Contains stepper and energy loss/noise matrix calculation. More...

#include <EicRoot/blob/master/GenfitTools/trackrep/RKTrackRep/GFMaterialEffects.h>

Inheritance diagram for GFMaterialEffects:

Collaboration diagram for GFMaterialEffects:

Public Member Functions
void	setNoEffects (bool opt=true)

void	setEnergyLossBetheBloch (bool opt=true)

void	setNoiseBetheBloch (bool opt=true)

void	setNoiseCoulomb (bool opt=true)

void	setEnergyLossBrems (bool opt=true)

void	setNoiseBrems (bool opt=true)

void	setMscModel (const std::string &modelName)
	Select the multiple scattering model that will be used during track fit. At the moment two model are available GEANE and Highland. GEANE is the model was was present in Genfit first. Note that using this function has no effect if setNoiseCoulomb(false) is set.

double	effects (const std::vector< GFPointPath > &points, const double &mom, const int &pdg, double &xx0, const bool &doNoise=false, double noise7x7=NULL, const double jacobian7x7=NULL, const TVector3 directionBefore=NULL, const TVector3 directionAfter=NULL)
	Calculates energy loss in the travelled path, optional calculation of noise matrix.

double	stepper (const double &maxStep, const double &maxAngleStep, const double &posx, const double &posy, const double &posz, const double &dirx, const double &diry, const double &dirz, const double &mom, double &relMomLoss, const int &pdg)
	Returns maximum length so that a specified momentum loss will not be exceeded.

	ClassDef (GFMaterialEffects, 2)
	depending on this number a specific msc model is chosen in the noiseCoulomb function.

Static Public Member Functions
static GFMaterialEffects *	getInstance ()

static void	destruct ()

Private Member Functions
	GFMaterialEffects ()

virtual	~GFMaterialEffects ()

void	getParticleParameters (double mom)
	sets fcharge, fmass and calculates fbeta, fgamma, fgammasquare;

void	getMaterialParameters (TGeoMaterial *mat)
	sets fmatDensity, fmatZ, fmatA, fradiationLength, fmEE;

double	energyLossBetheBloch (const double &mom)
	Returns energy loss.

void	noiseBetheBloch (const double &mom, double *noise) const
	calculation of energy loss straggeling

void	noiseCoulomb (const double &mom, double noise, const double jacobian, const TVector3 directionBefore, const TVector3 directionAfter) const
	calculation of multiple scattering

double	energyLossBrems (const double &mom) const
	Returns energy loss.

void	noiseBrems (const double &mom, double *noise) const
	calculation of energy loss straggeling

Private Attributes
bool	fNoEffects

bool	fEnergyLossBetheBloch

bool	fNoiseBetheBloch

bool	fNoiseCoulomb

bool	fEnergyLossBrems

bool	fNoiseBrems

const double	me

double	fstep

double	fbeta

double	fdedx

double	fgamma

double	fgammaSquare

double	fmatDensity

double	fmatZ

double	fmatA

double	fradiationLength

double	fmEE

int	fpdg

double	fcharge

double	fmass

int	fMscModelCode

Static Private Attributes
static GFMaterialEffects *	finstance = NULL

Detailed Description

Contains stepper and energy loss/noise matrix calculation.

Author: Christian Höppner (Technische Universität München, original author); Sebastian Neubert (Technische Universität München, original author); Johannes Rauch (Technische Universität München, author)

It provides functionality to limit the stepsize of an extrapolation in order not to exceed a specified maximum momentum loss. After propagation, the energy loss for the given length and (optionally) the noise matrix can be calculated. You have to set which energy-loss and noise mechanisms you want to use. At the moment, per default all energy loss and noise options are ON.

Definition at line 49 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 49 of file GFMaterialEffects.h

Constructor & Destructor Documentation

GFMaterialEffects::GFMaterialEffects ( )

private

Definition at line 45 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 45 of file GFMaterialEffects.cxx

Referenced by getInstance().

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GFMaterialEffects::~GFMaterialEffects ( )

privatevirtual

Definition at line 68 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 68 of file GFMaterialEffects.cxx

Member Function Documentation

GFMaterialEffects::ClassDef	(	GFMaterialEffects	,
		2
	)

depending on this number a specific msc model is chosen in the noiseCoulomb function.

void GFMaterialEffects::destruct ( )

static

Definition at line 78 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 78 of file GFMaterialEffects.cxx

References finstance.

double GFMaterialEffects::effects	(	const std::vector< GFPointPath > &	points,
		const double &	mom,
		const int &	pdg,
		double &	xx0,
		const bool &	doNoise = `false`,
		double *	noise7x7 = `NULL`,
		const double *	jacobian7x7 = `NULL`,
		const TVector3 *	directionBefore = `NULL`,
		const TVector3 *	directionAfter = `NULL`
	)

Calculates energy loss in the travelled path, optional calculation of noise matrix.

Definition at line 101 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 101 of file GFMaterialEffects.cxx

References energyLossBetheBloch(), energyLossBrems(), fEnergyLossBetheBloch, fEnergyLossBrems, fmatZ, fNoEffects, fNoiseBetheBloch, fNoiseBrems, fNoiseCoulomb, fpdg, fradiationLength, fstep, getMaterialParameters(), getParticleParameters(), noiseBetheBloch(), noiseBrems(), noiseCoulomb(), pdg, and Acts::Test::step().

Referenced by RKTrackRep::Extrap().

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double GFMaterialEffects::energyLossBetheBloch ( const double & mom )

private

Returns energy loss.

Uses Bethe Bloch formula to calculate energy loss. Calcuates and sets fdedx which needed also for noiseBetheBloch. Therefore it is not a const function!

Definition at line 276 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 276 of file GFMaterialEffects.cxx

References fbeta, fcharge, fdedx, fgammaSquare, fmass, fmatA, fmatDensity, fmatZ, fmEE, fstep, me, and charm_jet_coverage::mom.

Referenced by effects(), and stepper().

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double GFMaterialEffects::energyLossBrems ( const double & mom ) const

private

Returns energy loss.

Can be called with any pdg, but only calculates energy loss for electrons and positrons (otherwise returns 0). Uses a gaussian approximation (Bethe-Heitler formula with Migdal corrections). For positrons the energy loss is weighed with a correction factor.

Definition at line 485 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 485 of file GFMaterialEffects.cxx

References starlightConstants::AA, Acts::UnitConstants::C, starlightConstants::ETA, fbeta, fmass, fmatA, fmatDensity, fmatZ, fpdg, fstep, I, M_PI, me, charm_jet_coverage::mom, and T.

Referenced by effects(), and stepper().

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GFMaterialEffects * GFMaterialEffects::getInstance ( )

static

Definition at line 72 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 72 of file GFMaterialEffects.cxx

References finstance, and GFMaterialEffects().

Referenced by RKTrackRep::estimateStep(), and RKTrackRep::Extrap().

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void GFMaterialEffects::getMaterialParameters ( TGeoMaterial * mat )

private

sets fmatDensity, fmatZ, fmatA, fradiationLength, fmEE;

Definition at line 247 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 247 of file GFMaterialEffects.cxx

References fmatA, fmatDensity, fmatZ, fmEE, fradiationLength, and MeanExcEnergy_get().

Referenced by effects(), and stepper().

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void GFMaterialEffects::getParticleParameters ( double mom )

private

sets fcharge, fmass and calculates fbeta, fgamma, fgammasquare;

Definition at line 257 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 257 of file GFMaterialEffects.cxx

References fbeta, fcharge, fgamma, fgammaSquare, fmass, fpdg, and part.

Referenced by effects(), and stepper().

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void GFMaterialEffects::noiseBetheBloch	(	const double &	mom,
		double *	noise
	)		const

private

calculation of energy loss straggeling

For the energy loss straggeling, different formulas are used for different regions:

Vavilov-Gaussian regime
Urban/Landau approximation
truncated Landau distribution
Urban model

Needs fdedx, which is calculated in energyLossBetheBloch, so it has to be called afterwards!

Definition at line 300 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 300 of file GFMaterialEffects.cxx

References starlightConstants::alpha, f2(), fbeta, fcharge, fdedx, fgamma, fgammaSquare, fmass, fmatA, fmatDensity, fmatZ, fstep, I, and me.

Referenced by effects().

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void GFMaterialEffects::noiseBrems	(	const double &	mom,
		double *	noise
	)		const

private

calculation of energy loss straggeling

Can be called with any pdg, but only calculates straggeling for electrons and positrons.

Definition at line 646 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 646 of file GFMaterialEffects.cxx

References fmass, fpdg, fradiationLength, and fstep.

Referenced by effects().

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void GFMaterialEffects::noiseCoulomb	(	const double &	mom,
		double *	noise,
		const double *	jacobian,
		const TVector3 *	directionBefore,
		const TVector3 *	directionAfter
	)		const

private

calculation of multiple scattering

With the calculated multiple scattering angle, two noise matrices are calculated:

with respect to #directionBefore: #noiseBefore, which is then propagated with the jacobian
with respect to #directionAfter: #noiseAfter The mean value of these two matrices is added to the noise matrix #noise. This method gives better results than either calculating only noiseBefore or noiseAfter.

This is a detailed description of the mathematics involved:

We define a local coordinate system cs' with initial momentum in z-direction:

$\left(\begin{array}{c} x'\\ y'\\ z'\\ a_{x}'\\ a_{y}'\\ a_{z}'\\ \frac{q}{p}'\end{array}\right)=\left(\begin{array}{ccccccc} \cos\psi & \sin\psi & 0\\ -\cos\vartheta\sin\psi & \cos\vartheta\cos\psi & \sin\psi\\ \sin\vartheta\sin\psi & -\sin\vartheta\cos\psi & \cos\vartheta\\ & & & \cos\psi & \sin\psi & 0\\ & & & -\cos\vartheta\sin\psi & \cos\vartheta\cos\psi & \sin\psi\\ & & & \sin\vartheta\sin\psi & -\sin\vartheta\cos\psi & \cos\vartheta\\ & & & & & & 1\end{array}\right)\left(\begin{array}{c} x\\ y\\ z\\ a_{x}\\ a_{y}\\ a_{z}\\ \frac{q}{p}\end{array}\right)=R^{T}\left(\begin{array}{c} x\\ y\\ z\\ a_{x}\\ a_{y}\\ a_{z}\\ \frac{q}{p}\end{array}\right)$

Now the global coordinate system cs is:

$\left(\begin{array}{c} x\\ y\\ z\\ a_{x}\\ a_{y}\\ a_{z}\\ \frac{q}{p}\end{array}\right)=\left(\begin{array}{ccccccc} \cos\psi & -\cos\vartheta\sin\psi & \sin\vartheta\sin\psi\\ \sin\psi & \cos\vartheta\cos\psi & -\sin\vartheta\cos\psi\\ 0 & \sin\psi & \cos\vartheta\\ & & & \cos\psi & -\cos\vartheta\sin\psi & \sin\vartheta\sin\psi\\ & & & \sin\psi & \cos\vartheta\cos\psi & -\sin\vartheta\cos\psi\\ & & & 0 & \sin\psi & \cos\vartheta\\ & & & & & & 1\end{array}\right)\left(\begin{array}{c} x'\\ y'\\ z'\\ a_{x}'\\ a_{y}'\\ a_{z}'\\ \frac{q}{p}'\end{array}\right)=R\left(\begin{array}{c} x'\\ y'\\ z'\\ a_{x}'\\ a_{y}'\\ a_{z}'\\ \frac{q}{p}'\end{array}\right)$

with the Euler angles

$\begin{eqnarray*} \psi & = & \begin{cases} \begin{cases} \frac{\pi}{2} & a_{x} \geq 0 \\ \frac{3\pi}{2} & a_{x} < 0 \end{cases} & a_{y}=0 \mbox{ resp. } |a_{y}|<10^{-14} \\ - \arctan \frac{a_{x}}{a_{y}} & a_{y} < 0 \\ \pi - \arctan \frac{a_{x}}{a_{y}} & a_{y} > 0 \end{cases} \\ \vartheta & = & \arccos a_{z} \end{eqnarray*}$

$M$ is the multiple scattering error-matrix in the $\theta$ coordinate system. $\theta_{1/2}=0$ are the multiple scattering angles. There is only an error in direction (which later leads to an error in position, when $N_{before}$ is propagated with $T$ ).

$M=\left(\begin{array}{cc} \sigma^{2} & 0\\ 0 & \sigma^{2}\end{array}\right)$

This translates into the noise matrix $\overline{M}$ in the local cs' via jacobian J. The mean scattering angle is always 0, this means that $\theta_{1/2}=0$ ):

$\begin{eqnarray*} x' & = & x'\\ y' & = & y'\\ z' & = & z'\\ a_{x}' & = & \sin\theta_{1}\\ a_{y}' & = & \sin\theta_{2}\\ a_{z}' & = & \sqrt{1-\sin^{2}\theta_{1}-\sin^{2}\theta_{2}}\\ \frac{q}{p}' & = & \frac{q}{p}'\end{eqnarray*}$

$M=\left(\begin{array}{cc} \sigma^{2} & 0\\ 0 & \sigma^{2}\end{array}\right)$

$J=\frac{\partial\left(x',y',z',a_{x}',a_{y}',a_{z}',\frac{q}{p}'\right)}{\partial\left(\theta_{1},\theta_{2}\right)}$

$J=\left(\begin{array}{cc} 0 & 0\\ 0 & 0\\ 0 & 0\\ \cos\theta_{1} & 0\\ 0 & \cos\theta_{2}\\ -\frac{\cos\theta_{1}\sin\theta_{1}}{\sqrt{\cos^{2}\theta_{1}-\sin^{2}\theta_{2}}} & -\frac{\cos\theta_{2}\sin\theta_{2}}{\sqrt{\cos^{2}\theta_{1}-\sin^{2}\theta_{2}}}\\ 0 & 0\end{array}\right) \overset{\theta_{1/2}=0}{=} \left(\begin{array}{cc} 0 & 0\\ 0 & 0\\ 0 & 0\\ 1 & 0\\ 0 & 1\\ 0 & 0\\ 0 & 0\end{array}\right)$

$\overline{M}=J\: M\: J^{T}=\left(\begin{array}{ccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & \sigma^{2} & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & \sigma^{2} & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\end{array}\right)$

The following transformation brings the noise matrix into the global coordinate system cs, resulting in $N$ :

$N=R\overline{M}R^{T}=\sigma^{2}\left(\begin{array}{ccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & \cos^{2}\psi+\cos^{2}\theta-\cos^{2}\theta\cos^{2}\psi & \cos\psi\sin\psi\sin^{2}\theta & -\cos\theta\sin\psi\sin\theta & 0\\ 0 & 0 & 0 & \cos\psi\sin\psi\sin^{2}\theta & \sin^{2}\psi+\cos^{2}\theta\cos^{2}\psi & \cos\theta\cos\psi\sin\theta & 0\\ 0 & 0 & 0 & -\cos\theta\sin\psi\sin\theta & \cos\theta\cos\psi\sin\theta & \sin^{2}\theta & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0\end{array}\right)$

Now two $N$ are calculated: $N_{before}$ (at the start point, with initial direction #directionBefore) and $N_{after}$ (at the final point, with direction #directionAfter). $N_{before}$ is the propagated with the #jacobian of extrapolation $T$ . The new covariance matrix with multiple scattering in global cs is:

$\begin{eqnarray*} C_{new} & = C_{old} + 0.5 \cdot T N_{before} T^{T} + 0.5 \cdot N_{after} \end{eqnarray*}$

See also: Track following in dense media and inhomogeneous magnetic fields, A.Fontana, P.Genova, L.Lavezzi and A.Rotondi; PANDA Report PV/01-07

Definition at line 362 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 362 of file GFMaterialEffects.cxx

References cos(), fbeta, fcharge, fmatZ, fMscModelCode, fradiationLength, fstep, M_PI, and charm_jet_coverage::mom.

Referenced by effects().

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void GFMaterialEffects::setEnergyLossBetheBloch ( bool opt = true )

inline

Definition at line 62 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 62 of file GFMaterialEffects.h

References fEnergyLossBetheBloch, and fNoEffects.

void GFMaterialEffects::setEnergyLossBrems ( bool opt = true )

inline

Definition at line 65 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 65 of file GFMaterialEffects.h

References fEnergyLossBrems, and fNoEffects.

void GFMaterialEffects::setMscModel ( const std::string & modelName )

Select the multiple scattering model that will be used during track fit. At the moment two model are available GEANE and Highland. GEANE is the model was was present in Genfit first. Note that using this function has no effect if setNoiseCoulomb(false) is set.

Definition at line 86 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 86 of file GFMaterialEffects.cxx

References fMscModelCode, and GFException::setFatal().

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void GFMaterialEffects::setNoEffects ( bool opt = true )

inline

Definition at line 60 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 60 of file GFMaterialEffects.h

References fNoEffects.

void GFMaterialEffects::setNoiseBetheBloch ( bool opt = true )

inline

Definition at line 63 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 63 of file GFMaterialEffects.h

References fNoEffects, and fNoiseBetheBloch.

void GFMaterialEffects::setNoiseBrems ( bool opt = true )

inline

Definition at line 66 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 66 of file GFMaterialEffects.h

References fNoEffects, and fNoiseBrems.

void GFMaterialEffects::setNoiseCoulomb ( bool opt = true )

inline

Definition at line 64 of file GFMaterialEffects.h.

View newest version in sPHENIX GitHub at line 64 of file GFMaterialEffects.h

References fNoEffects, and fNoiseCoulomb.

double GFMaterialEffects::stepper	(	const double &	maxStep,
		const double &	maxAngleStep,
		const double &	posx,
		const double &	posy,
		const double &	posz,
		const double &	dirx,
		const double &	diry,
		const double &	dirz,
		const double &	mom,
		double &	relMomLoss,
		const int &	pdg
	)

Returns maximum length so that a specified momentum loss will not be exceeded.

The stepper returns the maximum length that the particle may travel, so that a specified relative momentum loss will not be exceeded, or the next material boundary is reached. The material crossed are stored together with their stepsizes.

Definition at line 173 of file GFMaterialEffects.cxx.

View newest version in sPHENIX GitHub at line 173 of file GFMaterialEffects.cxx

References energyLossBetheBloch(), energyLossBrems(), fEnergyLossBetheBloch, fEnergyLossBrems, fmatZ, fNoEffects, fpdg, fstep, getMaterialParameters(), getParticleParameters(), charm_jet_coverage::mom, and pdg.