Rivet  1.8.0
Public Member Functions | Protected Member Functions
Rivet::ParisiTensor Class Reference

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

#include <ParisiTensor.hh>

Inheritance diagram for Rivet::ParisiTensor:
Rivet::Projection Rivet::ProjectionApplier

List of all members.

Public Member Functions

 ParisiTensor (const FinalState &fsp)
 Constructor. The provided FinalState projection must live throughout the run.
virtual const Projectionclone () 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: