/data/refman/pasoursint/CMSSW_5_3_10/src/FastSimulation/BaseParticlePropagator/src/BaseParticlePropagator.cc

Go to the documentation of this file.

//FAMOS headers
#include "FastSimulation/BaseParticlePropagator/interface/BaseParticlePropagator.h"

BaseParticlePropagator::BaseParticlePropagator() :
  RawParticle(), rCyl(0.), rCyl2(0.), zCyl(0.), bField(0), properDecayTime(1E99)
{;}

BaseParticlePropagator::BaseParticlePropagator( 
         const RawParticle& myPart,double R, double Z, double B, double t ) :
  RawParticle(myPart), rCyl(R), rCyl2(R*R), zCyl(Z), bField(B), properDecayTime(t) 
{
  init();
}

BaseParticlePropagator::BaseParticlePropagator( 
         const RawParticle& myPart,double R, double Z, double B) :
  RawParticle(myPart), rCyl(R), rCyl2(R*R), zCyl(Z), bField(B), properDecayTime(1E99) 
{
  init();
}

void 
BaseParticlePropagator::init() {
  
  // The status of the propagation
  success = 0;
  // Propagate only for the first half-loop
  firstLoop = true;
  //
  fiducial = true;
  // The particle has not yet decayed
  decayed = false;
  // The proper time is set to zero
  properTime = 0.;
  // The propagation direction is along the momentum
  propDir = 1;
  //
  debug = false;

}

bool 
BaseParticlePropagator::propagate() { 


  //
  // Check that the particle is not already on the cylinder surface
  //
  double rPos2 = R2();

  if ( onBarrel(rPos2) ) { 
    success = 1;
    return true;
  }
  //
  if ( onEndcap(rPos2) ) { 
    success = 2;
    return true;
  }
  //
  // Treat neutral particles (or no magnetic field) first 
  //
  if ( fabs(charge()) < 1E-12 || bField < 1E-12 ) {

    //
    // First check that the particle crosses the cylinder
    //
    double pT2 = Perp2();
    //    double pT2 = pT*pT;
    //    double b2 = rCyl * pT;
    double b2 = rCyl2 * pT2;
    double ac = fabs ( X()*Py() - Y()*Px() );
    double ac2 = ac*ac;
    //
    // The particle never crosses (or never crossed) the cylinder
    //
    //    if ( ac > b2 ) return false;
    if ( ac2 > b2 ) return false;

    //    double delta  = std::sqrt(b2*b2 - ac*ac);
    double delta  = std::sqrt(b2 - ac2);
    double tplus  = -( X()*Px()+Y()*Py() ) + delta;
    double tminus = -( X()*Px()+Y()*Py() ) - delta;
    //
    // Find the first (time-wise) intersection point with the cylinder
    //

    double solution = tminus < 0 ? tplus/pT2 : tminus/pT2;
    if ( solution < 0. ) return false;
    //
    // Check that the particle does (did) not exit from the endcaps first.
    //
    double zProp = Z() + Pz() * solution;
    if ( fabs(zProp) > zCyl ) {
      tplus  = ( zCyl - Z() ) / Pz();
      tminus = (-zCyl - Z() ) / Pz();
      solution = tminus < 0 ? tplus : tminus;
      if ( solution < 0. ) return false;
      zProp = Z() + Pz() * solution;
      success = 2;
    }
    else {
      success = 1;
    }

    //
    // Check the decay time
    //
    double delTime = propDir * mass() * solution;
    double factor = 1.;
    properTime += delTime;
    if ( properTime > properDecayTime ) {
      factor = 1.-(properTime-properDecayTime)/delTime;
      properTime = properDecayTime;
      decayed = true;
    }

    //
    // Compute the coordinates of the RawParticle after propagation
    //
    double xProp = X() + Px() * solution * factor;
    double yProp = Y() + Py() * solution * factor;
           zProp = Z() + Pz() * solution * factor;
    double tProp = T() + E()  * solution * factor;

    //
    // Last check : Although propagated to the endcaps, R could still be
    // larger than rCyl because the cylinder was too short...
    //
    if ( success == 2 && xProp*xProp+yProp*yProp > rCyl2 ) { 
      success = -1;
      return true;
    }

    //
    // ... and update the particle with its propagated coordinates
    //
    setVertex( XYZTLorentzVector(xProp,yProp,zProp,tProp) );
    
    return true;
  }
  //
  // Treat charged particles with magnetic field next.
  //
  else {
    //
    // First check that the particle can cross the cylinder
    //
    double pT = Pt();
    double radius = helixRadius(pT);
    double phi0 = helixStartPhi();
    double xC = helixCentreX(radius,phi0);
    double yC = helixCentreY(radius,phi0);
    double dist = helixCentreDistToAxis(xC,yC);
    //
    // The helix either is outside or includes the cylinder -> no intersection
    //
    if ( fabs ( fabs(radius) - dist ) > rCyl ) return false;
    //
    // The particle is already away from the endcaps, and will never come back
    // Could be back-propagated, so warn the user that it is so.
    // 
    if ( Z() * Pz() > zCyl * fabs(Pz()) ) { 
      success = -2;
      return true;
    }

    double pZ = Pz();
    double phiProp, zProp;
    //
    // Does the helix cross the cylinder barrel ? If not, do the first half-loop
    //
    double rProp = std::min(fabs(radius)+dist-0.000001, rCyl);

    // Check for rounding errors in the ArcSin.
    double sinPhiProp = 
      (rProp*rProp-radius*radius-dist*dist)/( 2.*dist*radius);
    
    //
    double deltaPhi = 1E99;

    // Taylor development up to third order for large momenta 
    if ( 1.-fabs(sinPhiProp) < 1E-9 ) { 

      double cphi0 = std::cos(phi0);
      double sphi0 = std::sin(phi0);
      double r0 = (X()*cphi0 + Y()*sphi0)/radius;
      double q0 = (X()*sphi0 - Y()*cphi0)/radius;
      double rcyl2 = (rCyl2 - X()*X() - Y()*Y())/(radius*radius);
      double delta = r0*r0 + rcyl2*(1.-q0);

      // This is a solution of a second order equation, assuming phi = phi0 + epsilon
      // and epsilon is small. 
      deltaPhi = radius > 0 ? 
        ( -r0 + std::sqrt(delta ) ) / (1.-q0) :   
        ( -r0 - std::sqrt(delta ) ) / (1.-q0); 
      
    }

    // Use complete calculation otherwise, or if the delta phi is large anyway.
    if ( fabs(deltaPhi) > 1E-3 ) { 

    //    phiProp =  fabs(sinPhiProp) < 0.99999999  ? 
    //      std::asin(sinPhiProp) : M_PI/2. * sinPhiProp;
      phiProp =  std::asin(sinPhiProp);

      //
      // Compute phi after propagation (two solutions, but the asin definition
      // (between -pi/2 and +pi/2) takes care of the wrong one.
      //
      phiProp = helixCentrePhi(xC,yC) + 
        ( inside(rPos2) || onSurface(rPos2) ? phiProp : M_PI-phiProp ); 
      
      //
      // Solve the obvious two-pi ambiguities: more than one turn!
      //
      if ( fabs(phiProp - phi0) > 2.*M_PI )
        phiProp += ( phiProp > phi0 ? -2.*M_PI : +2.*M_PI );
      
      //
      // Check that the phi difference has the right sign, according to Q*B
      // (Another two pi ambuiguity, slightly more subtle)
      //
      if ( (phiProp-phi0)*radius < 0.0 )
        radius > 0.0 ? phiProp += 2 * M_PI : phiProp -= 2 * M_PI;
      
    } else { 

      // Use Taylor
      phiProp = phi0 + deltaPhi;

    }

    //
    // Check that the particle does not exit from the endcaps first.
    //
    zProp = Z() + ( phiProp - phi0 ) * pZ * radius / pT ;
    if ( fabs(zProp) > zCyl ) {

      zProp = zCyl * fabs(pZ)/pZ;
      phiProp = phi0 + (zProp - Z()) / radius * pT / pZ;
      success = 2;

    } else {

      //
      // If the particle does not cross the barrel, either process the
      // first-half loop only or propagate all the way down to the endcaps
      //
      if ( rProp < rCyl ) {

        if ( firstLoop || fabs(pZ)/pT < 1E-10 ) {

          success = 0;

        } else {

          zProp = zCyl * fabs(pZ)/pZ;
          phiProp = phi0 + (zProp - Z()) / radius * pT / pZ;
          success = 2;

        }
      //
      // The particle crossed the barrel 
      // 
      } else {

        success = 1;

      }
    }
    //
    // Compute the coordinates of the RawParticle after propagation
    //
    //
    // Check the decay time
    //
    double delTime = propDir * (phiProp-phi0)*radius*mass() / pT;
    double factor = 1.;
    properTime += delTime;
    if ( properTime > properDecayTime ) {
      factor = 1.-(properTime-properDecayTime)/delTime;
      properTime = properDecayTime;
      decayed = true;
    }

    zProp = Z() + (zProp-Z())*factor;

    phiProp = phi0 + (phiProp-phi0)*factor;

    double sProp = std::sin(phiProp);
    double cProp = std::cos(phiProp);
    double xProp = xC + radius * sProp;
    double yProp = yC - radius * cProp;
    double tProp = T() + (phiProp-phi0)*radius*E()/pT;
    double pxProp = pT * cProp;
    double pyProp = pT * sProp;

    //
    // Last check : Although propagated to the endcaps, R could still be
    // larger than rCyl because the cylinder was too short...
    //
    if ( success == 2 && xProp*xProp+yProp*yProp > rCyl2 ) { 
      success = -1;
      return true;
    }
    //
    // ... and update the particle vertex and momentum
    //
    setVertex( XYZTLorentzVector(xProp,yProp,zProp,tProp) );
    SetXYZT(pxProp,pyProp,pZ,E());
    //    SetPx(pxProp);
    //    SetPy(pyProp);
    return true;
 
  }
}

bool
BaseParticlePropagator::backPropagate() {

  // Backpropagate
  SetXYZT(-Px(),-Py(),-Pz(),E());
  setCharge(-charge());
  propDir = -1;
  bool done = propagate();
  SetXYZT(-Px(),-Py(),-Pz(),E());
  setCharge(-charge());
  propDir = +1;

  return done;
}

BaseParticlePropagator
BaseParticlePropagator::propagated() const {
  // Copy the input particle in a new instance
  BaseParticlePropagator myPropPart(*this);
  // Allow for many loops
  myPropPart.firstLoop=false;
  // Propagate the particle ! 
  myPropPart.propagate();
  // Back propagate if the forward propagation was not a success
  if (myPropPart.success < 0 )
    myPropPart.backPropagate();
  // Return the new instance
  return myPropPart;
}

void 
BaseParticlePropagator::setPropagationConditions(double R, double Z, bool f) { 
  rCyl = R;
  rCyl2 = R*R;
  zCyl = Z;
  firstLoop = f;
}

bool
BaseParticlePropagator::propagateToClosestApproach(double x0, double y0, bool first) {

  // Pre-computed quantities
  double pT = Pt();
  double radius = helixRadius(pT);
  double phi0 = helixStartPhi();

  // The Helix centre coordinates are computed wrt to the z axis
  // Actually the z axis might be centred on 0,0: it's the beam spot position (x0,y0)!
  double xC = helixCentreX(radius,phi0);
  double yC = helixCentreY(radius,phi0);
  double distz = helixCentreDistToAxis(xC-x0,yC-y0);
  double dist0 = helixCentreDistToAxis(xC,yC);

  //
  // Propagation to point of clostest approach to z axis
  //
  double rz,r0,z;
  if ( charge() != 0.0 && bField != 0.0 ) {
    rz = fabs ( fabs(radius) - distz ) + std::sqrt(x0*x0+y0*y0) + 0.0000001;
    r0 = fabs ( fabs(radius) - dist0 ) + 0.0000001;
  } else {
    rz = fabs( Px() * (Y()-y0) - Py() * (X()-x0) ) / Pt(); 
    r0 = fabs( Px() *  Y()     - Py() *  X() ) / Pt(); 
  }

  z = 999999.;

  // Propagate to the first interesection point 
  // with cylinder of radius sqrt(x0**2+y0**2)
  setPropagationConditions(rz , z, first);
  bool done = backPropagate();

  // Unsuccessful propagation - should not happen!
  if ( !done ) return done; 

  // The z axis is (0,0) - no need to go further
  if ( fabs(rz-r0) < 1E-10 ) return done;
  double dist1 = (X()-x0)*(X()-x0) + (Y()-y0)*(Y()-y0);

  // We are already at closest approach - no need to go further
  if ( dist1 < 1E-10 ) return done;

  // Keep for later if it happens to be the right solution
  XYZTLorentzVector vertex1 = vertex();
  XYZTLorentzVector momentum1 = momentum();
  
  // Propagate to the distance of closest approach to (0,0)
  setPropagationConditions(r0 , z, first);
  done = backPropagate();
  if ( !done ) return done; 

  // Propagate to the first interesection point 
  // with cylinder of radius sqrt(x0**2+y0**2)
  setPropagationConditions(rz , z, first);
  done = backPropagate();
  if ( !done ) return done; 
  double dist2 = (X()-x0)*(X()-x0) + (Y()-y0)*(Y()-y0);

  // Keep the good solution.
  if ( dist2 > dist1 ) { 
    setVertex(vertex1);
    SetXYZT(momentum1.X(),momentum1.Y(),momentum1.Z(),momentum1.E());
    dist2 = dist1;
  }

  // Done
  return done;

}

bool
BaseParticlePropagator::propagateToEcal(bool first) {
  //
  // Propagation to Ecal (including preshower) after the
  // last Tracker layer
  // TODO: include proper geometry
  // Geometry taken from CMS ECAL TDR
  //
  // First propagate to global barrel / endcap cylinder 
  //  setPropagationConditions(1290. , 3045 , first);
  //  New position of the preshower as of CMSSW_1_7_X
  setPropagationConditions(129.0 , 303.353 , first);
  return propagate();

}

bool
BaseParticlePropagator::propagateToPreshowerLayer1(bool first) {
  //
  // Propagation to Preshower Layer 1
  // TODO: include proper geometry
  // Geometry taken from CMS ECAL TDR
  //
  // First propagate to global barrel / endcap cylinder 
  //  setPropagationConditions(1290., 3045 , first);
  //  New position of the preshower as of CMSSW_1_7_X
  setPropagationConditions(129.0, 303.353 , first);
  bool done = propagate();

  // Check that were are on the Layer 1 
  if ( done && (R2() > 125.0*125.0 || R2() < 45.0*45.0) ) 
    success = 0;
  
  return done;
}

bool
BaseParticlePropagator::propagateToPreshowerLayer2(bool first) {
  //
  // Propagation to Preshower Layer 2
  // TODO: include proper geometry
  // Geometry taken from CMS ECAL TDR
  //
  // First propagate to global barrel / endcap cylinder 
  //  setPropagationConditions(1290. , 3090 , first);
  //  New position of the preshower as of CMSSW_1_7_X
  setPropagationConditions(129.0 , 307.838 , first);
  bool done = propagate();

  // Check that we are on Layer 2 
  if ( done && (R2() > 125.0*125.0 || R2() < 45.0*45.0 ) )
    success = 0;

  return done;

}

bool
BaseParticlePropagator::propagateToEcalEntrance(bool first) {
  //
  // Propagation to ECAL entrance
  // TODO: include proper geometry
  // Geometry taken from CMS ECAL TDR
  //
  // First propagate to global barrel / endcap cylinder 
  setPropagationConditions(129.0 , 320.9,first);
  bool done = propagate();

  // Go to endcap cylinder in the "barrel cut corner" 
  // eta = 1.479 -> cos^2(theta) = 0.81230
  //  if ( done && eta > 1.479 && success == 1 ) {
  if ( done && cos2ThetaV() > 0.81230 && success == 1 ) {
    setPropagationConditions(152.6 , 320.9, first);
    done = propagate();
  }

  // We are not in the ECAL acceptance
  // eta = 3.0 -> cos^2(theta) = 0.99013
  if ( cos2ThetaV() > 0.99014 ) success = 0;

  return done;
}

bool
BaseParticlePropagator::propagateToHcalEntrance(bool first) {
  //
  // Propagation to HCAL entrance
  // TODO: include proper geometry
  // Geometry taken from CMSSW_3_1_X xml (Sunanda)
  //

  // First propagate to global barrel / endcap cylinder 
  setPropagationConditions(177.5 , 335.0, first);
  propDir = 0;
  bool done = propagate();
  propDir = 1;

  // If went through the bottom of HB cylinder -> re-propagate to HE surface
  if (done && success == 2) {
    setPropagationConditions(300.0, 400.458, first);
    propDir = 0;
    done = propagate();
    propDir = 1;
  }


  // out of the HB/HE acceptance
  // eta = 3.0 -> cos^2(theta) = 0.99014
  if ( done && cos2ThetaV() > 0.99014 ) success = 0;

  return done;
}

bool
BaseParticlePropagator::propagateToVFcalEntrance(bool first) {
  //
  // Propagation to VFCAL entrance
  // TODO: include proper geometry
  // Geometry taken from DAQ TDR Chapter 13

  setPropagationConditions(400.0 , 1110.0, first);
  propDir = 0;
  bool done = propagate();
  propDir = 1;

  if (!done) success = 0;

  // We are not in the VFCAL acceptance
  // eta = 3.0  -> cos^2(theta) = 0.99014
  // eta = 5.2  -> cos^2(theta) = 0.9998755
  double c2teta = cos2ThetaV();
  if ( done && ( c2teta < 0.99014 || c2teta > 0.9998755 ) ) success = 0;

  return done;
}

bool
BaseParticlePropagator::propagateToHcalExit(bool first) {
  //
  // Propagation to HCAL exit
  // TODO: include proper geometry
  // Geometry taken from CMSSW_3_1_X xml (Sunanda)
  //

  // Approximate it to a single cylinder as it is not that crucial.
  setPropagationConditions(263.9 , 554.1, first);
  //  this->rawPart().setCharge(0.0); ?? Shower Propagation ??
  propDir = 0;
  bool done = propagate();
  propDir = 1;

  return done;
}

bool
BaseParticlePropagator::propagateToHOLayer(bool first) {
  //
  // Propagation to Layer0 of HO (Ring-0)
  // TODO: include proper geometry
  // Geometry taken from CMSSW_3_1_X xml (Sunanda)
  //

  // Approximate it to a single cylinder as it is not that crucial.
  setPropagationConditions(387.6, 1000.0, first); //Dia is the middle of HO \sqrt{384.8**2+46.2**2}
  //  setPropagationConditions(410.2, 1000.0, first); //sqrt{406.6**2+54.2**2} //for outer layer
  //  this->rawPart().setCharge(0.0); ?? Shower Propagation ??
  propDir = 0;
  bool done = propagate();
  propDir = 1;
  
  if ( done && abs(Z()) > 700.25) success = 0;
  
  return done;
}


bool
BaseParticlePropagator::propagateToNominalVertex(const XYZTLorentzVector& v) 
{


  // Not implemented for neutrals (used for electrons only)
  if ( charge() == 0. || bField == 0.) return false;

  // Define the proper pT direction to meet the point (vx,vy) in (x,y)
  double dx = X()-v.X();
  double dy = Y()-v.Y();
  double phi = std::atan2(dy,dx) + std::asin ( std::sqrt(dx*dx+dy*dy)/(2.*helixRadius()) );

  // The absolute pT (kept to the original value)
  double pT = pt();

  // Set the new pT
  SetPx(pT*std::cos(phi));
  SetPy(pT*std::sin(phi));

  return propagateToClosestApproach(v.X(),v.Y());
  
}

bool
BaseParticlePropagator::propagateToBeamCylinder(const XYZTLorentzVector& v, double radius) 
{

  // For neutral (or BField = 0, simply check that the track passes through the cylinder
  if ( charge() == 0. || bField == 0.) 
    return fabs( Px() * Y() - Py() * X() ) / Pt() < radius; 

  // Now go to the charged particles

  // A few needed intermediate variables (to make the code understandable)
  // The inner cylinder
  double r = radius;
  double r2 = r*r;
  double r4 = r2*r2;
  // The two hits
  double dx = X()-v.X();
  double dy = Y()-v.Y();
  double dz = Z()-v.Z();
  double Sxy = X()*v.X() + Y()*v.Y();
  double Dxy = Y()*v.X() - X()*v.Y();
  double Dxy2 = Dxy*Dxy;
  double Sxy2 = Sxy*Sxy;
  double SDxy = dx*dx + dy*dy;
  double SSDxy = std::sqrt(SDxy);
  double ATxy = std::atan2(dy,dx);
  // The coefficients of the second order equation for the trajectory radius
  double a = r2 - Dxy2/SDxy;
  double b = r * (r2 - Sxy);
  double c = r4 - 2.*Sxy*r2 + Sxy2 + Dxy2;

  // Here are the four possible solutions for
  // 1) The trajectory radius
  std::vector<double> helixRs(4,static_cast<double>(0.));
  helixRs[0] = (b - std::sqrt(b*b - a*c))/(2.*a); 
  helixRs[1] = (b + std::sqrt(b*b - a*c))/(2.*a); 
  helixRs[2] = -helixRs[0]; 
  helixRs[3] = -helixRs[1]; 
  // 2) The azimuthal direction at the second point
  std::vector<double> helixPhis(4,static_cast<double>(0.));
  helixPhis[0] = std::asin ( SSDxy/(2.*helixRs[0]) );
  helixPhis[1] = std::asin ( SSDxy/(2.*helixRs[1]) );
  helixPhis[2] = -helixPhis[0];
  helixPhis[3] = -helixPhis[1];
  // Only two solutions are valid though
  double solution1=0.;
  double solution2=0.;
  double phi1=0.;
  double phi2=0.;
  // Loop over the four possibilities
  for ( unsigned int i=0; i<4; ++i ) {
    helixPhis[i] = ATxy + helixPhis[i];
    // The centre of the helix
    double xC = helixCentreX(helixRs[i],helixPhis[i]);
    double yC = helixCentreY(helixRs[i],helixPhis[i]);
    // The distance of that centre to the origin
    double dist = helixCentreDistToAxis(xC, yC);
    /*
    std::cout << "Solution "<< i << " = " << helixRs[i] << " accepted ? " 
              << fabs(fabs(helixRs[i]) - dist ) << " - " << radius << " = " 
              << fabs(fabs(helixRs[i]) - dist ) - fabs(radius) << " " 
              << ( fabs( fabs(fabs(helixRs[i]) - dist) -fabs(radius) ) < 1e-6)  << std::endl;
    */
    // Check that the propagation will lead to a trajectroy tangent to the inner cylinder
    if ( fabs( fabs(fabs(helixRs[i]) - dist) -fabs(radius) ) < 1e-6 ) { 
      // Fill first solution
      if ( solution1 == 0. ) { 
        solution1 = helixRs[i];
        phi1 = helixPhis[i];
      // Fill second solution (ordered)
      } else if ( solution2 == 0. ) {
        if ( helixRs[i] < solution1 ) {
          solution2 = solution1;
          solution1 = helixRs[i];
          phi2 = phi1;
          phi1 = helixPhis[i];
        } else {
          solution2 = helixRs[i];
          phi2 = helixPhis[i];
        }
      // Must not happen! 
      } else { 
        std::cout << "warning !!! More than two solutions for this track !!! " << std::endl;
      }
    }
  }

  // Find the largest possible pT compatible with coming from within the inne cylinder
  double pT = 0.;
  double helixPhi = 0.;
  double helixR = 0.;
  // This should not happen
  if ( solution1*solution2 == 0. ) { 
    std::cout << "warning !!! Less than two solution for this track! " 
              << solution1 << " " << solution2 << std::endl;
    return false;
  // If the two solutions have opposite sign, it means that pT = infinity is a possibility.
  } else if ( solution1*solution2 < 0. ) { 
    pT = 1000.;
    double norm = pT/SSDxy;
    setCharge(+1.);
    SetXYZT(dx*norm,dy*norm,dz*norm,0.);
    SetE(std::sqrt(Vect().Mag2()));
  // Otherwise take the solution that gives the largest transverse momentum 
  } else { 
    if (solution1<0.) { 
      helixR   = solution1;
      helixPhi = phi1;
      setCharge(+1.);
    } else {
      helixR = solution2;
      helixPhi = phi2;
      setCharge(-1.);
    }
    pT = fabs(helixR) * 1e-5 * c_light() *bField;
    double norm = pT/SSDxy;
    SetXYZT(pT*std::cos(helixPhi),pT*std::sin(helixPhi),dz*norm,0.);
    SetE(std::sqrt(Vect().Mag2()));      
  }
    
  // Propagate to closest approach to get the Z value (a bit of an overkill)
  return propagateToClosestApproach();
  
}

double 
BaseParticlePropagator::xyImpactParameter(double x0, double y0) const {

  double ip=0.;
  double pT = Pt();

  if ( charge() != 0.0 && bField != 0.0 ) {
    double radius = helixRadius(pT);
    double phi0 = helixStartPhi();
    
    // The Helix centre coordinates are computed wrt to the z axis
    double xC = helixCentreX(radius,phi0);
    double yC = helixCentreY(radius,phi0);
    double distz = helixCentreDistToAxis(xC-x0,yC-y0);
    ip = distz - fabs(radius);
  } else {
    ip = fabs( Px() * (Y()-y0) - Py() * (X()-x0) ) / pT; 
  }

  return ip;

}