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#include "Alignment/TwoBodyDecay/interface/TwoBodyDecayDerivatives.h"
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#include "Alignment/TwoBodyDecay/interface/TwoBodyDecayModel.h"
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#include "FWCore/Utilities/interface/Exception.h"
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#include <algorithm>
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TwoBodyDecayDerivatives::TwoBodyDecayDerivatives( double mPrimary, double mSecondary ) :
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thePrimaryMass( mPrimary ), theSecondaryMass( mSecondary ) {}
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TwoBodyDecayDerivatives::~TwoBodyDecayDerivatives() {}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix >
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TwoBodyDecayDerivatives::derivatives( const TwoBodyDecay & tbd ) const
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{
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return derivatives( tbd.decayParameters() );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix >
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TwoBodyDecayDerivatives::derivatives( const TwoBodyDecayParameters & param ) const
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{
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// get the derivatives with respect to all parameters
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdpx = this->dqsdpx( param );
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdpy = this->dqsdpy( param );
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdpz = this->dqsdpz( param );
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdtheta = this->dqsdtheta( param );
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdphi = this->dqsdphi( param );
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdm = this->dqsdm( param );
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AlgebraicMatrix dqplusdz( 3, dimension );
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dqplusdz.sub( 1, px, dqsdpx.first );
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dqplusdz.sub( 1, py, dqsdpy.first );
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dqplusdz.sub( 1, pz, dqsdpz.first );
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dqplusdz.sub( 1, theta, dqsdtheta.first );
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dqplusdz.sub( 1, phi, dqsdphi.first );
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dqplusdz.sub( 1, mass, dqsdm.first );
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AlgebraicMatrix dqminusdz( 3, dimension );
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dqminusdz.sub( 1, px, dqsdpx.second );
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dqminusdz.sub( 1, py, dqsdpy.second );
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dqminusdz.sub( 1, pz, dqsdpz.second );
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dqminusdz.sub( 1, theta, dqsdtheta.second );
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dqminusdz.sub( 1, phi, dqsdphi.second );
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dqminusdz.sub( 1, mass, dqsdm.second );
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return std::make_pair( dqplusdz, dqminusdz );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix >
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TwoBodyDecayDerivatives::selectedDerivatives( const TwoBodyDecay & tbd, const std::vector< bool > & selector ) const
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{
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return selectedDerivatives( tbd.decayParameters(), selector );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix >
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TwoBodyDecayDerivatives::selectedDerivatives( const TwoBodyDecayParameters & param, const std::vector< bool > & selector ) const
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{
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if ( selector.size() != dimension )
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{
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throw cms::Exception( "BadConfig" ) << "@SUB=TwoBodyDecayDerivatives::selectedDerivatives"
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<< "selector has bad dimension (size=" << selector.size() << ").";
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}
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int nSelected = std::count( selector.begin(), selector.end(), true );
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int iSelected = 1;
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AlgebraicMatrix dqplusdz( 3, nSelected );
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AlgebraicMatrix dqminusdz( 3, nSelected );
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std::pair< AlgebraicMatrix, AlgebraicMatrix > dqsdzi;
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for ( unsigned int i = 1; i <= dimension; i++ )
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{
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if ( selector[i] )
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{
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dqsdzi = this->dqsdzi( param, DerivativeParameterName(i) );
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dqplusdz.sub( 1, iSelected, dqsdzi.first );
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dqminusdz.sub( 1, iSelected, dqsdzi.second );
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iSelected++;
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}
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}
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return std::make_pair( dqplusdz, dqminusdz );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix > TwoBodyDecayDerivatives::dqsdpx( const TwoBodyDecayParameters & param ) const
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{
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double px = param[TwoBodyDecayParameters::px];
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double py = param[TwoBodyDecayParameters::py];
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double pz = param[TwoBodyDecayParameters::pz];
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double theta = param[TwoBodyDecayParameters::theta];
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double phi = param[TwoBodyDecayParameters::phi];
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// compute transverse and absolute momentum
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double pT2 = px*px + py*py;
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double p2 = pT2 + pz*pz;
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double pT = sqrt( pT2 );
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double p = sqrt( p2 );
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double sphi = sin( phi );
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double cphi = cos( phi );
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double stheta = sin( theta );
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double ctheta = cos( theta );
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// some constants from kinematics
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double c1 = 0.5*thePrimaryMass/theSecondaryMass;
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double c2 = sqrt( c1*c1 - 1. );
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double c3 = 0.5*c2*ctheta/c1;
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double c4 = sqrt( p2 + thePrimaryMass*thePrimaryMass );
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// momentum of decay particle 1 in the primary's boosted frame
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AlgebraicMatrix pplus( 3, 1 );
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pplus[0][0] = theSecondaryMass*c2*stheta*cphi;
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pplus[1][0] = theSecondaryMass*c2*stheta*sphi;
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pplus[2][0] = 0.5*p + c3*c4;
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// momentum of decay particle 2 in the primary's boosted frame
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AlgebraicMatrix pminus( 3, 1 );
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pminus[0][0] = -pplus[0][0];
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pminus[1][0] = -pplus[1][0];
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pminus[2][0] = 0.5*p - c3*c4;
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// derivative of rotation matrix w.r.t. px
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AlgebraicMatrix dRotMatdpx( 3, 3 );
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dRotMatdpx[0][0] = pz/(pT*p)*(1.-px*px*(1./pT2+1./p2));
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dRotMatdpx[0][1] = px*py/(pT*pT2);
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dRotMatdpx[0][2] = (1.-px*px/p2)/p;
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dRotMatdpx[1][0] = -px*py*pz/(pT*p)*(1./pT2+1./p2);
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dRotMatdpx[1][1] = (1.-px*px/pT2)/pT;
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dRotMatdpx[1][2] = -px*py/(p*p2);
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dRotMatdpx[2][0] = -(1./pT-pT/p2)*px/p;
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dRotMatdpx[2][1] = 0.;
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dRotMatdpx[2][2] = -px*pz/(p*p2);
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// derivative of the momentum of particle 1 in the lab frame w.r.t. px
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double dpplusdpx = px*( 0.5/p + c3/c4 );
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AlgebraicMatrix dqplusdpx = dRotMatdpx*pplus;
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dqplusdpx[0][0] += px*dpplusdpx/p;
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dqplusdpx[1][0] += py*dpplusdpx/p;
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dqplusdpx[2][0] += pz*dpplusdpx/p;
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// derivative of the momentum of particle 2 in the lab frame w.r.t. px
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double dpminusdpx = px*( 0.5/p - c3/c4 );
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AlgebraicMatrix dqminusdpx = dRotMatdpx*pminus;
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dqminusdpx[0][0] += px*dpminusdpx/p;
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dqminusdpx[1][0] += py*dpminusdpx/p;
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dqminusdpx[2][0] += pz*dpminusdpx/p;
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// return result
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return std::make_pair( dqplusdpx, dqminusdpx );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix > TwoBodyDecayDerivatives::dqsdpy( const TwoBodyDecayParameters & param ) const
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{
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double px = param[TwoBodyDecayParameters::px];
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double py = param[TwoBodyDecayParameters::py];
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double pz = param[TwoBodyDecayParameters::pz];
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double theta = param[TwoBodyDecayParameters::theta];
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double phi = param[TwoBodyDecayParameters::phi];
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// compute transverse and absolute momentum
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double pT2 = px*px + py*py;
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double p2 = pT2 + pz*pz;
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double pT = sqrt( pT2 );
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double p = sqrt( p2 );
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double sphi = sin( phi );
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double cphi = cos( phi );
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double stheta = sin( theta );
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double ctheta = cos( theta );
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// some constants from kinematics
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double c1 = 0.5*thePrimaryMass/theSecondaryMass;
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double c2 = sqrt( c1*c1 - 1. );
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double c3 = 0.5*c2*ctheta/c1;
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double c4 = sqrt( p2 + thePrimaryMass*thePrimaryMass );
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// momentum of decay particle 1 in the rest frame of the primary
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AlgebraicMatrix pplus( 3, 1 );
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pplus[0][0] = theSecondaryMass*c2*stheta*cphi;
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pplus[1][0] = theSecondaryMass*c2*stheta*sphi;
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pplus[2][0] = 0.5*p + c3*c4;
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// momentum of decay particle 2 in the rest frame of the primary
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AlgebraicMatrix pminus( 3, 1 );
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pminus[0][0] = -pplus[0][0];
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pminus[1][0] = -pplus[1][0];
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pminus[2][0] = 0.5*p - c3*c4;
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// derivative of rotation matrix w.r.t. py
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AlgebraicMatrix dRotMatdpy( 3, 3 );
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dRotMatdpy[0][0] = -px*py*pz/(pT*p)*(1./pT2+1./p2);
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dRotMatdpy[0][1] = (py*py/pT2-1.)/pT;
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dRotMatdpy[0][2] = -px*py/(p*p2);
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dRotMatdpy[1][0] = pz/(pT*p)*(1.-py*py*(1./pT2+1./p2));
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dRotMatdpy[1][1] = -px*py/(pT*pT2);
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dRotMatdpy[1][2] = (1.-py*py/p2)/p;
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dRotMatdpy[2][0] = -(1./pT-pT/p2)*py/p;
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dRotMatdpy[2][1] = 0.;
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dRotMatdpy[2][2] = -py*pz/(p*p2);
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// derivative of the momentum of particle 1 in the lab frame w.r.t. py
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double dpplusdpy = py*( 0.5/p + c3/c4 );
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AlgebraicMatrix dqplusdpy = dRotMatdpy*pplus;
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dqplusdpy[0][0] += px*dpplusdpy/p;
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dqplusdpy[1][0] += py*dpplusdpy/p;
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dqplusdpy[2][0] += pz*dpplusdpy/p;
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// derivative of the momentum of particle 2 in the lab frame w.r.t. py
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double dpminusdpy = py*( 0.5/p - c3/c4 );
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AlgebraicMatrix dqminusdpy = dRotMatdpy*pminus;
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dqminusdpy[0][0] += px*dpminusdpy/p;
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dqminusdpy[1][0] += py*dpminusdpy/p;
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dqminusdpy[2][0] += pz*dpminusdpy/p;
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// return result
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return std::make_pair( dqplusdpy, dqminusdpy );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix > TwoBodyDecayDerivatives::dqsdpz( const TwoBodyDecayParameters & param ) const
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{
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double px = param[TwoBodyDecayParameters::px];
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double py = param[TwoBodyDecayParameters::py];
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double pz = param[TwoBodyDecayParameters::pz];
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double theta = param[TwoBodyDecayParameters::theta];
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double phi = param[TwoBodyDecayParameters::phi];
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// compute transverse and absolute momentum
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double pT2 = px*px + py*py;
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double p2 = pT2 + pz*pz;
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double pT = sqrt( pT2 );
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double p = sqrt( p2 );
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double sphi = sin( phi );
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double cphi = cos( phi );
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double stheta = sin( theta );
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double ctheta = cos( theta );
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// some constants from kinematics
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double c1 = 0.5*thePrimaryMass/theSecondaryMass;
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double c2 = sqrt( c1*c1 - 1. );
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double c3 = 0.5*c2*ctheta/c1;
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double c4 = sqrt( p2 + thePrimaryMass*thePrimaryMass );
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// momentum of decay particle 1 in the rest frame of the primary
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AlgebraicMatrix pplus( 3, 1 );
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pplus[0][0] = theSecondaryMass*c2*stheta*cphi;
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pplus[1][0] = theSecondaryMass*c2*stheta*sphi;
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pplus[2][0] = 0.5*p + c3*c4;
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// momentum of decay particle 2 in the rest frame of the primary
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AlgebraicMatrix pminus( 3, 1 );
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pminus[0][0] = -pplus[0][0];
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pminus[1][0] = -pplus[1][0];
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pminus[2][0] = 0.5*p - c3*c4;
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// derivative of rotation matrix w.r.t. py
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AlgebraicMatrix dRotMatdpz( 3, 3 );
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dRotMatdpz[0][0] = px/(pT*p)*(1.-pz*pz/p2);
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dRotMatdpz[0][1] = 0.;
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dRotMatdpz[0][2] = -px*pz/(p*p2);
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dRotMatdpz[1][0] = py/(p*pT)*(1.-pz*pz/p2);
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dRotMatdpz[1][1] = 0.;
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dRotMatdpz[1][2] = -py*pz/(p*p2);
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dRotMatdpz[2][0] = pT*pz/(p*p2);
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dRotMatdpz[2][1] = 0.;
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dRotMatdpz[2][2] = (1.-pz*pz/p2)/p;
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// derivative of the momentum of particle 1 in the lab frame w.r.t. pz
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double dpplusdpz = pz*( 0.5/p + c3/c4 );
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AlgebraicMatrix dqplusdpz = dRotMatdpz*pplus;
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dqplusdpz[0][0] += px*dpplusdpz/p;
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dqplusdpz[1][0] += py*dpplusdpz/p;
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dqplusdpz[2][0] += pz*dpplusdpz/p;
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// derivative of the momentum of particle 2 in the lab frame w.r.t. pz
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double dpminusdpz = pz*( 0.5/p - c3/c4 );
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AlgebraicMatrix dqminusdpz = dRotMatdpz*pminus;
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dqminusdpz[0][0] += px*dpminusdpz/p;
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dqminusdpz[1][0] += py*dpminusdpz/p;
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dqminusdpz[2][0] += pz*dpminusdpz/p;
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// return result
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return std::make_pair( dqplusdpz, dqminusdpz );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix > TwoBodyDecayDerivatives::dqsdtheta( const TwoBodyDecayParameters & param ) const
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{
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double px = param[TwoBodyDecayParameters::px];
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double py = param[TwoBodyDecayParameters::py];
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double pz = param[TwoBodyDecayParameters::pz];
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double theta = param[TwoBodyDecayParameters::theta];
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double phi = param[TwoBodyDecayParameters::phi];
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// compute transverse and absolute momentum
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double pT2 = px*px + py*py;
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double p2 = pT2 + pz*pz;
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double sphi = sin( phi );
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double cphi = cos( phi );
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double stheta = sin( theta );
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double ctheta = cos( theta );
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// some constants from kinematics
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double c1 = 0.5*thePrimaryMass/theSecondaryMass;
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double c2 = sqrt( c1*c1 - 1. );
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double c3 = -0.5*c2*stheta/c1;
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double c4 = sqrt( p2 + thePrimaryMass*thePrimaryMass );
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// derivative of the momentum of particle 1 in the primary's rest frame w.r.t. theta
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AlgebraicMatrix dpplusdtheta( 3, 1 );
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dpplusdtheta[0][0] = theSecondaryMass*c2*ctheta*cphi;
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dpplusdtheta[1][0] = theSecondaryMass*c2*ctheta*sphi;
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dpplusdtheta[2][0] = c3*c4;
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// derivative of the momentum of particle 2 in the primary's rest frame w.r.t. theta
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AlgebraicMatrix dpminusdtheta( 3, 1 );
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dpminusdtheta[0][0] = -theSecondaryMass*c2*ctheta*cphi;
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dpminusdtheta[1][0] = -theSecondaryMass*c2*ctheta*sphi;
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dpminusdtheta[2][0] = -c3*c4;
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TwoBodyDecayModel decayModel;
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AlgebraicMatrix rotMat = decayModel.rotationMatrix( px, py, pz );
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AlgebraicMatrix dqplusdtheta = rotMat*dpplusdtheta;
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AlgebraicMatrix dqminusdtheta = rotMat*dpminusdtheta;
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return std::make_pair( dqplusdtheta, dqminusdtheta );
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}
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const std::pair< AlgebraicMatrix, AlgebraicMatrix > TwoBodyDecayDerivatives::dqsdphi( const TwoBodyDecayParameters & param ) const
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{
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double px = param[TwoBodyDecayParameters::px];
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double py = param[TwoBodyDecayParameters::py];
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double pz = param[TwoBodyDecayParameters::pz];
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double theta = param[TwoBodyDecayParameters::theta];
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double phi = param[TwoBodyDecayParameters::phi];
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double sphi = sin( phi );
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double cphi = cos( phi );
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double stheta = sin( theta );
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// some constants from kinematics
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double c1 = 0.5*thePrimaryMass/theSecondaryMass;
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double c2 = sqrt( c1*c1 - 1. );
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// derivative of the momentum of particle 1 in the primary's rest frame w.r.t. phi
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AlgebraicMatrix dpplusdphi( 3, 1 );
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dpplusdphi[0][0] = -theSecondaryMass*c2*stheta*sphi;
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dpplusdphi[1][0] = theSecondaryMass*c2*stheta*cphi;
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dpplusdphi[2][0] = 0.;
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|
| 377 |
// derivative of the momentum of particle 2 in the primary's rest frame w.r.t. phi
|
| 378 |
AlgebraicMatrix dpminusdphi( 3, 1 );
|
| 379 |
dpminusdphi[0][0] = theSecondaryMass*c2*stheta*sphi;
|
| 380 |
dpminusdphi[1][0] = -theSecondaryMass*c2*stheta*cphi;
|
| 381 |
dpminusdphi[2][0] = 0.;
|
| 382 |
|
| 383 |
TwoBodyDecayModel decayModel;
|
| 384 |
AlgebraicMatrix rotMat = decayModel.rotationMatrix( px, py, pz );
|
| 385 |
|
| 386 |
AlgebraicMatrix dqplusdphi = rotMat*dpplusdphi;
|
| 387 |
AlgebraicMatrix dqminusdphi = rotMat*dpminusdphi;
|
| 388 |
|
| 389 |
return std::make_pair( dqplusdphi, dqminusdphi );
|
| 390 |
}
|
| 391 |
|
| 392 |
|
| 393 |
const std::pair< AlgebraicMatrix, AlgebraicMatrix > TwoBodyDecayDerivatives::dqsdm( const TwoBodyDecayParameters & param ) const
|
| 394 |
{
|
| 395 |
double px = param[TwoBodyDecayParameters::px];
|
| 396 |
double py = param[TwoBodyDecayParameters::py];
|
| 397 |
double pz = param[TwoBodyDecayParameters::pz];
|
| 398 |
double theta = param[TwoBodyDecayParameters::theta];
|
| 399 |
double phi = param[TwoBodyDecayParameters::phi];
|
| 400 |
|
| 401 |
double pT2 = px*px + py*py;
|
| 402 |
double p2 = pT2 + pz*pz;
|
| 403 |
|
| 404 |
double sphi = sin( phi );
|
| 405 |
double cphi = cos( phi );
|
| 406 |
double ctheta = cos( theta );
|
| 407 |
double stheta = sin( theta );
|
| 408 |
|
| 409 |
// some constants from kinematics
|
| 410 |
double c1 = 0.5*thePrimaryMass/theSecondaryMass;
|
| 411 |
double c2 = 1./sqrt( c1*c1 - 1. );
|
| 412 |
double m2 = thePrimaryMass*thePrimaryMass;
|
| 413 |
|
| 414 |
// derivative of the momentum of particle 1 in the primary's rest frame w.r.t. the primary's mass
|
| 415 |
AlgebraicMatrix dpplusdm( 3, 1 );
|
| 416 |
dpplusdm[0][0] = c2*0.5*c1*stheta*cphi;
|
| 417 |
dpplusdm[1][0] = c2*0.5*c1*stheta*sphi;
|
| 418 |
dpplusdm[2][0] = c2*theSecondaryMass*( c1*c1 + p2/m2 )/sqrt( p2 + m2 )*ctheta;
|
| 419 |
|
| 420 |
// derivative of the momentum of particle 2 in the primary's rest frame w.r.t. the primary's mass
|
| 421 |
AlgebraicMatrix dpminusdm( 3, 1 );
|
| 422 |
dpminusdm[0][0] = -dpplusdm[0][0];
|
| 423 |
dpminusdm[1][0] = -dpplusdm[1][0];
|
| 424 |
dpminusdm[2][0] = -dpplusdm[2][0];
|
| 425 |
|
| 426 |
TwoBodyDecayModel decayModel;
|
| 427 |
AlgebraicMatrix rotMat = decayModel.rotationMatrix( px, py, pz );
|
| 428 |
|
| 429 |
AlgebraicMatrix dqplusdm = rotMat*dpplusdm;
|
| 430 |
AlgebraicMatrix dqminusdm = rotMat*dpminusdm;
|
| 431 |
|
| 432 |
return std::make_pair( dqplusdm, dqminusdm );
|
| 433 |
}
|
| 434 |
|
| 435 |
|
| 436 |
const std::pair< AlgebraicMatrix, AlgebraicMatrix >
|
| 437 |
TwoBodyDecayDerivatives::dqsdzi( const TwoBodyDecayParameters & param, const DerivativeParameterName & i ) const
|
| 438 |
{
|
| 439 |
switch ( i )
|
| 440 |
{
|
| 441 |
case TwoBodyDecayDerivatives::px :
|
| 442 |
return dqsdpx( param );
|
| 443 |
break;
|
| 444 |
case TwoBodyDecayDerivatives::py :
|
| 445 |
return dqsdpy( param );
|
| 446 |
break;
|
| 447 |
case TwoBodyDecayDerivatives::pz :
|
| 448 |
return dqsdpz( param );
|
| 449 |
break;
|
| 450 |
case TwoBodyDecayDerivatives::theta :
|
| 451 |
return dqsdtheta( param );
|
| 452 |
break;
|
| 453 |
case TwoBodyDecayDerivatives::phi :
|
| 454 |
return dqsdphi( param );
|
| 455 |
break;
|
| 456 |
case TwoBodyDecayDerivatives::mass :
|
| 457 |
return dqsdm( param );
|
| 458 |
break;
|
| 459 |
default:
|
| 460 |
throw cms::Exception( "BadConfig" ) << "@SUB=TwoBodyDecayDerivatives::dqsdzi"
|
| 461 |
<< "no decay parameter related to selector (" << i << ").";
|
| 462 |
};
|
| 463 |
|
| 464 |
return std::make_pair( AlgebraicMatrix( 3, 1, 0 ), AlgebraicMatrix( 3, 1, 0 ) );
|
| 465 |
}
|
