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)

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)

	TNamed (const TString &name, const TString &title)

virtual	~TNamed ()

TObject *	Clone (const char *newname="") const override

Int_t	Compare (const TObject *obj) const override

virtual void	FillBuffer (char *&buffer)

const char *	GetName () const override

const char *	GetTitle () const override

ULong_t	Hash () const override

TClass *	IsA () const override

Bool_t	IsSortable () const override

void	ls (Option_t *option="") const override

TNamed &	operator= (const TNamed &rhs)

virtual void	SetName (const char *name)

virtual void	SetNameTitle (const char name, const char title)

virtual void	SetTitle (const char *title="")

virtual Int_t	Sizeof () const

void	Streamer (TBuffer &) override

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TObject
	TObject ()

	TObject (const TObject &object)

virtual	~TObject ()

void	AbstractMethod (const char *method) const

virtual void	AppendPad (Option_t *option="")

virtual void	Browse (TBrowser *b)

ULong_t	CheckedHash ()

virtual const char *	ClassName () const

virtual void	Delete (Option_t *option="")

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)

virtual void	DrawClass () const

virtual TObject *	DrawClone (Option_t *option="") const

virtual void	Dump () const

virtual void	Error (const char method, const char msgfmt,...) const

virtual void	Execute (const char method, const char params, Int_t *error=nullptr)

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=nullptr)

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)

virtual void	Fatal (const char method, const char msgfmt,...) const

virtual TObject *	FindObject (const char *name) const

virtual TObject *	FindObject (const TObject *obj) const

virtual Option_t *	GetDrawOption () const

virtual const char *	GetIconName () const

virtual char *	GetObjectInfo (Int_t px, Int_t py) const

virtual Option_t *	GetOption () const

virtual UInt_t	GetUniqueID () const

virtual Bool_t	HandleTimer (TTimer *timer)

Bool_t	HasInconsistentHash () const

virtual void	Info (const char method, const char msgfmt,...) const

virtual Bool_t	InheritsFrom (const char *classname) const

virtual Bool_t	InheritsFrom (const TClass *cl) const

virtual void	Inspect () const

void	InvertBit (UInt_t f)

Bool_t	IsDestructed () const

virtual Bool_t	IsEqual (const TObject *obj) const

virtual Bool_t	IsFolder () const

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

void	MayNotUse (const char *method) const

virtual Bool_t	Notify ()

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const

void	operator delete (void *ptr)

void	operator delete (void ptr, void vp)

void	operator delete[] (void *ptr)

void	operator delete[] (void ptr, void vp)

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)

virtual void	Paint (Option_t *option="")

virtual void	Pop ()

virtual Int_t	Read (const char *name)

virtual void	RecursiveRemove (TObject *obj)

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)

virtual void	SetDrawOption (Option_t *option="")

virtual void	SetUniqueID (UInt_t uid)

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

virtual void	SysError (const char method, const char msgfmt,...) const

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()

virtual void	Warning (const char method, const char msgfmt,...) const

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const

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) }

Public Types inherited from TObject
enum	EDeprecatedStatusBits

enum	EStatusBits

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 ()

Static Public Member Functions inherited from TNamed
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()

static Bool_t	GetObjectStat ()

static void	SetDtorOnly (void *obj)

static void	SetObjectStat (Bool_t stat)

Public Attributes inherited from TObject
	kBitMask

	kCanDelete

	kCannotPick

	kHasUUID

	kInconsistent

	kInvalidObject

	kIsOnHeap

	kIsReferenced

	kMustCleanup

	kNoContextMenu

	kNotDeleted

	kObjInCanvas

	kOverwrite

	kSingleKey

	kWriteDelete

	kZombie

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const

void	MakeZombie ()

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Protected Attributes inherited from TObject
	kOnlyPrepStep

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 = "" )

inlinevirtual

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

Parameters

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

Reimplemented from TObject.

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