Detailed Description

Class implementing parametrizable impact parameter distributions.

Unbiased impact parameter distributions are determined by simple geometric considerations,

\[ P(b)\,\mathrm{d}b=\frac{2\pi b}{\sigma_{R}}\,\mathrm{d}b \]

The sharp cut-off approximation assumes that the measured reaction cross-section $\sigma_R$ for any selected data has a triangular distribution up to the impact parameter $b_{\mathrm{max}}$ where $\sigma_R=\pi b^2_{\mathrm{max}}$ and the centrality is given in this case by $c_b=(b/b_{\mathrm{max}})^2$.

More generally, simulations of reactions detected by large multidetector arrays operating with a minimum bias multiplicity trigger indicate that the impact parameter distribution for the measured collisions is triangular with a more gradual fall-off at the largest impact parameters, and can be well-described by the distribution

\[ P(b)=\frac{2\pi b}{\sigma_{R}}\left[1+\exp\left(\frac{b-b_{0}}{\Delta b}\right)\right]^{-1} \]

In this case the total reaction cross-section is given by

\[ \sigma_{R}=-2\pi(\Delta b)^{2}\mathrm{Li}_{2}\left(-\exp\left(\frac{b_{0}}{\Delta b}\right)\right) \]

and the centrality is related to impact parameter by

\[ c_{b}=\frac{2\pi(\Delta b)^{2}}{\sigma_{R}}\left[\mathrm{-Li}_{2}\left(-\exp\left(\frac{b_{0}}{\Delta b}\right)\right)-\frac{\pi^{2}}{6}+\frac{(b^{2}-b_{0}^{2})}{2(\Delta b)^{2}}-\frac{b}{\Delta b}\ln\left(1+\exp\left((b-b_{0})/\Delta b\right)\right)-\mathrm{Li}_{2}\left(-\mathrm{e}^{(b-b_{0})/\Delta b}\right)\right] \]

Definition at line 44 of file impact_parameter_distribution.h.

#include <impact_parameter_distribution.h>

Inheritance diagram for KVImpactParameters::impact_parameter_distribution:

[legend]

Public Member Functions
	impact_parameter_distribution ()

	impact_parameter_distribution (TH1 *)

virtual	~impact_parameter_distribution ()

Double_t	Calculate_b (Double_t centrality) const

void	Draw (Option_t *opt="")

void	FitIPDist (TH1 *)

Double_t	GetB0 () const

const TF1 &	GetCentrality ()

TH1 *	GetCentralityFromHisto ()

Double_t	GetCrossSection () const

Double_t	GetCrossSectionPerEvent () const

Double_t	GetDeltaB () const

Double_t	GetDifferentialCrossSection (double b) const

Double_t	GetDifferentialCrossSectionFromHisto (double bb)

TF1 &	GetIPDist ()

Double_t	GetRelativeCrossSection (double b) const

const TF1 &	GetSigmaR ()

void	MakeDifferentialCrossSection ()

void	NormalizeIPDistToCrossSection ()

void	SetB0 (Double_t x)

void	SetDeltaB (Double_t x)

void	SetDeltaB_WithConstantCrossSection (Double_t deltab, Double_t sigmaR=0)

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)

Private Attributes
TF1	fCentrality
	centrality as function of impact parameter More...

TH1 *	fHisto
	! last fitted histogram More...

TF1	fIPdist
	impact parameter distribution More...

TF1	fSigmaR
	total reaction cross section More...

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

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 ()

Constructor & Destructor Documentation

◆ impact_parameter_distribution() [1/2]

KVImpactParameters::impact_parameter_distribution::impact_parameter_distribution ( )

Initialize a default distribution which is triangular (sharp cut-off approximation) with $b_0=1$ and $\Delta b=0$.

Definition at line 95 of file impact_parameter_distribution.cpp.

◆ impact_parameter_distribution() [2/2]

KVImpactParameters::impact_parameter_distribution::impact_parameter_distribution ( TH1 * h )

Fit $P(b)$ to the distribution in the histogram

Parameters

[in] h histogram containing impact parameter distribution

Definition at line 118 of file impact_parameter_distribution.cpp.

◆ ~impact_parameter_distribution()

virtual KVImpactParameters::impact_parameter_distribution::~impact_parameter_distribution ( )

inlinevirtual

Definition at line 55 of file impact_parameter_distribution.h.

Member Function Documentation

◆ Calculate_b()

Double_t KVImpactParameters::impact_parameter_distribution::Calculate_b ( Double_t centrality ) const

Returns: value of impact parameter $b$ for given value of centrality $c_b$ using current parameters

Parameters

[in] centrality value of $c_b$

Definition at line 214 of file impact_parameter_distribution.cpp.

◆ Draw()

void KVImpactParameters::impact_parameter_distribution::Draw ( Option_t * opt = "" )

inline

Draw the impact parameter distribution (differential cross-section in [mb fm ${}^{-1}$])

Parameters

[in] opt Usual drawing option, passed to TF1::Draw()

Definition at line 95 of file impact_parameter_distribution.h.

◆ FitIPDist()

void KVImpactParameters::impact_parameter_distribution::FitIPDist ( TH1 * h )

Fit impact parameter distribution given in histogram.

Parameters

[in] h histogram containing impact parameter distribution

Definition at line 139 of file impact_parameter_distribution.cpp.

◆ GetB0()

Double_t KVImpactParameters::impact_parameter_distribution::GetB0 ( ) const

inline

Returns: current value of $b_0$

Definition at line 60 of file impact_parameter_distribution.h.

◆ GetCentrality()

const TF1& KVImpactParameters::impact_parameter_distribution::GetCentrality ( )

inline

Returns: reference to TF1 implementing centrality as a function of $b$.

Definition at line 107 of file impact_parameter_distribution.h.

◆ GetCentralityFromHisto()

TH1 * KVImpactParameters::impact_parameter_distribution::GetCentralityFromHisto ( )

Call this method to use the (model-dependent) histogram containing the impact parameter distribution to compute the centrality

Returns: the actual centrality histogram from the histogram containing impact parameter distribution (if set)

Definition at line 228 of file impact_parameter_distribution.cpp.

◆ GetCrossSection()

Double_t KVImpactParameters::impact_parameter_distribution::GetCrossSection ( ) const

Returns: Total reaction cross-section $\sigma_R$ in [mb] using current values of $b_0$ and $\Delta b$.

Definition at line 165 of file impact_parameter_distribution.cpp.

◆ GetCrossSectionPerEvent()

Double_t KVImpactParameters::impact_parameter_distribution::GetCrossSectionPerEvent ( ) const

Returns: Cross-section per event in [mb] for last fitted histogram. This is the total reaction cross-section calculated using GetCrossSection() divided by the number of entries in the histogram.

Definition at line 179 of file impact_parameter_distribution.cpp.

◆ GetDeltaB()

Double_t KVImpactParameters::impact_parameter_distribution::GetDeltaB ( ) const

inline

Returns: current value of $\Delta b$

Definition at line 65 of file impact_parameter_distribution.h.

◆ GetDifferentialCrossSection()

Double_t KVImpactParameters::impact_parameter_distribution::GetDifferentialCrossSection ( double b ) const

inline

Returns: differential cross-section for impact parameter $b$ in [mb fm ${}^{-1}$]

Definition at line 129 of file impact_parameter_distribution.h.

◆ GetDifferentialCrossSectionFromHisto()

Double_t KVImpactParameters::impact_parameter_distribution::GetDifferentialCrossSectionFromHisto ( double bb )

inline

Call this method to evaluate P(b) directly from the (model-dependent) histogram containing the impact parameter distribution

Definition at line 151 of file impact_parameter_distribution.h.

◆ GetIPDist()

TF1& KVImpactParameters::impact_parameter_distribution::GetIPDist ( )

inline

Returns: reference to TF1 implementing impact parameter distribution

Note: this should be the differential cross-section in [mb fm ${}^{-1}$], but if an un-normalized histogram was fitted to find the parameters of the distribution, this function includes an arbitrary normalization depending on the integral of the histogram

Definition at line 85 of file impact_parameter_distribution.h.

◆ GetRelativeCrossSection()

Double_t KVImpactParameters::impact_parameter_distribution::GetRelativeCrossSection ( double b ) const

inline

Returns: differential cross-section relative to $2\pi b$

Definition at line 122 of file impact_parameter_distribution.h.

◆ GetSigmaR()

const TF1& KVImpactParameters::impact_parameter_distribution::GetSigmaR ( )

inline

Returns: reference to TF1 implementing total cross-section in [mb] as a function of $b_0$.

Definition at line 101 of file impact_parameter_distribution.h.

◆ MakeDifferentialCrossSection()

void KVImpactParameters::impact_parameter_distribution::MakeDifferentialCrossSection ( )

inline

Call this method to ensure that the distribution returned by GetIPDist() is indeed the differential cross-section in [mb fm ${}^{-1}$].

This is normally the default if parameters like $b_0$ or $\Delta b$ are set by hand, but not if the parameters were deduced from a fit to a histogram: in this case the distribution has an arbitrary normalization factor in order to fit the histogram.

Definition at line 138 of file impact_parameter_distribution.h.

◆ NormalizeIPDistToCrossSection()

void KVImpactParameters::impact_parameter_distribution::NormalizeIPDistToCrossSection ( )

inline

Changes impact parameter distribution from differential cross-section to probability distribution $P(b)$

Definition at line 115 of file impact_parameter_distribution.h.

◆ SetB0()

void KVImpactParameters::impact_parameter_distribution::SetB0 ( Double_t x )

inline

Parameters

[in] x value of $b_0$

Definition at line 71 of file impact_parameter_distribution.h.

◆ SetDeltaB()

void KVImpactParameters::impact_parameter_distribution::SetDeltaB ( Double_t x )

inline

Parameters

[in] x value of $\Delta b$

Definition at line 77 of file impact_parameter_distribution.h.

◆ SetDeltaB_WithConstantCrossSection()

void KVImpactParameters::impact_parameter_distribution::SetDeltaB_WithConstantCrossSection	(	Double_t	deltab,
		Double_t	sigmaR = `0`
	)

Changes $\Delta b$ and $b_0$ for a given total cross-section.

Parameters

[in]	deltab	new value of $\Delta b$
[in]	sigmaR	required total cross-section $\sigma_R$. If sigmaR=0 (default), keep current total cross section

Definition at line 195 of file impact_parameter_distribution.cpp.

Member Data Documentation

◆ fCentrality

TF1 KVImpactParameters::impact_parameter_distribution::fCentrality

private

centrality as function of impact parameter

Definition at line 50 of file impact_parameter_distribution.h.

◆ fHisto

TH1* KVImpactParameters::impact_parameter_distribution::fHisto

private

! last fitted histogram

Definition at line 47 of file impact_parameter_distribution.h.

◆ fIPdist

TF1 KVImpactParameters::impact_parameter_distribution::fIPdist

private

impact parameter distribution

Definition at line 48 of file impact_parameter_distribution.h.

◆ fSigmaR

TF1 KVImpactParameters::impact_parameter_distribution::fSigmaR

private

total reaction cross section

Definition at line 49 of file impact_parameter_distribution.h.

[in]	deltab	new value of \(\Delta b\)
[in]	sigmaR	required total cross-section \(\sigma_R\). If sigmaR=0 (default), keep current total cross section

Detailed Description

Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ impact_parameter_distribution() [1/2]

◆ impact_parameter_distribution() [2/2]

◆ ~impact_parameter_distribution()

Member Function Documentation

◆ Calculate_b()

◆ Draw()

◆ FitIPDist()

◆ GetB0()

◆ GetCentrality()

◆ GetCentralityFromHisto()

◆ GetCrossSection()

◆ GetCrossSectionPerEvent()

◆ GetDeltaB()

◆ GetDifferentialCrossSection()

◆ GetDifferentialCrossSectionFromHisto()

◆ GetIPDist()

◆ GetRelativeCrossSection()

◆ GetSigmaR()

◆ MakeDifferentialCrossSection()

◆ NormalizeIPDistToCrossSection()

◆ SetB0()

◆ SetDeltaB()

◆ SetDeltaB_WithConstantCrossSection()

Member Data Documentation

◆ fCentrality

◆ fHisto

◆ fIPdist

◆ fSigmaR