Parametrization of delta-ray PDF in pixels of single module. More...

#include <DeltaRayPDF.h>

Classes
struct	GausXY
	Normal (Gaussian) distribution: an entry for the table. More...

Public Member Functions
	DeltaRayPDF (int moduleID)
	Class constructor.

void	prepare (const TOPTrack &track, const Const::ChargedStable &hypothesis)
	Prepare the object.

int	getModuleID () const
	Returns slot ID.

double	getNumPhotons () const
	Returns number of photons.

double	getFraction () const
	Returns fraction of delta-ray photons in the time window.

double	getPDFValue (int pixelID, double time) const
	Returns PDF value at given time and pixel.

double	getPDFValue (double time, double dt0=0, double acc=1) const
	Returns PDF value at given time and integrated over all pixels.

double	getIntegral (double minTime, double maxTime) const
	Returns integral of PDF from minTime to maxTime.

Private Member Functions
double	angularDistr (double kz) const
	Angular distribution of photons from delta rays w/ total reflection requirement.

double	timeDistr (double t, double t0) const
	Time distribution of photons from delta rays (normalized).

double	smearedTimeDistr (double t, double t0) const
	Smeared time distribution of photons from delta rays (normalized).

double	peakFraction (double tmin, double tmax, double t0) const
	Fraction of delta-ray photons within given propagation time interval for single peak at t0.

double	totalFraction (double tmin, double tmax) const
	Total fraction of delta-ray photons within given propagation time interval.

double	directFraction (double z) const
	Fraction of direct photons from delta-rays, e.g direct/(direct+reflected)

double	photonYield (double beta, int PDGCode) const
	Photon yield from delta-rays per track length in quartz for nominal photon detection efficiency.

Private Attributes
int	m_moduleID
	slot ID

const BackgroundPDF *	m_background = 0
	background PDF

const PixelPositions *	m_pixelPositions = 0
	pixel positions

double	m_zD = 0
	detector (photo-cathode) position in z

double	m_zM = 0
	spherical mirror position in z

double	m_phaseIndex = 0
	phase refractive index

double	m_groupIndex = 0
	group refractive index

double	m_dispersion = 0
	dispersion coefficient

double	m_angularNorm = 0
	angular distribution normalization constant

std::vector< double >	m_norms
	relative angular distribution normalization constants (cumulative)

std::vector< GausXY >	m_tableGaus
	table of normal (Gaussian) distribution

double	m_xE = 0
	average photon emission position in x

double	m_yE = 0
	average photon emission position in y

double	m_zE = 0
	average photon emission position in z

double	m_dirFrac = 0
	fraction of direct photons

double	m_dirT0 = 0
	minimal propagation time of direct photons

double	m_reflT0 = 0
	minimal propagation time of reflected photons

double	m_TOF = 0
	time-of-flight of particle

double	m_fraction = 0
	fraction of delta-ray photons within time window

double	m_numPhotons = 0
	number of photons

std::vector< double >	m_pixelAcceptances
	pixel angular acceptances for direct peak (index = pixelID - 1)

Detailed Description

Parametrization of delta-ray PDF in pixels of single module.

Definition at line 27 of file DeltaRayPDF.h.

Constructor & Destructor Documentation

◆ DeltaRayPDF()

DeltaRayPDF ( int moduleID )

explicit

Class constructor.

Parameters

moduleID slot ID

Definition at line 24 of file DeltaRayPDF.cc.

                                        :
      m_moduleID(moduleID), m_background(TOPRecoManager::getBackgroundPDF(moduleID))
    {
      if (not m_background) {
        B2ERROR("TOP::DeltaRayPDF: background PDF not found");
        return;
      }
 
      const auto* yScanner = TOPRecoManager::getYScanner(moduleID);
      if (not yScanner) {
        B2ERROR("TOP::DeltaRayPDF: YScanner not found");
        return;
      }
 
      m_pixelPositions = &(yScanner->getPixelPositions());
 
      m_zD = yScanner->getPrism().zD;
      m_zM = yScanner->getBars().back().zR;
      double meanE = yScanner->getMeanEnergyBeta1();
      double sigE = yScanner->getRMSEnergyBeta1();
      m_phaseIndex = TOPGeometryPar::Instance()->getPhaseIndex(meanE);
      m_groupIndex = TOPGeometryPar::Instance()->getGroupIndex(meanE);
      double dng_de = TOPGeometryPar::Instance()->getGroupIndexDerivative(meanE);
      m_dispersion = dng_de / m_groupIndex * sigE;
 
      const int N = 1000;
      double dkz = 1.0 / N;
      m_norms.push_back(0);
      for (int i = 0; i < N; i++) {
        double kz = (i + 0.5) * dkz;
        m_angularNorm += angularDistr(kz) * dkz;
        m_norms.push_back(m_angularNorm);
      }
      for (auto& norm : m_norms) norm /= m_angularNorm;
 
      const int Np = 101;
      double dx = 6.0 / (Np - 1);
      for (int i = 0; i < Np; i++) {
        double x = i * dx - 3.0;
        m_tableGaus.push_back(GausXY(x));
      }
      double sum = 0;
      for (const auto& gaus : m_tableGaus) sum += gaus.y;
      for (auto& gaus : m_tableGaus) gaus.y /= sum;
    }

Member Function Documentation

◆ angularDistr()

double angularDistr ( double kz ) const

inlineprivate

Angular distribution of photons from delta rays w/ total reflection requirement.

Distribution is not normalized.

Parameters

kz	z-component of photon direction

Returns: distribution value

Definition at line 190 of file DeltaRayPDF.h.

    {
      if (std::abs(kz) < 1 / m_phaseIndex) {
        double x = sqrt((1 - 1 / pow(m_phaseIndex, 2)) / (1 - pow(kz, 2)));
        return 1 - acos(x) * 4 / M_PI;
      }
      return 1;
    }

◆ directFraction()

double directFraction ( double z ) const

private

Fraction of direct photons from delta-rays, e.g direct/(direct+reflected)

Parameters

z	local z position of track at TOP

Returns: fraction of direct photons

Definition at line 155 of file DeltaRayPDF.cc.

    {
      // coefficients of 5th order polynom (from fit to MC, see B2GM/TOP Software status, June 2020)
      const double par[] = {0.332741, -0.00331502, 2.0801e-05, -3.43689e-09, -6.35849e-10, 3.54556e-12};
 
      double x = 1;
      double f = 0;
      for (auto p : par) {
        f += p * x;
        x *= z;
      }
      return f;
    }

◆ getFraction()

double getFraction ( ) const

inline

Returns fraction of delta-ray photons in the time window.

Returns: fraction of delta-ray photons in the time window

Definition at line 60 of file DeltaRayPDF.h.

60{return m_fraction;}

Belle2::TOP::DeltaRayPDF::m_fraction

double m_fraction

fraction of delta-ray photons within time window

Definition: DeltaRayPDF.h:181

◆ getIntegral()

double getIntegral	(	double	minTime,
		double	maxTime
	)		const

inline

Returns integral of PDF from minTime to maxTime.

Parameters

minTime	integral lower limit
maxTime	integral upper limit

Returns: integral of PDF

Definition at line 213 of file DeltaRayPDF.h.

    {
      return totalFraction(minTime, maxTime) / m_fraction;
    }

◆ getModuleID()

int getModuleID ( ) const

inline

Returns slot ID.

Returns: slot ID

Definition at line 48 of file DeltaRayPDF.h.

48{return m_moduleID;}

◆ getNumPhotons()

double getNumPhotons ( ) const

inline

Returns number of photons.

Returns: number of photons

Definition at line 54 of file DeltaRayPDF.h.

54{return m_numPhotons;}

Belle2::TOP::DeltaRayPDF::m_numPhotons

double m_numPhotons

number of photons

Definition: DeltaRayPDF.h:182

◆ getPDFValue() [1/2]

double getPDFValue	(	double	time,
		double	dt0 = `0`,
		double	acc = `1`
	)		const

inline

Returns PDF value at given time and integrated over all pixels.

Parameters

time	photon hit time
dt0	direct peak position correction
acc	acceptance correction factor for direct peak

Returns: PDF value (projection to time axis)

Definition at line 205 of file DeltaRayPDF.h.

    {
      double t = time - m_TOF;
      double pdfDirect = smearedTimeDistr(t, m_dirT0 + dt0) * acc;
      double pdfReflec = smearedTimeDistr(t, m_reflT0);
      return m_dirFrac * pdfDirect + (1 - m_dirFrac) * pdfReflec;
    }

◆ getPDFValue() [2/2]

double getPDFValue	(	int	pixelID,
		double	time
	)		const

Returns PDF value at given time and pixel.

Parameters

pixelID	pixel ID
time	photon hit time

Returns: PDF value

Definition at line 113 of file DeltaRayPDF.cc.

    {
      const auto& pixelPDF = m_background->getPDF();
      unsigned k = pixelID - 1;
      if (k < pixelPDF.size()) {
        const auto& pixel = m_pixelPositions->get(pixelID);
        double t0 = sqrt(pow(pixel.xc - m_xE, 2) + pow(pixel.yc - m_yE, 2) + pow(m_zD - m_zE, 2))
                    * m_groupIndex / Const::speedOfLight;
        return getPDFValue(time, t0 - m_dirT0, m_pixelAcceptances[k]) * pixelPDF[k];
      }
      return 0;
    }

◆ peakFraction()

double peakFraction	(	double	tmin,
		double	tmax,
		double	t0
	)		const

private

Fraction of delta-ray photons within given propagation time interval for single peak at t0.

Parameters

tmin	time interval lower edge
tmax	time interval upper edge
t0	minimal possible propagation time

Returns: fraction of photons within time interval for single peak

Definition at line 138 of file DeltaRayPDF.cc.

    {
      int nt = m_norms.size() - 1;
      int i1 = nt;
      if (tmax > t0) i1 = t0 / tmax * nt;
      int i2 = nt;
      if (tmin > t0) i2 = t0 / tmin * nt;
      return std::abs(m_norms[i2] - m_norms[i1]);
    }

◆ photonYield()

double photonYield	(	double	beta,
		int	PDGCode
	)		const

private

Photon yield from delta-rays per track length in quartz for nominal photon detection efficiency.

Parameters

beta	particle velocity
PDGCode	PDG code

Returns: photon yield per cm

Definition at line 169 of file DeltaRayPDF.cc.

    {
      // for parametrizations see B2GM/TOP Software status, June 2020
      const double averagePDE = 1.06404889; // relative to nominal PDE
      const double scaleFactor = 0.79;
 
      if (std::abs(PDGCode) == 11) { // electorns and positrons
        return 5.30 * scaleFactor / averagePDE;
      } else if (PDGCode == -2212) { // anti-protons
        const double par[] = {13.5859, -28.0625, 17.2684};
        double f = par[0] + par[1] * beta + par[2] * beta * beta;
        return f * scaleFactor / averagePDE;
      } else { // other charged particles
        const double par[] = { -8.15871, 10.0082, -1.25140, -120.225, 120.210};
        double f = exp(par[0] + par[1] * beta + par[2] * beta * beta) + exp(par[3] + par[4] * beta);
        return f * scaleFactor / averagePDE;
      }
    }

◆ prepare()

void prepare	(	const TOPTrack &	track,
		const Const::ChargedStable &	hypothesis
	)

Prepare the object.

Parameters

track	track at TOP
hypothesis	particle hypothesis

Definition at line 70 of file DeltaRayPDF.cc.

    {
      const auto& emi = track.getEmissionPoint().position;
      m_xE = emi.X();
      m_yE = emi.Y();
      m_zE = emi.Z();
      m_dirFrac = directFraction(m_zE);
      m_dirT0 = (m_zE - m_zD) * m_groupIndex / Const::speedOfLight;
      m_reflT0 = (2 * m_zM - m_zD - m_zE) * m_groupIndex / Const::speedOfLight;
      m_TOF = track.getTOF(hypothesis);
 
      if (m_dirT0 < 0) {
        B2ERROR("TOP::DeltaRayPDF::prepare: T0 direct is negative -> set to 0");
        m_dirT0 = 0;
      }
      if (m_reflT0 < 0) {
        B2ERROR("TOP::DeltaRayPDF::prepare: T0 reflected is negative -> set to 0");
        m_reflT0 = 0;
      }
 
      double beta = track.getBeta(hypothesis);
      int PDGCode = std::abs(hypothesis.getPDGCode());
      if (PDGCode < 20) PDGCode = -PDGCode;
      if (track.getCharge() < 0) PDGCode = -PDGCode;
      double tlen = track.getLengthInQuartz();
      double tmin = TOPRecoManager::getMinTime();
      double tmax = TOPRecoManager::getMaxTime();
      double relEffi = m_background->getEfficiency();
      m_fraction = totalFraction(tmin, tmax);
      m_numPhotons = photonYield(beta, PDGCode) * tlen * m_fraction * relEffi;
 
      for (const auto& pixel : m_pixelPositions->getPixels()) {
        double dfi_dx = std::abs(m_zD - m_zE) / (pow(pixel.xc - m_xE, 2) + pow(pixel.yc - m_yE, 2) + pow(m_zD - m_zE, 2));
        m_pixelAcceptances.push_back(dfi_dx * pixel.Dx);
      }
      double sum = 0;
      const auto& pixelPDF = m_background->getPDF();
      for (size_t k = 0; k < m_pixelAcceptances.size(); k++) {
        sum += m_pixelAcceptances[k] * pixelPDF[k];
      }
      for (auto& x : m_pixelAcceptances) x /= sum;
    }

◆ smearedTimeDistr()

double smearedTimeDistr	(	double	t,
		double	t0
	)		const

private

Smeared time distribution of photons from delta rays (normalized).

Parameters

t	photon propagation time
t0	minimal possible propagation time

Returns: normalized time distribution value at given propagaton time

Definition at line 126 of file DeltaRayPDF.cc.

    {
      const double sigma0 = 0.15;
      double sigma = sqrt(pow(sigma0, 2) + pow(m_dispersion * t, 2));
 
      if (sigma < 0.001) return timeDistr(t, t0);
 
      double f = 0;
      for (const auto& gaus : m_tableGaus) f += timeDistr(t - gaus.x * sigma, t0) * gaus.y;
      return f;
    }

◆ timeDistr()

double timeDistr	(	double	t,
		double	t0
	)		const

inlineprivate

Time distribution of photons from delta rays (normalized).

Parameters

t	photon propagation time
t0	minimal possible propagation time

Returns: normalized time distribution value at given propagaton time

Definition at line 199 of file DeltaRayPDF.h.

    {
      if (t < t0) return 0;
      return angularDistr(t0 / t) / m_angularNorm * t0 / pow(t, 2);
    }

◆ totalFraction()

double totalFraction	(	double	tmin,
		double	tmax
	)		const

private

Total fraction of delta-ray photons within given propagation time interval.

Parameters

tmin	time interval lower edge
tmax	time interval upper edge

Returns: fraction of photons within time interval including direct and reflected peaks

Definition at line 148 of file DeltaRayPDF.cc.

    {
      double dirPeak =  peakFraction(tmin - m_TOF, tmax - m_TOF, m_dirT0);
      double reflPeak = peakFraction(tmin - m_TOF, tmax - m_TOF, m_reflT0);
      return m_dirFrac * dirPeak + (1 - m_dirFrac) * reflPeak;
    }

Member Data Documentation

◆ m_angularNorm

double m_angularNorm = 0

private

angular distribution normalization constant

Definition at line 169 of file DeltaRayPDF.h.

◆ m_background

const BackgroundPDF* m_background = 0

private

background PDF

Definition at line 162 of file DeltaRayPDF.h.

◆ m_dirFrac

double m_dirFrac = 0

private

fraction of direct photons

Definition at line 177 of file DeltaRayPDF.h.

◆ m_dirT0

double m_dirT0 = 0

private

minimal propagation time of direct photons

Definition at line 178 of file DeltaRayPDF.h.

◆ m_dispersion

double m_dispersion = 0

private

dispersion coefficient

Definition at line 168 of file DeltaRayPDF.h.

◆ m_fraction

double m_fraction = 0

private

fraction of delta-ray photons within time window

Definition at line 181 of file DeltaRayPDF.h.

◆ m_groupIndex

double m_groupIndex = 0

private

group refractive index

Definition at line 167 of file DeltaRayPDF.h.

◆ m_moduleID

int m_moduleID

private

slot ID

Definition at line 161 of file DeltaRayPDF.h.

◆ m_norms

std::vector<double> m_norms

private

relative angular distribution normalization constants (cumulative)

Definition at line 170 of file DeltaRayPDF.h.

◆ m_numPhotons

double m_numPhotons = 0

private

number of photons

Definition at line 182 of file DeltaRayPDF.h.

◆ m_phaseIndex

double m_phaseIndex = 0

private

phase refractive index

Definition at line 166 of file DeltaRayPDF.h.

◆ m_pixelAcceptances

std::vector<double> m_pixelAcceptances

private

pixel angular acceptances for direct peak (index = pixelID - 1)

Definition at line 183 of file DeltaRayPDF.h.

◆ m_pixelPositions

const PixelPositions* m_pixelPositions = 0

private

pixel positions

Definition at line 163 of file DeltaRayPDF.h.

◆ m_reflT0

double m_reflT0 = 0

private

minimal propagation time of reflected photons

Definition at line 179 of file DeltaRayPDF.h.

◆ m_tableGaus

std::vector<GausXY> m_tableGaus

private

table of normal (Gaussian) distribution

Definition at line 171 of file DeltaRayPDF.h.

◆ m_TOF

double m_TOF = 0

private

time-of-flight of particle

Definition at line 180 of file DeltaRayPDF.h.

◆ m_xE

double m_xE = 0

private

average photon emission position in x

Definition at line 174 of file DeltaRayPDF.h.

◆ m_yE

double m_yE = 0

private

average photon emission position in y

Definition at line 175 of file DeltaRayPDF.h.

◆ m_zD

double m_zD = 0

private

detector (photo-cathode) position in z

Definition at line 164 of file DeltaRayPDF.h.

◆ m_zE

double m_zE = 0

private

average photon emission position in z

Definition at line 176 of file DeltaRayPDF.h.

◆ m_zM

double m_zM = 0

private

spherical mirror position in z

Definition at line 165 of file DeltaRayPDF.h.

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

top/reconstruction_cpp/include/DeltaRayPDF.h
top/reconstruction_cpp/src/DeltaRayPDF.cc

Classes

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ DeltaRayPDF()

Member Function Documentation

◆ angularDistr()

◆ directFraction()

◆ getFraction()

◆ getIntegral()

◆ getModuleID()

◆ getNumPhotons()

◆ getPDFValue() [1/2]

◆ getPDFValue() [2/2]

◆ peakFraction()

◆ photonYield()

◆ prepare()

◆ smearedTimeDistr()

◆ timeDistr()

◆ totalFraction()

Member Data Documentation

◆ m_angularNorm

◆ m_background

◆ m_dirFrac

◆ m_dirT0

◆ m_dispersion

◆ m_fraction

◆ m_groupIndex

◆ m_moduleID

◆ m_norms

◆ m_numPhotons

◆ m_phaseIndex

◆ m_pixelAcceptances

◆ m_pixelPositions

◆ m_reflT0

◆ m_tableGaus

◆ m_TOF

◆ m_xE

◆ m_yE

◆ m_zD

◆ m_zE

◆ m_zM