pK);
DPHelpers::Belle(myMuPlus, myMuMinus, myPi, myK
, belle_m23
, belle_cosKPi
, belle_cosPsi
, belle_phiKPiPsi
, belle_m13
, belle_cosZ
, belle_cosPsi_Z
, belle_phiPsiZ
, belle_phiZPsiPsi
);
//cout << "K* ntuple " << m23 << " " << cosTheta2 << " " << cosTheta1 << " " << phi << " " << pionID << endl;
//cout << "K* calcul " << belle_m23 << " " << belle_cosKPi << " " << belle_cosPsi << " " << belle_phiKPiPsi << endl;
//cout << "Z ntuple " << m13 << " " << cosZ << " " << cosPsiZ << " " << phiZ << " " << alpha << endl;
//cout << "Z calcul " << belle_m13 << " " << belle_cosZ << " " << belle_cosPsi_Z << " " << belle_phiPsiZ << " " << belle_phiZPsiPsi << endl;
double result = 0.;
TComplex tmp(0,0);
// This deals with the separate Kpi components
unsigned int lower = (unsigned)(componentIndex - 1);
unsigned int upper = (unsigned)componentIndex;
unsigned int lowerZ = 0;
unsigned int upperZ = 0;
// And this switchs things to deal with the Z components.
if ( (unsigned)componentIndex > KpiComponents.size() )
{
lower = 0;
upper = 0;
lowerZ = (unsigned)(componentIndex - KpiComponents.size() - 1);
upperZ = (unsigned)(componentIndex - KpiComponents.size());
}
// just plot the background
if ( componentIndex == 13 )
{
lower = 0;
upper = 0;
lowerZ = 0;
upperZ = 0;
}
if ( componentIndex == 100 ){
lower = 0;
upper = (unsigned)KpiComponents.size();
lowerZ = 0;
upperZ = 0;
}
// Finally, for the total of all components
if ( componentIndex == 0 ) {
lower = 0;
upper = (unsigned)KpiComponents.size();
lowerZ = 0;
upperZ = (unsigned)ZComponents.size();
}
// Now sum over final state helicities (this is not general code, but
// knows about internals of components
for (int twoLambda = -2; twoLambda <= 2; twoLambda += 4) // Sum over +-1
{
tmp = TComplex(0,0);
for (int twoLambdaPsi = -2; twoLambdaPsi <= 2; twoLambdaPsi += 2) // Sum over -1,0,+1
{
for (unsigned int i = lower; i < upper; ++i) // sum over all components
{
tmp += KpiComponents[i]->amplitude(m23, cosTheta1, cosTheta2, phi,
twoLambda, twoLambdaPsi);
}
// Now comes sum over Z+ components and lambdaPsiPrime
for (unsigned int i = lowerZ; i < upperZ; ++i)
{
//tmp += ZComponents[i]->amplitudeProperVars(belle_m13, belle_cosZ, belle_cosPsi_Z, belle_phiPsiZ, pionID, twoLambda, twoLambdaPsi);
tmp += TComplex::Exp((0.5*TComplex::I())*(twoLambda*belle_phiZPsiPsi))*(ZComponents[i]->amplitudeProperVars(belle_m13, belle_cosZ, belle_cosPsi_Z, belle_phiPsiZ, pionID, twoLambda, twoLambdaPsi));
//std::cout << TComplex::Exp(0.5*TComplex::I()*twoLambda*belle_phiZPsiPsi) << " " << TComplex(cos(belle_phiZPsiPsi), 0.5*twoLambda*sin(belle_phiZPsiPsi)) << std::endl;
}
}
result += tmp.Rho2();
}
//momenta are defined on eq 39.20a/b of the 2010 PDG
const double m1 = 0.493677; // kaon mass
const double m2 = 0.139570; // pion mass
const double MB0= massB; // B0 mass
double t1 = m23*m23-(m1+m2)*(m1+m2);
double t2 = m23*m23-(m1-m2)*(m1-m2);
double t31 = MB0*MB0 - (m23 + massPsi)*(m23 + massPsi);
double t32 = MB0*MB0 - (m23 - massPsi)*(m23 - massPsi);
double p1_st = sqrt(t1*t2)/m23/2.;
double p3 = sqrt(t31*t32)/MB0/2.;
//std::cout << result << " " << angularAcc << " " << p1_st << " " << p3 << " " << result*p1_st*p3 << std::endl;
double returnable_value = result * angularAcc * p1_st * p3;
double background(0.);
if ( (componentIndex == 0 || componentIndex == 13) && fraction > 0. )
{
for ( int l = 0; l < l_max_b+1; l++ )
{
for ( int i = 0; i < i_max_b+1; i++ )
{
for ( int k = 0; k < k_max_b+1; k++)
{
for ( int j = 0; j < 3; j+=2 ) // limiting the loop here to only look at terms we need
{
//cout << "likj" << l << " " << i << " " << k << " " << j << endl;
if (j < k) continue; // must have l >= k
Q_l = gsl_sf_legendre_Pl (l, m23_mapped);
P_i = gsl_sf_legendre_Pl (i, cosTheta2);
// only consider case where k >= 0
// these are the real valued spherical harmonics
if ( k == 0 ) Y_jk = gsl_sf_legendre_sphPlm (j, k, cosTheta1);
else Y_jk = sqrt(2) * gsl_sf_legendre_sphPlm (j, k, cosTheta1) * cos(k*phi);
background += b[l][i][k][j]*(Q_l * P_i * Y_jk);
}
}
}
}
}
//cout << background << " " << fraction << " " << returnable_value << endl;
//returnable_value = background;
returnable_value = returnable_value + fraction*background;
if( std::isnan(returnable_value) || returnable_value < 0. ) return 0.;
else return returnable_value;
#endif
return 0.;
}
/* See Remark 2.17 */
double pkd_eval_square( int j, int k, point p) {
double leg = gsl_sf_legendre_Pl( j, p.x);
double pwr = gsl_pow_int( (1.0-p.y)/2.0, j);
double jac = jacobi( k, 2.0*j+1.0, p.y);
return leg*pwr*jac;
}
