HelixUtils Class Reference

utility for helix<->x,p conversions More...

#include <HelixUtils.h>

Public Types
enum	VertexCoor {   iX = 0 ,   iY ,   iZ ,   iPx ,   iPy ,   iPz }
	Parameters of the vertex
enum	HelixCoor {   iD0 = 0 ,   iPhi0 ,   iOmega ,   iZ0 ,   iTanLambda ,   iArcLength2D }
	Parameters of the helix.

Static Public Member Functions
static void	helixFromVertexNumerical (const Eigen::Matrix< double, 3, 1 > &position, const Eigen::Matrix< double, 3, 1 > &momentum, int charge, double Bz, Belle2::Helix &helix, double &flt, Eigen::Matrix< double, 5, 6 > &jacobian)
	get helix from a vertex
static void	getJacobianToCartesianFrameworkHelix (Eigen::Matrix< double, 5, 6 > &jacobian, const double x, const double y, const double z, const double px, const double py, const double pz, const double bfield, const double charge)
	get the jacobian dh={helix pars}/dx={x,y,z,px,py,pz} for the implementation of the framework helix. More...
static void	getHelixAndJacobianFromVertexNumerical (const Eigen::Matrix< double, 1, 6 > &positionAndMom, int charge, double Bz, Belle2::Helix &helix, Eigen::Matrix< double, 5, 6 > &jacobian)
	get helix and jacobian from a vertex
static void	getJacobianFromVertexNumerical (const Eigen::Matrix< double, 1, 6 > &positionAndMom, int charge, double Bz, const Belle2::Helix &helix, Eigen::Matrix< double, 5, 6 > &jacobian, double delta=1e-5)
	get jacobian from a vertex
static void	helixFromVertex (const Eigen::Matrix< double, 1, 6 > &positionAndMomentum, int charge, double Bz, Belle2::Helix &helix, double &L, Eigen::Matrix< double, 5, 6 > &jacobian)
	vertex --> helix
static void	vertexFromHelix (const Belle2::Helix &helix, double L, double Bz, ROOT::Math::XYZVector &position, ROOT::Math::XYZVector &momentum, int &charge)
	helix --> vertex
static std::string	helixParName (int i)
	map of the helix parameters by list index
static std::string	vertexParName (int i)
	map of the vertex parameters by list index
static void	printVertexPar (const Belle2::B2Vector3D &position, const Belle2::B2Vector3D &momentum, int charge)
	Print the vertex parameters.
static double	helixPoca (const Belle2::Helix &helix1, const Belle2::Helix &helix2, double &flt1, double &flt2, Belle2::B2Vector3D &vertex, bool parallel=false)
	POCA between two tracks.
static double	helixPoca (const Belle2::Helix &helix, const Belle2::B2Vector3D &point, double &flt)
	POCA between a track and a point.
static double	phidomain (const double phi)
	the domain of phi

Detailed Description

utility for helix<->x,p conversions

Definition at line 20 of file HelixUtils.h.

Member Function Documentation

getJacobianToCartesianFrameworkHelix()

void getJacobianToCartesianFrameworkHelix ( Eigen::Matrix< double, 5, 6 > &  jacobian, const double  x, const double  y, const double  z, const double  px, const double  py, const double  pz, const double  bfield, const double  charge  )

static

get the jacobian dh={helix pars}/dx={x,y,z,px,py,pz} for the implementation of the framework helix.

WARNING only valid right after initialisation!

Definition at line 407 of file HelixUtils.cc.

  {
    const double alpha = 1.0 / (bfield * Belle2::Const::speedOfLight) * 1E4;
    const double aq = charge / alpha;
 
    const double pt = std::hypot(px, py);
    const double pt2 = pt * pt;
    const double pt3 = pt2 * pt;
    const double aq2 = aq * aq;
 
    const double x2 = x * x;
    const double y2 = y * y;
    const double r  = x2 + y2;
 
    const double px2 = px * px;
    const double py2 = py * py;
 
    const double px0 = px - aq * y;
    const double py0 = py + aq * x;
 
    const double pt02 = px0 * px0 + py0 * py0;
    const double pt0 = std::sqrt(pt02);
    double sqrt13 = pt0 / pt;
 
    // D d0 / Dx_i
    jacobian(0, 0) = py0 / pt0;
    jacobian(0, 1) = -px0 / pt0;
    jacobian(0, 2) = 0;
    jacobian(0, 3) = (-(y * (aq2 * r + 2 * aq * py * x + 2 * py2 * (1 + sqrt13))) - px * (2 * py * x * (1 + sqrt13) + aq * (y2 *
                      (-1 + sqrt13) + x2 * (1 + sqrt13)))) /
                     (pt2 * pt0 * (1 + sqrt13) * (1 + sqrt13));
 
    jacobian(0, 4) = (2 * px2 * x * (1 + sqrt13) + 2 * px * y * (py - aq * x + py * sqrt13) + aq * (aq * r * x - py * (x2 *
                      (-1 + sqrt13) + y2 * (1 + sqrt13)))) /
                     (pt2 * pt0 * (1 + sqrt13) * (1 + sqrt13));
    jacobian(0, 5) = 0;
 
    // D phi0 / Dx_i0;
    jacobian(1, 0) = aq * px0 / pt02;
    jacobian(1, 1) = aq * py0 / pt02;
    jacobian(1, 2) = 0;
    jacobian(1, 3) = -py0 / pt02;
    jacobian(1, 4) = px0 / pt02;
    jacobian(1, 5) = 0;
 
    // D omega / Dx_i
    jacobian(2, 0) = 0;
    jacobian(2, 1) = 0;
    jacobian(2, 2) = 0;
    jacobian(2, 3) = - aq * px / pt3;
    jacobian(2, 4) = - aq * py / pt3;
    jacobian(2, 5) = 0;
 
    // D z0 / Dx_i
    jacobian(3, 0) = -pz * px0 / pt02;
    jacobian(3, 1) = -pz * py0 / pt02;
    jacobian(3, 2) = 1;
    jacobian(3, 3) = (pz * (px2 * x - py * (aq * r + py * x) + 2 * px * py * y)) / (pt2 * pt02);
    jacobian(3, 4) = (pz * (px * (aq * r + 2 * py * x) - px2 * y + py2 * y)) / (pt2 * pt02);
    jacobian(3, 5) = std::atan2(-(aq * (px * x + py * y)), (px2 + py * py0 - aq * px * y)) / aq; //pt on num. and denom cancels.
 
    // D tan lambda / Dx_i
    jacobian(4, 0) = 0;
    jacobian(4, 1) = 0;
    jacobian(4, 2) = 0;
    jacobian(4, 3) = -pz * px / pt3;
    jacobian(4, 4) = -pz * py / pt3;
    jacobian(4, 5) = 1. / pt;
  }

---

The documentation for this class was generated from the following files:

• analysis/VertexFitting/TreeFitter/include/HelixUtils.h
• analysis/VertexFitting/TreeFitter/src/HelixUtils.cc