Rivet: Rivet::ParisiTensor Class Reference

Calculate the Parisi event shape tensor (or linear momentum tensor). More...

#include <ParisiTensor.hh>

Inheritance diagram for Rivet::ParisiTensor:

Public Member Functions
	ParisiTensor (const FinalState &fsp)
	Constructor. The provided FinalState projection must live throughout the run.
virtual const Projection *	clone () const
	Clone on the heap.
void	clear ()
	Clear the projection.
Access the C and D params.
double	C () const
double	D () const
Access the eigenvalues of \f$\theta\f$.
double	lambda1 () const
double	lambda2 () 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.

Detailed Description

Calculate the Parisi event shape tensor (or linear momentum tensor).

The Parisi event shape C and D variables are derived from the eigenvalues of the linear momentum tensor

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

which is actually a linearized (and hence infra-red safe) version of the Sphericity tensor.

Defining the three eigenvalues of $\theta$ $\lambda_1 \ge \lambda_2 \ge \lambda_3$ , with $\lambda_1 + \lambda_2 + \lambda_3 = 1$ , the C and D parameters are defined as

$C = 3(\lambda_1\lambda_2 + \lambda_1\lambda_3 + \lambda_2\lambda_3)$

and

$D = 27 \lambda_1\lambda_2\lambda_3$

Internally, this Projection uses the Sphericity projection with the generalising $r$ parameter set to 1.

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

include/Rivet/Projections/ParisiTensor.hh
src/Projections/ParisiTensor.cc

Public Member Functions

Protected Member Functions

Detailed Description