Sphericity Class Reference

#include <Sphericity.hh>

Inheritance diagram for Sphericity:

[legend]Collaboration diagram for Sphericity:

[legend]List of all members.

Detailed Description

Calculate the sphericity event shape.

The sphericity tensor (or quadratic momentum tensor) is defined as

$S^{\alpha \beta} = \frac{\sum_i p_i^\alpha p_i^\beta}{\sum_i |\mathbf{p}_i|^2}$

, where the Greek indices are spatial components and the Latin indices are used for sums over particles. From this, the sphericity, aplanarity and planarity can be calculated by combinations of eigenvalues.

Defining the three eigenvalues $\lambda_1 \ge \lambda_2 \ge \lambda_3$ , with $\lambda_1 + \lambda_2 + \lambda_3 = 1$ , the sphericity is

$S = \frac{3}{2} (\lambda_2 + \lambda_3)$

The aplanarity is $A = \frac{3}{2}\lambda_3$ and the planarity is $P = \frac{2}{3}(S-2A) = \lambda_2 - \lambda_3$ . The eigenvectors define a set of spatial axes comparable with the thrust axes, but more sensitive to high momentum particles due to the quadratic sensitivity of the tensor to the particle momenta.

Since the sphericity is quadratic in the particle momenta, it is not an infrared safe observable in perturbative QCD. This can be fixed by adding a regularizing power of $r$ to the definition:

$S^{\alpha \beta} = \frac{\sum_i |\mathbf{p}_i|^{r-2} p_i^\alpha p_i^\beta} {\sum_i |\mathbf{p}_i|^r}$

$r$ is available as a constructor argument on this class and will be taken into account by the Cmp<Projection> operation, so a single analysis can use several sphericity projections with different $r$ values without fear of a clash.

Definition at line 50 of file Sphericity.hh.


Public Member Functions
	Sphericity (FinalState &fsp, double rparam=2.0)
	Constructor. Supplied FinalState projection must live throughout the run.
string	getName () const
	Return the name of the projection.
bool	before (const Projection &p) const
virtual const Cuts	getCuts () const
virtual const set< BeamPair >	getBeamPairs () const
set< Projection * >	getProjections () const
	Get the contained projections, including recursion.

const double	sphericity () const
const double	planarity () const
	Planarity.
const double	aplanarity () const
	Aplanarity.

const Vector3	sphericityAxis () const
const Vector3	sphericityMajorAxis () const
const Vector3	sphericityMinorAxis () const

const double	lambda1 () const
	Access the momentum tensor eigenvalues.
const double	lambda2 () const
const double	lambda3 () const
Protected Member Functions
void	project (const Event &e)
	Perform the projection on the Event.
int	compare (const Projection &p) const
	Compare with other projections.
Projection &	addProjection (Projection &proj)
	Add a projection dependency to the projection list.
Projection &	addBeamPair (const ParticleName &beam1, const ParticleName &beam2)
	Add a colliding beam pair.
Projection &	addCut (const string &quantity, const Comparison &comparison, const double value)
	Add a cut.
Log &	getLog ()
	Get a Log object based on the getName() property of the calling projection object.
Protected Attributes
Cuts	_cuts
	Parameter constraints.
set< BeamPair >	_beamPairs
	Beam-type constraint.
set< Projection * >	_projections
	Collection of pointers to projections, for automatically combining constraints.
Friends
class	Event
	Event is a friend.
class	Cmp<Projection>
	The Cmp specialization for Projection is a friend.

Constructor & Destructor Documentation

Sphericity	(	FinalState &	fsp,
		double	rparam = `2.0`
	)	`[inline]`

Constructor. Supplied FinalState projection must live throughout the run.

Definition at line 55 of file Sphericity.hh.

Member Function Documentation

Projection& addBeamPair	(	const ParticleName &	beam1,
		const ParticleName &	beam2
	)	`[inline, protected, inherited]`

Add a colliding beam pair.

Definition at line 145 of file Projection.hh.

References Rivet::BeamPair.

Projection& addCut	(	const string &	quantity,
		const Comparison &	comparison,
		const double	value
	)	`[inline, protected, inherited]`

Add a cut.

Definition at line 151 of file Projection.hh.

Projection& addProjection ( Projection & proj ) [inline, protected, inherited]

Add a projection dependency to the projection list.

Definition at line 139 of file Projection.hh.

const double aplanarity ( ) const [inline]

Aplanarity.

Definition at line 84 of file Sphericity.hh.

Referenced by ZPhys73C11::analyze(), and PL273B181::analyze().

bool before ( const Projection & p ) const [inline, inherited]

Determine whether this object should be ordered before the object p given as argument. If p is of a different class than this, the before() function of the corresponding type_info objects is used. Otherwise, if the objects are of the same class, the virtual compare(const Projection &) will be returned.

Definition at line 88 of file Projection.hh.

Referenced by less< const Rivet::Projection * >::operator()().

int compare ( const Projection & p ) const [protected, virtual]

Compare with other projections.

Implements Projection.

Definition at line 13 of file Sphericity.cc.

References Sphericity::_fsproj, Sphericity::_regparam, and Rivet::pcmp().

virtual const set<BeamPair> getBeamPairs ( ) const [inline, virtual, inherited]

Return the BeamConstraints for this projection. Derived classes should ensure that all contained projections are registered in the _projections set for the beam constraint chaining to work.

Definition at line 114 of file Projection.hh.

References Cuts::end(), and Rivet::intersection().

virtual const Cuts getCuts ( ) const [inline, virtual, inherited]

Return the Cuts objects for this projection. Derived classes should ensure that all contained projections are registered in the _projections set for the cut chaining to work.

Definition at line 102 of file Projection.hh.

References Cuts::addCuts().

Log & getLog ( ) [protected, inherited]