Detailed Description

Impact parameter estimation neglecting using sharp cut-off approximation.

This class implements impact parameter estimation using the method of Cavata et al., Phys. Rev. C 72, 1460(1990). Given an observable $X$ which is assumed monotonically decreasing with impact parameter, the upper limit $b\leq b_0$ corresponding to a cut $X\geq X_0$ is estimated by equating the fraction of the total measured cross-section retained by the cut with the ratio of the cross-sections for the two triangular impact parameter distributions $b\leq b_0$ and $b\leq b_{max}$, where $\sigma=\pi b_{max}^2$ is the total measured cross-section for all reactions:

\[ \frac{b_0}{b_{max}}=\left[\int_{X_0}^{\infty} P(X) dX \right]^{\frac{1}{2}} \]

where $P(X)$ is the probability distribution of $X$ for all measured reactions.

This relationship is strictly true if fluctuations of $X$ for a fixed $b$ are negligible, which is never the case in heavy-ion collisions at intermediate energies. The Cavata prescription implies a one-to-one correspondence between each value of $X$ i.e. each event and a unique value of $b$, which is clearly not true. Although for peripheral collisions this prescription gives a reasonable estimation of the mean value of impact parameter associated with selected events, it greatly underestimates the widths of the actual distributions of impact parameter, and the more "central" the event selection the more Cavata underestimates the mean impact parameters, giving a false impression that higher and higher cuts in $X$ produce event samples with smaller and smaller $\langle b\rangle$.

See also: bayesian_estimator

Definition at line 46 of file cavata_prescription.h.

#include <cavata_prescription.h>

Inheritance diagram for KVImpactParameters::cavata_prescription:

[legend]

Public Member Functions
	cavata_prescription ()

	cavata_prescription (const cavata_prescription &)=delete

	cavata_prescription (TH1 h, Option_t evol="D")

virtual	~cavata_prescription ()
	Destructor. More...

Double_t	BTransform (Double_t , Double_t )

Double_t	GetCrossSection (Double_t obs)

Double_t	GetImpactParameter (Double_t obs)

TH1 *	GetIPDistribution (TH1 obs, Int_t nbinx=100, Option_t norm="")

TGraph *	GetIPEvolution (TH2 *obscor, TString moment, TString axis="Y")

double	GetMeanBForSCA (double bmin, double bmax) const

Double_t	GetObservable (Double_t b)

Double_t	GetObservableXSec (Double_t sigma)

TGraph *	GetScale () const

double	GetSigmaBForSCA (double bmin, double bmax) const

TF1 *	GetTransFunc () const

TH1 *	GetXSecDistribution (TH1 obs, Int_t nbinx=100, Option_t norm="")

TGraph *	GetXSecEvolution (TH2 *obscor, TString moment, TString axis="Y")

TGraph *	GetXSecScale () const

TF1 *	GetXSecTransFunc () const

void	MakeAbsoluteScale (Int_t npoints=100, Double_t bmax=1.0)

void	MakeScale (Int_t npoints=100, Double_t bmax=1.0)

std::vector< Double_t >	SliceXSec (Int_t nslices, Double_t totXsec)

Double_t	XTransform (Double_t , Double_t )

Public Member Functions inherited from KVBase
	KVBase ()
	Default constructor. More...

	KVBase (const Char_t name, const Char_t title="")
	Ctor for object with given name and type. More...

	KVBase (const KVBase &)
	copy ctor More...

virtual	~ KVBase ()

virtual void	Clear (Option_t *opt="")
	Clear object properties : name, type/title, number, label. More...

virtual void	Copy (TObject &) const
	Make a copy of this object. More...

const Char_t *	GetLabel () const

UInt_t	GetNumber () const

UInt_t	GetNumberOfObjects () const

virtual TObject *	GetObject () const

virtual const Char_t *	GetType () const

Bool_t	HasLabel () const

virtual Bool_t	IsCalled (const Char_t *name) const

Bool_t	IsLabelled (const Char_t *l) const

virtual Bool_t	IsType (const Char_t *typ) const

virtual void	List ()

KVBase &	operator= (const KVBase &)
	copy assignment operator More...

virtual void	Print (Option_t *option="") const

Double_t	ProtectedGetX (const TF1 *func, Double_t val, int &status, Double_t xmin=0.0, Double_t xmax=0.0) const

void	SetLabel (const Char_t *lab)

virtual void	SetNumber (UInt_t num)

virtual void	SetType (const Char_t *str)

Static Public Member Functions
static Double_t	GetIPFromXSec (Double_t xsec)

static Double_t	GetXSecFromIP (Double_t bmax)

Static Public Member Functions inherited from KVBase
static Bool_t	AreEqual (Double_t x, Double_t y, Long64_t maxdif=1)
	Comparison between two 64-bit floating-point values. More...

static void	BackupFileWithDate (const Char_t *path)

static void	CombineFiles (const Char_t file1, const Char_t file2, const Char_t *newfilename, Bool_t keep=kTRUE)

static void	Deprecated (const char method, const char advice)

static Bool_t	FindClassSourceFiles (const Char_t class_name, KVString &imp_file, KVString &dec_file, const Char_t dir_name=".")

static Bool_t	FindExecutable (TString &exec, const Char_t *path="$(PATH)")

static const Char_t *	FindFile (const Char_t *search, TString &wfil)

static const Char_t *	GetBINDIRFilePath (const Char_t *namefile="")

static const Char_t *	GetDATABASEFilePath ()

static const Char_t *	GetDATADIRFilePath (const Char_t *namefile="")

static Bool_t	GetDataSetEnv (const Char_t dataset, const Char_t type, Bool_t defval)

static const Char_t *	GetDataSetEnv (const Char_t dataset, const Char_t type, const Char_t *defval)

static Double_t	GetDataSetEnv (const Char_t dataset, const Char_t type, Double_t defval)

static const Char_t *	GetETCDIRFilePath (const Char_t *namefile="")

static const Char_t *	GetExampleFilePath (const Char_t library, const Char_t namefile)
	Return full path to example file for given library (="KVMultiDet", "BackTrack", etc.) More...

static const Char_t *	GetINCDIRFilePath (const Char_t *namefile="")

static const Char_t *	GetKVBuildDate ()
	Returns KaliVeda build date. More...

static const Char_t *	GetKVBuildDir ()
	Returns top-level directory used for build. More...

static const Char_t *	GetKVBuildTime ()
	Returns KaliVeda build time. More...

static const Char_t *	GetKVBuildType ()
	Returns KaliVeda build type (cmake build: Release, Debug, RelWithDebInfo, ...) More...

static const Char_t *	GetKVBuildUser ()
	Returns username of person who performed build. More...

static const Char_t *	GetKVSourceDir ()
	Returns top-level directory of source tree used for build. More...

static const Char_t *	GetKVVersion ()
	Returns KaliVeda version string. More...

static const Char_t *	GetLIBDIRFilePath (const Char_t *namefile="")

static const Char_t *	GetListOfPlugins (const Char_t *base)

static const Char_t *	GetListOfPluginURIs (const Char_t *base)

static const Char_t *	GetPluginURI (const Char_t base, const Char_t plugin)

static void	GetTempFileName (TString &base)

static const Char_t *	GetTEMPLATEDIRFilePath (const Char_t *namefile="")

static const Char_t *	GetWORKDIRFilePath (const Char_t *namefile="")

static const Char_t *	gitBranch ()
	Returns git branch of sources. More...

static const Char_t *	gitCommit ()
	Returns last git commit of sources. More...

static void	InitEnvironment ()

static bool	is_gnuinstall ()

static Bool_t	IsThisAPlugin (const TString &uri, TString &base)

static TPluginHandler *	LoadPlugin (const Char_t base, const Char_t uri="0")

static Bool_t	OpenContextMenu (const char method, TObject obj, const char *alt_method_name="")

static void	OpenTempFile (TString &base, std::ofstream &fp)

static void	PrintSplashScreen ()
	Prints welcome message and infos on version etc. More...

static Bool_t	SearchAndOpenKVFile (const Char_t name, KVSQLite::database &dbfile, const Char_t kvsubdir="")

static Bool_t	SearchAndOpenKVFile (const Char_t name, std::ifstream &file, const Char_t kvsubdir="", KVLockfile *locks=0)

static Bool_t	SearchAndOpenKVFile (const Char_t name, std::ofstream &file, const Char_t kvsubdir="", KVLockfile *locks=0)

static Bool_t	SearchKVFile (const Char_t name, TString &fullpath, const Char_t kvsubdir="")

static const Char_t *	WorkingDirectory ()

Private Member Functions
void	make_scale (Int_t npoints)

Private Attributes
Double_t	Bmax
	maximum of ip scale More...

TH1 *	fData
	histogram containing distribution of ip-related observable More...

TString	fEvol
	how the observable evolves with b More...

TGraph *	fIPScale
	derived relation between observable and impact-parameter More...

TF1 *	fObsTransform
	function for transforming observable into impact parameter More...

TF1 *	fObsTransformXSec
	function for transforming observable into cross-section More...

TGraph *	fXSecScale
	derived relation between observable and cross-section More...

KVHistoManipulator	HM
	for scaling transormations of histograms, graphs, etc. More...

Double_t	Smax
	maximum of cross-section scale More...

Additional Inherited Members
Public Types inherited from KVBase
enum	EKaliVedaBits { kIsKaliVedaObject = BIT(23) }

Constructor & Destructor Documentation

◆ cavata_prescription() [1/3]

KVImpactParameters::cavata_prescription::cavata_prescription ( const cavata_prescription & )

delete

◆ cavata_prescription() [2/3]

KVImpactParameters::cavata_prescription::cavata_prescription ( )

inline

Definition at line 65 of file cavata_prescription.h.

◆ cavata_prescription() [3/3]

KVImpactParameters::cavata_prescription::cavata_prescription	(	TH1 *	h,
		Option_t *	evol = `"D"`
	)

Constructor for impact parameter estimator

Parameters

[in]	h	Histogram containing distribution of the observable used to calculate impact parameter.
[in]	evol	Determine whether observable is monotonically decreasing ("D") or increasing ("C")

Definition at line 12 of file cavata_prescription.cpp.

◆ ~cavata_prescription()

KVImpactParameters::cavata_prescription::~cavata_prescription ( )

virtual

Destructor.

Definition at line 26 of file cavata_prescription.cpp.

Member Function Documentation

◆ BTransform()

Double_t KVImpactParameters::cavata_prescription::BTransform	(	Double_t *	x,
		Double_t *
	)

Function using the TGraph calculated with MakeScale() or MakeAbsoluteScale() in order to transform distributions of the observable histogrammed in fData into distributions of the impact parameter.

This function is used to generate the TF1 fObsTransform

Parameters

[in] x[0] value of observable

Definition at line 164 of file cavata_prescription.cpp.

◆ GetCrossSection()

Double_t KVImpactParameters::cavata_prescription::GetCrossSection ( Double_t obs )

inline

Parameters

[in] obs value of observable

Returns: cross section for given value of the observable.

Definition at line 116 of file cavata_prescription.h.

◆ GetImpactParameter()

Double_t KVImpactParameters::cavata_prescription::GetImpactParameter ( Double_t obs )

inline

Parameters

[in] obs value of observable

Returns: impact parameter for given value of the observable.

Definition at line 110 of file cavata_prescription.h.

◆ GetIPDistribution()

TH1 * KVImpactParameters::cavata_prescription::GetIPDistribution	(	TH1 *	obs,
		Int_t	nbinx = `100`,
		Option_t *	norm = `""`
	)

Transform the distribution of the observable contained in the histogram 'obs' into a distribution of the impact parameter.

Parameters

[in]	obs	pointer to histogram containing observable distribution for some selected events
[in]	nbinx	number of bins in created impact parameter histo (default = 100)
[in]	norm	norm = "" (default) no adjustment is made for the change in bin width due to the transformation norm = "width" bin contents are adjusted for width change, so that the integral of the histogram contents taking into account the bin width (i.e. TH1::Integral("width")) is the same.

Returns: pointer to histogram filled with impact parameter distribution

Definition at line 219 of file cavata_prescription.cpp.

◆ GetIPEvolution()

TGraph * KVImpactParameters::cavata_prescription::GetIPEvolution	(	TH2 *	obscor,
		TString	moment,
		TString	axis = `"Y"`
	)

Draw evolution of any observable as function of impact parameter

Parameters

[in]	obscor	pointer to histogram containing bidim correlating some observable on Y axis with the observable used to calculate the impact parameter on the X axis
[in]	moment	give moment of Y to use for evolution ("GetMean", "GetRMS", "GetKurtosis", etc. methods of TH1)
[in]	axis	if the impact parameter observable is on the Y-axis of obscor, use axis="X" by default axis="Y", i.e. we assume that the I.P. observable is on the X axis)

Returns: pointer to TGraph giving evolution of given moment of Y as a function of the impact parameter

Definition at line 259 of file cavata_prescription.cpp.

◆ GetIPFromXSec()

static Double_t KVImpactParameters::cavata_prescription::GetIPFromXSec ( Double_t xsec )

inlinestatic

Utility function

Parameters

[in] xsec cross-section

Returns: maximum impact parameter in [fm] corresponding to cross-section in [mb] using sharp cut-off approximation

Definition at line 146 of file cavata_prescription.h.

◆ GetMeanBForSCA()

double KVImpactParameters::cavata_prescription::GetMeanBForSCA	(	double	bmin,
		double	bmax
	)		const

Calculate the mean impact parameter for b in [bmin,bmax] in sharp cut-off approximation i.e. assuming a triangular distribution:

\[ \bar{b} = \frac{2(b^3_{max}-b^3_{min})}{3(b^2_{max}-b^2_{min})} \]

Definition at line 447 of file cavata_prescription.cpp.

◆ GetObservable()

Double_t KVImpactParameters::cavata_prescription::GetObservable ( Double_t b )

inline

Parameters

[in] b impact parameter

Returns: corresponding value of observable

Definition at line 122 of file cavata_prescription.h.

◆ GetObservableXSec()

Double_t KVImpactParameters::cavata_prescription::GetObservableXSec ( Double_t sigma )

inline

Parameters

[in] sigma cross-section

Returns: corresponding value of observable

Definition at line 128 of file cavata_prescription.h.

◆ GetScale()

TGraph* KVImpactParameters::cavata_prescription::GetScale ( ) const

inline

Returns: pointer to TGraph showing relationship between the observable histogrammed in fData and the impact parameter.

Warning: only call after calling MakeScale() or MakeAbsoluteScale().

Definition at line 84 of file cavata_prescription.h.

◆ GetSigmaBForSCA()

double KVImpactParameters::cavata_prescription::GetSigmaBForSCA	(	double	bmin,
		double	bmax
	)		const

Calculate the standard deviation of impact parameter for b in [bmin,bmax] in sharp cut-off approximation i.e. assuming a triangular distribution:

\[ \sigma^2_b = \frac{(b^4_{max}-b^4_{min})}{2(b^2_{max}-b^2_{min})} - \bar{b}^2 \]

Definition at line 467 of file cavata_prescription.cpp.

◆ GetTransFunc()

TF1* KVImpactParameters::cavata_prescription::GetTransFunc ( ) const

inline

Returns: pointer to function giving b for any value of observable

Definition at line 100 of file cavata_prescription.h.

◆ GetXSecDistribution()

TH1 * KVImpactParameters::cavata_prescription::GetXSecDistribution	(	TH1 *	obs,
		Int_t	nbinx = `100`,
		Option_t *	norm = `""`
	)

Transform the distribution of the observable contained in the histogram obs into a distribution of cross-section

Parameters

[in]	obs	pointer to histogram containing observable distribution for some selected events
[in]	nbinx	number of bins in created impact parameter histo (default = 100)
[in]	norm	norm = "" (default) no adjustment is made for the change in bin width due to the transformation norm = "width" bin contents are adjusted for width change, so that the integral of the histogram contents taking into account the bin width (i.e. TH1::Integral("width")) is the same.

Returns: pointer to histogram filled with cross-section distribution

Definition at line 303 of file cavata_prescription.cpp.

◆ GetXSecEvolution()

TGraph * KVImpactParameters::cavata_prescription::GetXSecEvolution	(	TH2 *	obscor,
		TString	moment,
		TString	axis = `"Y"`
	)

Draw evolution of any observable as function of cross-section

Parameters

[in]	obscor	pointer to histogram containing bidim correlating some observable on Y axis with the observable used to calculate the impact parameter on the X axis
[in]	moment	give moment of Y to use for evolution ("GetMean", "GetRMS", "GetKurtosis", etc. methods of TH1)
[in]	axis	if the impact parameter observable is on the Y-axis of obscor, use axis="X" by default axis="Y", i.e. we assume that the I.P. observable is on the X axis)

Returns: pointer to TGraph giving evolution of given moment of Y as a function of cross-section

Definition at line 343 of file cavata_prescription.cpp.

◆ GetXSecFromIP()

static Double_t KVImpactParameters::cavata_prescription::GetXSecFromIP ( Double_t bmax )

inlinestatic

Utility function

Parameters

[in] bmax maximum value of impact parameter

Returns: cross-section in [mb] corresponding to maximum impact parameter in [fm] using sharp cut-off approximation

Definition at line 139 of file cavata_prescription.h.

◆ GetXSecScale()

TGraph* KVImpactParameters::cavata_prescription::GetXSecScale ( ) const

inline

Returns: pointer to TGraph showing relationship between the observable histogrammed in fData and the cross section.

Warning: only call after calling MakeScale() or MakeAbsoluteScale().

Definition at line 91 of file cavata_prescription.h.

◆ GetXSecTransFunc()

TF1* KVImpactParameters::cavata_prescription::GetXSecTransFunc ( ) const

inline

Returns: pointer to function giving cross section for any value of observable

Definition at line 105 of file cavata_prescription.h.

◆ make_scale()

void KVImpactParameters::cavata_prescription::make_scale ( Int_t npoints )

private

Definition at line 85 of file cavata_prescription.cpp.

◆ MakeAbsoluteScale()

void KVImpactParameters::cavata_prescription::MakeAbsoluteScale	(	Int_t	npoints = `100`,
		Double_t	bmax = `1.0`
	)

Calculate the relationship between the impact parameter and the observable whose distribution is contained in the histogram given to the constructor.

Parameters

[in]	npoints	number of points to use to calculate scale (points in generated TGraph). The greater the number of points, the more accurate the results. Default value is 100. Maximum value is number of bins in histogram of observable, fData.
[in]	bmax	the maximum absolute impact parameter for the data in [fm]

For a given value $X$ of the observable $x$, the reduced impact parameter $\hat{b}$ is calculated from the distribution of $x$, $Y(x)$, using the following formula:

\[ \hat{b}^{2} = \frac{\int^{\infty}_{x=X} Y(x) dx}{\int_{0}^{\infty} Y(x) dx} \]

Remarks: To obtain reduced values of impact parameter/cross-section use MakeScale().

Definition at line 130 of file cavata_prescription.cpp.

◆ MakeScale()

void KVImpactParameters::cavata_prescription::MakeScale	(	Int_t	npoints = `100`,
		Double_t	bmax = `1.0`
	)

Calculate the relationship between the impact parameter and the observable whose distribution is contained in the histogram given to the constructor.

Parameters

[in]	npoints	number of points to use to calculate scale (points in generated TGraph). The greater the number of points, the more accurate the results. Default value is 100. Maximum value is number of bins in histogram of observable, fData.
[in]	bmax	the maximum reduced impact parameter for the data

For a given value $X$ of the observable $x$, the reduced impact parameter $\hat{b}$ is calculated from the distribution of $x$, $Y(x)$, using the following formula:

\[ \hat{b}^{2} = \frac{\int^{\infty}_{x=X} Y(x) dx}{\int_{0}^{\infty} Y(x) dx} \]

Remarks: To obtain absolute values of impact parameter/cross-section use MakeAbsoluteScale().

Definition at line 53 of file cavata_prescription.cpp.

◆ SliceXSec()

std::vector< Double_t > KVImpactParameters::cavata_prescription::SliceXSec	(	Int_t	nslices,
		Double_t	totXsec
	)

Generate vector of observable values which can be used to select nslices of constant cross-section.

Note: the vector will contain (nslices-1) values

Parameters

[in]	nslices	number of slices to generates
[in]	totXsec	total cross-section to slice

Returns: vector containing (nslices-1) values of the observable to make cuts

Example:

KVImpactParameter ip(data); // histo containing observable distribution
ip.MakeAbsoluteScale(100,ip.GetIPFromXSec(data->Integral()))
std::vector<Double_t> slices = ip.SliceXSec(5, Xsec);
if(obs > slices[0]){
// most central events (observable increases when b decreases)
// with cross-section Xsec/5
} else if(obs > slices[1]){
// next most central events, cross-section=Xsec/5
}
...
} else if(obs > slices[3]){
// next-to-most-peripheral events
} else {
// most peripheral events (obs < slices[3])
}

Definition at line 400 of file cavata_prescription.cpp.

◆ XTransform()

Double_t KVImpactParameters::cavata_prescription::XTransform	(	Double_t *	x,
		Double_t *
	)

Function using the TGraph calculated with MakeScale() or MakeAbsoluteScale() in order to transform distributions of the observable histogrammed in fData into distributions of cross-section.

This function is used to generate the TF1 fObsTransformXsec

Parameters

[in] x[0] value of observable

Definition at line 188 of file cavata_prescription.cpp.

Member Data Documentation

◆ Bmax

Double_t KVImpactParameters::cavata_prescription::Bmax

private

maximum of ip scale

Definition at line 54 of file cavata_prescription.h.

◆ fData

TH1* KVImpactParameters::cavata_prescription::fData

private

histogram containing distribution of ip-related observable

Definition at line 47 of file cavata_prescription.h.

◆ fEvol

TString KVImpactParameters::cavata_prescription::fEvol

private

how the observable evolves with b

Definition at line 48 of file cavata_prescription.h.

◆ fIPScale

TGraph* KVImpactParameters::cavata_prescription::fIPScale

private

derived relation between observable and impact-parameter

Definition at line 49 of file cavata_prescription.h.

◆ fObsTransform

TF1* KVImpactParameters::cavata_prescription::fObsTransform

private

function for transforming observable into impact parameter

Definition at line 51 of file cavata_prescription.h.

◆ fObsTransformXSec

TF1* KVImpactParameters::cavata_prescription::fObsTransformXSec

private

function for transforming observable into cross-section

Definition at line 52 of file cavata_prescription.h.

◆ fXSecScale

TGraph* KVImpactParameters::cavata_prescription::fXSecScale

private

derived relation between observable and cross-section

Definition at line 50 of file cavata_prescription.h.

◆ HM

KVHistoManipulator KVImpactParameters::cavata_prescription::HM

private

for scaling transormations of histograms, graphs, etc.

Definition at line 53 of file cavata_prescription.h.

◆ Smax

Double_t KVImpactParameters::cavata_prescription::Smax

private

maximum of cross-section scale

Definition at line 55 of file cavata_prescription.h.

Detailed Description

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ cavata_prescription() [1/3]

◆ cavata_prescription() [2/3]

◆ cavata_prescription() [3/3]

◆ ~cavata_prescription()

Member Function Documentation

◆ BTransform()

◆ GetCrossSection()

◆ GetImpactParameter()

◆ GetIPDistribution()

◆ GetIPEvolution()

◆ GetIPFromXSec()

◆ GetMeanBForSCA()

◆ GetObservable()

◆ GetObservableXSec()

◆ GetScale()

◆ GetSigmaBForSCA()

◆ GetTransFunc()

◆ GetXSecDistribution()

◆ GetXSecEvolution()

◆ GetXSecFromIP()

◆ GetXSecScale()

◆ GetXSecTransFunc()

◆ make_scale()

◆ MakeAbsoluteScale()

◆ MakeScale()

◆ SliceXSec()

◆ XTransform()

Member Data Documentation

◆ Bmax

◆ fData

◆ fEvol

◆ fIPScale

◆ fObsTransform

◆ fObsTransformXSec

◆ fXSecScale

◆ HM

◆ Smax